(The rows for Th, ^{2}E_{6}(2), ^{2}E_{6}(2).2 are marked with a star (*) in the third column. This means that not the given matrix representation was used for the computations but a faithful permutation representation of smallest degree that had been obtained from the matrix representation.)
Group | Representation | Magma input file | Runtime |
---|---|---|---|
A_{5} | Atlas of Group Representations: G ≤ Sym(5), generators are A5G1-p5B0.m1, A5G1-p5B0.m2 | A5 | 0.020 |
A_{5}.2 | Atlas of Group Representations: G ≤ Sym(5), generators are S5G1-p5B0.m1, S5G1-p5B0.m2 | A5.2 | 0.010 |
2.A_{5} | Atlas of Group Representations: G ≤ Sym(24), generators are 2A5G1-p24B0.m1, 2A5G1-p24B0.m2 | 2.A5 | 0.010 |
2.A_{5}.2 | Atlas of Group Representations: G ≤ Sym(40), generators are 2S5G1-p40aB0.m1, 2S5G1-p40aB0.m2 | 2.A5.2 | 0.030 |
L_{3}(2) | Atlas of Group Representations: G ≤ Sym(7), generators are L27G1-p7aB0.m1, L27G1-p7aB0.m2 | L3(2) | 0.020 |
L_{3}(2).2 | Atlas of Group Representations: G ≤ Sym(8), generators are L27d2G1-p8B0.m1, L27d2G1-p8B0.m2 | L3(2).2 | 0.020 |
2.L_{3}(2) | Atlas of Group Representations: G ≤ Sym(16), generators are 2L27G1-p16B0.m1, 2L27G1-p16B0.m2 | 2.L3(2) | 0.020 |
2.L_{3}(2).2 | Atlas of Group Representations: G ≤ Sym(32), generators are 2L27d2G1-p32B0.m1, 2L27d2G1-p32B0.m2 | 2.L3(2).2 | 0.030 |
A_{6} | Atlas of Group Representations: G ≤ Sym(6), generators are A6G1-p6aB0.m1, A6G1-p6aB0.m2 | A6 | 0.020 |
A_{6}.2_{1} | Atlas of Group Representations: G ≤ Sym(6), generators are S6G1-p6aB0.m1, S6G1-p6aB0.m2 | A6.2_1 | 0.020 |
A_{6}.2_{2} | Atlas of Group Representations: G ≤ Sym(10), generators are PGL29G1-p10B0.m1, PGL29G1-p10B0.m2 | A6.2_2 | 0.030 |
A_{6}.2_{3} | Atlas of Group Representations: G ≤ Sym(10), generators are M10G1-p10B0.m1, M10G1-p10B0.m2 | A6.2_3 | 0.020 |
2.A_{6} | Atlas of Group Representations: G ≤ Sym(80), generators are 2A6G1-p80B0.m1, 2A6G1-p80B0.m2 | 2.A6 | 0.020 |
2.A_{6}.2_{1} | Atlas of Group Representations: G ≤ Sym(80), generators are 2S6G1-p80B0.m1, 2S6G1-p80B0.m2 | 2.A6.2_1 | 0.020 |
2.A_{6}.2_{2} | SmallGroup( 1440, 4594 ): G ≤ Sym(160), generators are magmaoutput/2.A6.2_2-p160.m1, magmaoutput/2.A6.2_2-p160.m2 | 2.A6.2_2 | 0.030 |
3.A_{6} | Atlas of Group Representations: G ≤ Sym(18), generators are 3A6G1-p18aB0.m1, 3A6G1-p18aB0.m2 | 3.A6 | 0.020 |
3.A_{6}.2_{1} | Atlas of Group Representations: G ≤ Sym(18), generators are 3S6G1-p18aB0.m1, 3S6G1-p18aB0.m2 | 3.A6.2_1 | 0.030 |
3.A_{6}.2_{2} | Atlas of Group Representations: restriction from J_{2} to its 2nd maximal subgroup, G ≤ Sym(100), generators of J_{2} are J2G1-p100B0.m1, J2G1-p100B0.m2, the script for restricting is J2G1-max2W1 | 3.A6.2_2 | 0.030 |
3.A_{6}.2_{3} | Atlas of Group Representations: restriction from 3.M_{22} to its 7th maximal subgroup, G ≤ Sym(693), generators of 3.M_{22} are 3M22G1-p693B0.m1, 3M22G1-p693B0.m2, the script for restricting is M22G1-max7W1 | 3.A6.2_3 | 0.040 |
4.A_{6}.2_{3} | subgroup of index 4 in GammaL(2,9) that has centre of order 2 and cyclic commutator factor group: G ≤ Sym(80), generators are magmaoutput/4.A6.2_3-p80.m1, magmaoutput/4.A6.2_3-p80.m2 | 4.A6.2_3 | 0.040 |
6.A_{6} | Atlas of Group Representations: G ≤ Sym(432), generators are 6A6G1-p432B0.m1, 6A6G1-p432B0.m2 | 6.A6 | 0.050 |
6.A_{6}.2_{1} | Atlas of Group Representations: G ≤ Sym(720), generators are 6S6G1-p720aB0.m1, 6S6G1-p720aB0.m2 | 6.A6.2_1 | 0.070 |
6.A_{6}.2_{2} | subdirect product of 2.A_{6}.2_{2} and 3.A_{6}.2_{2}: G ≤ Sym(196), generators are magmaoutput/6.A6.2_2-p196.m1, magmaoutput/6.A6.2_2-p196.m2, magmaoutput/6.A6.2_2-p196.m3 | 6.A6.2_2 | 0.060 |
12.A_{6}.2_{3} | subdirect product of 3.A_{6}.2_{3} and 4.A_{6}.2_{3}: G ≤ Sym(170), generators are magmaoutput/12.A6.2_3-p170.m1, magmaoutput/12.A6.2_3-p170.m2, magmaoutput/12.A6.2_3-p170.m3 | 12.A6.2_3 | 0.230 |
L_{2}(8) | Atlas of Group Representations: G ≤ Sym(9), generators are L28G1-p9B0.m1, L28G1-p9B0.m2 | L2(8) | 0.020 |
L_{2}(8).3 | Atlas of Group Representations: G ≤ Sym(9), generators are L28d3G1-p9B0.m1, L28d3G1-p9B0.m2 | L2(8).3 | 0.030 |
L_{2}(11) | Atlas of Group Representations: G ≤ Sym(11), generators are L211G1-p11aB0.m1, L211G1-p11aB0.m2 | L2(11) | 0.020 |
L_{2}(11).2 | Atlas of Group Representations: G ≤ Sym(12), generators are L211d2G1-p12B0.m1, L211d2G1-p12B0.m2 | L2(11).2 | 0.030 |
2.L_{2}(11) | Atlas of Group Representations: G ≤ GL(2,11), generators are 2L211G1-f11r2B0.m1, 2L211G1-f11r2B0.m2 | 2.L2(11) | 0.100 |
2.L_{2}(11).2 | index 5 subgroup in the isoclinic variant of GL(2,11): G ≤ GL(2,121), generators are magmaoutput/2.L2(11).2-r2f121.m1, magmaoutput/2.L2(11).2-r2f121.m2, magmaoutput/2.L2(11).2-r2f121.m3 | 2.L2(11).2 | 0.240 |
L_{2}(13) | Atlas of Group Representations: G ≤ Sym(14), generators are L213G1-p14B0.m1, L213G1-p14B0.m2 | L2(13) | 0.020 |
L_{2}(13).2 | Atlas of Group Representations: G ≤ Sym(14), generators are L213d2G1-p14B0.m1, L213d2G1-p14B0.m2 | L2(13).2 | 0.020 |
2.L_{2}(13) | Atlas of Group Representations: G ≤ GL(6,3), generators are 2L213G1-f3r6aB0.m1, 2L213G1-f3r6aB0.m2 | 2.L2(13) | 0.230 |
2.L_{2}(13).2 | Atlas of Group Representations: G ≤ GL(12,3), generators are 2L213d2G1-f3r12aB0.m1, 2L213d2G1-f3r12aB0.m2 | 2.L2(13).2 | 1.040 |
L_{2}(17) | Atlas of Group Representations: G ≤ Sym(18), generators are L217G1-p18B0.m1, L217G1-p18B0.m2 | L2(17) | 0.020 |
L_{2}(17).2 | Atlas of Group Representations: G ≤ Sym(18), generators are L217d2G1-p18B0.m1, L217d2G1-p18B0.m2 | L2(17).2 | 0.040 |
2.L_{2}(17) | Atlas of Group Representations: G ≤ GL(8,9), generators are 2L217G1-f9r8aB0.m1, 2L217G1-f9r8aB0.m2 | 2.L2(17) | 1.090 |
2.L_{2}(17).2 | Atlas of Group Representations: G ≤ GL(16,3), generators are 2L217d2G1-f3r16B0.m1, 2L217d2G1-f3r16B0.m2 | 2.L2(17).2 | 0.780 |
A_{7} | Atlas of Group Representations: G ≤ Sym(7), generators are A7G1-p7B0.m1, A7G1-p7B0.m2 | A7 | 0.020 |
A_{7}.2 | Atlas of Group Representations: G ≤ Sym(7), generators are S7G1-p7B0.m1, S7G1-p7B0.m2 | A7.2 | 0.050 |
2.A_{7} | Atlas of Group Representations: G ≤ Sym(240), generators are 2A7G1-p240B0.m1, 2A7G1-p240B0.m2 | 2.A7 | 0.060 |
2.A_{7}.2 | Atlas of Group Representations: G ≤ GL(8,7), generators are 2S7G1-f7r8B0.m1, 2S7G1-f7r8B0.m2 | 2.A7.2 | 0.210 |
3.A_{7} | Atlas of Group Representations: G ≤ Sym(45), generators are 3A7G1-p45aB0.m1, 3A7G1-p45aB0.m2 | 3.A7 | 0.080 |
3.A_{7}.2 | Atlas of Group Representations: G ≤ Sym(63), generators are 3S7G1-p63B0.m1, 3S7G1-p63B0.m2 | 3.A7.2 | 0.100 |
6.A_{7} | Atlas of Group Representations: G ≤ Sym(720), generators are 6A7G1-p720B0.m1, 6A7G1-p720B0.m2 | 6.A7 | 0.200 |
6.A_{7}.2 | Atlas of Group Representations: G ≤ GL(12,7), generators are 6S7G1-f7r12B0.m1, 6S7G1-f7r12B0.m2 | 6.A7.2 | 0.700 |
L_{2}(19) | Atlas of Group Representations: G ≤ Sym(20), generators are L219G1-p20B0.m1, L219G1-p20B0.m2 | L2(19) | 0.020 |
L_{2}(19).2 | Atlas of Group Representations: G ≤ Sym(20), generators are L219d2G1-p20B0.m1, L219d2G1-p20B0.m2 | L2(19).2 | 0.060 |
2.L_{2}(19) | Atlas of Group Representations: G ≤ Sym(40), generators are 2L219G1-p40B0.m1, 2L219G1-p40B0.m2 | 2.L2(19) | 0.070 |
2.L_{2}(19).2 | index 9 subgroup in the isoclinic variant of GL(2,19): G ≤ GL(2,361), generators are magmaoutput/2.L2(19).2-r2f361.m1, magmaoutput/2.L2(19).2-r2f361.m2, magmaoutput/2.L2(19).2-r2f361.m3 | 2.L2(19).2 | 0.150 |
L_{2}(16) | Atlas of Group Representations: G ≤ Sym(17), generators are L216G1-p17B0.m1, L216G1-p17B0.m2 | L2(16) | 0.030 |
L_{2}(16).2 | Atlas of Group Representations: G ≤ GL(4,4), generators are L216d2G1-f4r4aB0.m1, L216d2G1-f4r4aB0.m2 | L2(16).2 | 0.140 |
L_{2}(16).4 | Atlas of Group Representations: G ≤ GL(8,2), generators are L216d4G1-f2r8aB0.m1, L216d4G1-f2r8aB0.m2 | L2(16).4 | 0.140 |
L_{3}(3) | Atlas of Group Representations: G ≤ Sym(13), generators are L33G1-p13aB0.m1, L33G1-p13aB0.m2 | L3(3) | 0.060 |
L_{3}(3).2 | Atlas of Group Representations: G ≤ Sym(26), generators are L33d2G1-p26B0.m1, L33d2G1-p26B0.m2 | L3(3).2 | 0.090 |
U_{3}(3) | Atlas of Group Representations: G ≤ Sym(28), generators are U33G1-p28B0.m1, U33G1-p28B0.m2 | U3(3) | 0.080 |
U_{3}(3).2 | Atlas of Group Representations: G ≤ Sym(63), generators are U33d2G1-p63bB0.m1, U33d2G1-p63bB0.m2 | U3(3).2 | 0.100 |
L_{2}(23) | Atlas of Group Representations: G ≤ Sym(24), generators are L223G1-p24B0.m1, L223G1-p24B0.m2 | L2(23) | 0.040 |
L_{2}(23).2 | Atlas of Group Representations: G ≤ GL(22,2), generators are L223d2G1-f2r22aB0.m1, L223d2G1-f2r22aB0.m2 | L2(23).2 | 0.190 |
2.L_{2}(23) | Atlas of Group Representations: G ≤ GL(2,23), generators are 2L223G1-f23r2B0.m1, 2L223G1-f23r2B0.m2 | 2.L2(23) | 0.120 |
2.L_{2}(23).2 | index 11 subgroup in the isoclinic variant of GL(2,23): G ≤ GL(2,529), generators are magmaoutput/2.L2(23).2-r2f529.m1, magmaoutput/2.L2(23).2-r2f529.m2, magmaoutput/2.L2(23).2-r2f529.m3 | 2.L2(23).2 | 0.150 |
L_{2}(25) | Atlas of Group Representations: restriction from ^{2}F_{4}(2)' to its 4th maximal subgroup, G ≤ Sym(1600), generators of ^{2}F_{4}(2)' are TF42G1-p1600B0.m1, TF42G1-p1600B0.m2, the script for restricting is TF42G1-max4W1 | L2(25) | 0.200 |
L_{2}(25).2_{1} | PrimitiveGroup( 26, 2 ): G ≤ Sym(26), generators are magmaoutput/L2(25).2_1-p26.m1, magmaoutput/L2(25).2_1-p26.m2, magmaoutput/L2(25).2_1-p26.m3, magmaoutput/L2(25).2_1-p26.m4 | L2(25).2_1 | 0.100 |
L_{2}(25).2_{2} | Atlas of Group Representations: restriction from S_{4}(5) to its 3rd maximal subgroup, G ≤ Sym(156), generators of S_{4}(5) are S45G1-p156aB0.m1, S45G1-p156aB0.m2, the script for restricting is S45G1-max3W1 | L2(25).2_2 | 0.130 |
L_{2}(25).2_{3} | Atlas of Group Representations: point stabilizer in ^{2}F_{4}(2)'.2, G ≤ Sym(2304), generators of ^{2}F_{4}(2)'.2 are TF42d2G1-p2304B0.m1, TF42d2G1-p2304B0.m2 | L2(25).2_3 | 0.400 |
2.L_{2}(25) | Atlas of Group Representations: restriction from 2.Suz to its 16th maximal subgroup, G ≤ Sym(65520), generators of 2.Suz are 2SuzG1-p65520B0.m1, 2SuzG1-p65520B0.m2, the script for restricting is SuzG1-max16W1 | 2.L2(25) | 11.090 |
2.L_{2}(25).2_{1} | index 13 subgroup in the isoclinic variant of GU(2,25): G ≤ GL(2,625), generators are magmaoutput/2.L2(25).2_1-r2f625.m1, magmaoutput/2.L2(25).2_1-r2f625.m2, magmaoutput/2.L2(25).2_1-r2f625.m3 | 2.L2(25).2_1 | 0.180 |
2.L_{2}(25).2_{2} | SigmaL( 2, 25 ): G ≤ GL(4,5), generators are magmaoutput/2.L2(25).2_2-r4f5.m1, magmaoutput/2.L2(25).2_2-r4f5.m2, magmaoutput/2.L2(25).2_2-r4f5.m3 | 2.L2(25).2_2 | 0.200 |
4.L_{2}(25).2_{3} | a central extension of (2 × L_{2}(25)).2_{3}: G ≤ Sym(416), generators are magmaoutput/4.L2(25).2_3-p416.m1, magmaoutput/4.L2(25).2_3-p416.m2 | 4.L2(25).2_3 | 0.190 |
M_{11} | Atlas of Group Representations: G ≤ Sym(11), generators are M11G1-p11B0.m1, M11G1-p11B0.m2 | M11 | 0.060 |
L_{2}(27) | Atlas of Group Representations: G ≤ Sym(28), generators are L227G1-p28B0.m1, L227G1-p28B0.m2 | L2(27) | 0.080 |
L_{2}(27).2 | PrimitiveGroup( 28, 10 ): G ≤ Sym(28), generators are magmaoutput/L2(27).2-p28.m1, magmaoutput/L2(27).2-p28.m2, magmaoutput/L2(27).2-p28.m3, magmaoutput/L2(27).2-p28.m4 | L2(27).2 | 0.120 |
L_{2}(27).3 | Atlas of Group Representations: restriction from S_{6}(3) to its 6th maximal subgroup, G ≤ Sym(364), generators of S_{6}(3) are S63G1-p364B0.m1, S63G1-p364B0.m2, the script for restricting is S63G1-max6W1 | L2(27).3 | 0.140 |
L_{2}(27).6 | PrimitiveGroup( 28, 12 ): G ≤ Sym(28), generators are magmaoutput/L2(27).6-p28.m1, magmaoutput/L2(27).6-p28.m2, magmaoutput/L2(27).6-p28.m3, magmaoutput/L2(27).6-p28.m4 | L2(27).6 | 0.080 |
2.L_{2}(27) | Atlas of Group Representations: G ≤ GL(2,27), generators are 2L227G1-f27r2aB0.m1, 2L227G1-f27r2aB0.m2 | 2.L2(27) | 0.200 |
2.L_{2}(27).2 | index 13 subgroup in the isoclinic variant of GL(2,27): G ≤ GL(2,729), generators are magmaoutput/2.L2(27).2-r2f729.m1, magmaoutput/2.L2(27).2-r2f729.m2, magmaoutput/2.L2(27).2-r2f729.m3 | 2.L2(27).2 | 0.230 |
2.L_{2}(27).3 | SigmaL( 2, 27 ): G ≤ GL(6,3), generators are magmaoutput/2.L2(27).3-r6f3.m1, magmaoutput/2.L2(27).3-r6f3.m2, magmaoutput/2.L2(27).3-r6f3.m3 | 2.L2(27).3 | 0.240 |
2.L_{2}(27).6 | index 13 subgroup in the isoclinic variant of GammaL(2,27): G ≤ GL(6,9), generators are magmaoutput/2.L2(27).6-r6f9.m1, magmaoutput/2.L2(27).6-r6f9.m2, magmaoutput/2.L2(27).6-r6f9.m3, magmaoutput/2.L2(27).6-r6f9.m4 | 2.L2(27).6 | 0.300 |
L_{2}(29) | Atlas of Group Representations: G ≤ Sym(30), generators are L229G1-p30B0.m1, L229G1-p30B0.m2 | L2(29) | 0.060 |
L_{2}(29).2 | PrimitiveGroup( 30, 2 ): G ≤ Sym(30), generators are magmaoutput/L2(29).2-p30.m1, magmaoutput/L2(29).2-p30.m2 | L2(29).2 | 0.090 |
2.L_{2}(29) | Atlas of Group Representations: G ≤ GL(2,29), generators are 2L229G1-f29r2B0.m1, 2L229G1-f29r2B0.m2 | 2.L2(29) | 0.150 |
2.L_{2}(29).2 | index 15 subgroup in the isoclinic variant of GU(2,29): G ≤ GL(2,841), generators are magmaoutput/2.L2(29).2-r2f841.m1, magmaoutput/2.L2(29).2-r2f841.m2, magmaoutput/2.L2(29).2-r2f841.m3 | 2.L2(29).2 | 0.190 |
L_{2}(31) | Atlas of Group Representations: G ≤ Sym(32), generators are L231G1-p32B0.m1, L231G1-p32B0.m2 | L2(31) | 0.060 |
L_{2}(31).2 | Atlas of Group Representations: G ≤ GL(30,2), generators are L231d2G1-f2r30B0.m1, L231d2G1-f2r30B0.m2 | L2(31).2 | 1.080 |
2.L_{2}(31) | Atlas of Group Representations: G ≤ GL(16,5), generators are 2L231G1-f5r16aB0.m1, 2L231G1-f5r16aB0.m2 | 2.L2(31) | 0.330 |
2.L_{2}(31).2 | index 15 subgroup in the isoclinic variant of GL(2,31): G ≤ GL(2,961), generators are magmaoutput/2.L2(31).2-r2f961.m1, magmaoutput/2.L2(31).2-r2f961.m2, magmaoutput/2.L2(31).2-r2f961.m3 | 2.L2(31).2 | 0.210 |
A_{8} | Atlas of Group Representations: G ≤ Sym(8), generators are A8G1-p8B0.m1, A8G1-p8B0.m2 | A8 | 0.080 |
A_{8}.2 | Atlas of Group Representations: G ≤ Sym(8), generators are S8G1-p8B0.m1, S8G1-p8B0.m2 | A8.2 | 0.080 |
2.A_{8} | Atlas of Group Representations: G ≤ Sym(240), generators are 2A8G1-p240aB0.m1, 2A8G1-p240aB0.m2 | 2.A8 | 0.220 |
2.A_{8}.2 | SchurCoverOfSymmetricGroup( 8, 3, -1 ): G ≤ GL(8,9), generators are magmaoutput/2.A8.2-r8f9.m1, magmaoutput/2.A8.2-r8f9.m2 | 2.A8.2 | 0.450 |
L_{3}(4) | Atlas of Group Representations: G ≤ Sym(21), generators are L34G1-p21aB0.m1, L34G1-p21aB0.m2 | L3(4) | 0.090 |
L_{3}(4).2_{1} | Atlas of Group Representations: G ≤ GL(16,2), generators are L34d2aG1-f2r16aB0.m1, L34d2aG1-f2r16aB0.m2 | L3(4).2_1 | 0.290 |
L_{3}(4).2_{2} | Atlas of Group Representations: restriction from M_{22}.2 to its 2nd maximal subgroup, G ≤ Sym(22), generators of M_{22}.2 are M22d2G1-p22B0.m1, M22d2G1-p22B0.m2, the script for restricting is M22d2G1-max2W1 | L3(4).2_2 | 0.130 |
L_{3}(4).2_{3} | GroupForTom( "L3(4).2^2", 286 ): G ≤ Sym(42), generators are magmaoutput/L3(4).2_3-p42.m1, magmaoutput/L3(4).2_3-p42.m2 | L3(4).2_3 | 0.110 |
L_{3}(4).3 | GroupForTom( "L3(4).3" ): G ≤ Sym(21), generators are magmaoutput/L3(4).3-p21.m1, magmaoutput/L3(4).3-p21.m2 | L3(4).3 | 0.090 |
L_{3}(4).6 | GroupForTom( "L3(4).6" ): G ≤ Sym(105), generators are magmaoutput/L3(4).6-p105.m1, magmaoutput/L3(4).6-p105.m2 | L3(4).6 | 0.120 |
2.L_{3}(4) | Atlas of Group Representations: G ≤ Sym(112), generators are 2L34G1-p112aB0.m1, 2L34G1-p112aB0.m2 | 2.L3(4) | 0.160 |
2.L_{3}(4).2_{1} | Atlas of Group Representations: G ≤ GL(20,3), generators are 2L34d2aG1-f3r20aB0.m1, 2L34d2aG1-f3r20aB0.m2 | 2.L3(4).2_1 | 0.360 |
2.L_{3}(4).2_{2} | Multiplicity-free permutation representations: restriction from 2.M_{22}.2 to its 2nd maximal subgroup, G ≤ Sym(660), generators of 2.M_{22}.2 are 2M22d2G1-p660aB0.m1, 2M22d2G1-p660aB0.m2, the script for restricting is M22d2G1-max2W1 | 2.L3(4).2_2 | 0.200 |
2.L_{3}(4).2_{3} | factor group of 4_{1}.L_{3}(4).2_{3}: G ≤ Sym(112), generators are magmaoutput/2.L3(4).2_3-p112.m1, magmaoutput/2.L3(4).2_3-p112.m2 | 2.L3(4).2_3 | 0.160 |
3.L_{3}(4) | Atlas of Group Representations: G ≤ Sym(63), generators are 3L34G1-p63aB0.m1, 3L34G1-p63aB0.m2 | 3.L3(4) | 0.130 |
3.L_{3}(4).2_{1} | Atlas of Group Representations: G ≤ GL(6,4), generators are 3L34d2aG1-f4r6aB0.m1, 3L34d2aG1-f4r6aB0.m2 | 3.L3(4).2_1 | 0.310 |
3.L_{3}(4).2_{2} | Multiplicity-free permutation representations: restriction from 3.M_{22}.2 to its 2nd maximal subgroup, G ≤ Sym(693), generators of 3.M_{22}.2 are 3M22d2G1-p693B0.m1, 3M22d2G1-p693B0.m2, the script for restricting is M22d2G1-max2W1 | 3.L3(4).2_2 | 0.180 |
3.L_{3}(4).2_{3} | Atlas of Group Representations: restriction from G_{2}(4) to its 5th maximal subgroup, G ≤ Sym(416), generators of G_{2}(4) are G24G1-p416B0.m1, G24G1-p416B0.m2, the script for restricting is G24G1-max5W1 | 3.L3(4).2_3 | 0.190 |
3.L_{3}(4).3 | GL( 3, 4 ): G ≤ GL(3,4), generators are magmaoutput/3.L3(4).3-r3f4.m1, magmaoutput/3.L3(4).3-r3f4.m2 | 3.L3(4).3 | 0.220 |
3.L_{3}(4).6 | semidirect product of SL(3,4) with an outer automorphism of order 6: G ≤ Sym(126), generators are magmaoutput/3.L3(4).6-p126.m1, magmaoutput/3.L3(4).6-p126.m2, magmaoutput/3.L3(4).6-p126.m3 | 3.L3(4).6 | 0.310 |
4_{1}.L_{3}(4) | Atlas of Group Representations: G ≤ Sym(224), generators are 4aL34G1-p224B0.m1, 4aL34G1-p224B0.m2 | 4_1.L3(4) | 0.140 |
4_{1}.L_{3}(4).2_{1} | Atlas of Group Representations: G ≤ GL(16,3), generators are 4aL34d2aG1-f3r16aB0.m1, 4aL34d2aG1-f3r16aB0.m2 | 4_1.L3(4).2_1 | 0.580 |
4_{1}.L_{3}(4).2_{2} | semidirect product of 4_{1}.L_{3}(4) with an outer automorphism: G ≤ Sym(1344), generators are magmaoutput/4_1.L3(4).2_2-p1344.m1, magmaoutput/4_1.L3(4).2_2-p1344.m2 | 4_1.L3(4).2_2 | 0.290 |
4_{1}.L_{3}(4).2_{3} | semidirect product of 4_{1}.L_{3}(4) with an outer automorphism: G ≤ Sym(224), generators are magmaoutput/4_1.L3(4).2_3-p224.m1, magmaoutput/4_1.L3(4).2_3-p224.m2 | 4_1.L3(4).2_3 | 0.230 |
4_{2}.L_{3}(4) | Atlas of Group Representations: G ≤ Sym(224), generators are 4bL34G1-p224B0.m1, 4bL34G1-p224B0.m2 | 4_2.L3(4) | 0.150 |
4_{2}.L_{3}(4).2_{1} | Atlas of Group Representations: G ≤ GL(8,3), generators are 4bL34d2aG1-f3r8aB0.m1, 4bL34d2aG1-f3r8aB0.m2 | 4_2.L3(4).2_1 | 0.460 |
4_{2}.L_{3}(4).2_{2} | semidirect product of 4_{2}.L_{3}(4) with an outer automorphism: G ≤ Sym(224), generators are magmaoutput/4_2.L3(4).2_2-p224.m1, magmaoutput/4_2.L3(4).2_2-p224.m2 | 4_2.L3(4).2_2 | 0.260 |
4_{2}.L_{3}(4).2_{3} | semidirect product of 4_{2}.L_{3}(4) with an outer automorphism: G ≤ Sym(224), generators are magmaoutput/4_2.L3(4).2_3-p224.m1, magmaoutput/4_2.L3(4).2_3-p224.m2 | 4_2.L3(4).2_3 | 0.210 |
6.L_{3}(4) | Atlas of Group Representations: G ≤ Sym(720), generators are 6L34G1-p720aB0.m1, 6L34G1-p720aB0.m2 | 6.L3(4) | 0.240 |
6.L_{3}(4).2_{1} | Atlas of Group Representations: G ≤ GL(6,7), generators are 6L34d2aG1-f7r6aB0.m1, 6L34d2aG1-f7r6aB0.m2 | 6.L3(4).2_1 | 0.680 |
6.L_{3}(4).2_{2} | Multiplicity-free permutation representations: restriction from 6.M_{22}.2 to its 2nd maximal subgroup, G ≤ Sym(1980), generators of 6.M_{22}.2 are 6M22d2G1-p1980aB0.m1, 6M22d2G1-p1980aB0.m2, the script for restricting is M22d2G1-max2W1 | 6.L3(4).2_2 | 0.460 |
6.L_{3}(4).2_{3} | subdirect product of 2.L_{3}(4).2_{3} and 3.L_{3}(4).2_{3}: G ≤ Sym(238), generators are magmaoutput/6.L3(4).2_3-p238.m1, magmaoutput/6.L3(4).2_3-p238.m2 | 6.L3(4).2_3 | 0.290 |
12_{1}.L_{3}(4) | Atlas of Group Representations: G ≤ Sym(1440), generators are 12aL34G1-p1440B0.m1, 12aL34G1-p1440B0.m2 | 12_1.L3(4) | 0.560 |
12_{1}.L_{3}(4).2_{1} | Atlas of Group Representations: G ≤ GL(48,7), generators are 12aL34d2aG1-f7r48aB0.m1, 12aL34d2aG1-f7r48aB0.m2 | 12_1.L3(4).2_1 | 6.890 |
12_{1}.L_{3}(4).2_{2} | subdirect product of 4_{1}.L_{3}(4).2_{2} and 3.L_{3}(4).2_{2}: G ≤ Sym(1407), generators are magmaoutput/12_1.L3(4).2_2-p1407.m1, magmaoutput/12_1.L3(4).2_2-p1407.m2 | 12_1.L3(4).2_2 | 0.660 |
12_{1}.L_{3}(4).2_{3} | subdirect product of 4_{1}.L_{3}(4).2_{3} and 3.L_{3}(4).2_{3}: G ≤ Sym(350), generators are magmaoutput/12_1.L3(4).2_3-p350.m1, magmaoutput/12_1.L3(4).2_3-p350.m2 | 12_1.L3(4).2_3 | 0.450 |
12_{2}.L_{3}(4) | Atlas of Group Representations: G ≤ Sym(1440), generators are 12bL34G1-p1440B0.m1, 12bL34G1-p1440B0.m2 | 12_2.L3(4) | 0.590 |
12_{2}.L_{3}(4).2_{1} | Atlas of Group Representations: G ≤ GL(24,7), generators are 12bL34d2aG1-f7r24aB0.m1, 12bL34d2aG1-f7r24aB0.m2 | 12_2.L3(4).2_1 | 3.360 |
12_{2}.L_{3}(4).2_{2} | subdirect product of 4_{2}.L_{3}(4).2_{2} and 3.L_{3}(4).2_{2}: G ≤ Sym(287), generators are magmaoutput/12_2.L3(4).2_2-p287.m1, magmaoutput/12_2.L3(4).2_2-p287.m2 | 12_2.L3(4).2_2 | 0.540 |
12_{2}.L_{3}(4).2_{3} | subdirect product of 4_{2}.L_{3}(4).2_{3} and 3.L_{3}(4).2_{3}: G ≤ Sym(350), generators are magmaoutput/12_2.L3(4).2_3-p350.m1, magmaoutput/12_2.L3(4).2_3-p350.m2 | 12_2.L3(4).2_3 | 0.520 |
U_{4}(2) | Atlas of Group Representations: G ≤ Sym(27), generators are U42G1-p27B0.m1, U42G1-p27B0.m2 | U4(2) | 0.120 |
U_{4}(2).2 | Atlas of Group Representations: G ≤ Sym(27), generators are U42d2G1-p27B0.m1, U42d2G1-p27B0.m2 | U4(2).2 | 0.100 |
2.U_{4}(2) | Atlas of Group Representations: G ≤ Sym(80), generators are 2U42G1-p80B0.m1, 2U42G1-p80B0.m2 | 2.U4(2) | 0.170 |
2.U_{4}(2).2 | Atlas of Group Representations: G ≤ Sym(240), generators are 2U42d2G1-p240B0.m1, 2U42d2G1-p240B0.m2 | 2.U4(2).2 | 0.190 |
Sz(8) | Atlas of Group Representations: G ≤ Sym(65), generators are Sz8G1-p65B0.m1, Sz8G1-p65B0.m2 | Sz(8) | 0.100 |
Sz(8).3 | Atlas of Group Representations: G ≤ Sym(65), generators are Sz8d3G1-p65B0.m1, Sz8d3G1-p65B0.m2 | Sz(8).3 | 0.080 |
2.Sz(8) | Atlas of Group Representations: G ≤ Sym(1040), generators are 2Sz8G1-p1040B0.m1, 2Sz8G1-p1040B0.m2 | 2.Sz(8) | 0.120 |
L_{2}(32) | Atlas of Group Representations: G ≤ Sym(33), generators are L232G1-p33B0.m1, L232G1-p33B0.m2 | L2(32) | 0.120 |
L_{2}(32).5 | Atlas of Group Representations: G ≤ Sym(33), generators are L232d5G1-p33B0.m1, L232d5G1-p33B0.m2 | L2(32).5 | 0.070 |
U_{3}(4) | Atlas of Group Representations: G ≤ Sym(65), generators are U34G1-p65B0.m1, U34G1-p65B0.m2 | U3(4) | 0.090 |
U_{3}(4).2 | Atlas of Group Representations: G ≤ Sym(65), generators are U34d2G1-p65B0.m1, U34d2G1-p65B0.m2 | U3(4).2 | 0.090 |
U_{3}(4).4 | Atlas of Group Representations: G ≤ Sym(65), generators are U34d4G1-p65B0.m1, U34d4G1-p65B0.m2 | U3(4).4 | 0.090 |
M_{12} | Atlas of Group Representations: G ≤ Sym(12), generators are M12G1-p12aB0.m1, M12G1-p12aB0.m2 | M12 | 0.080 |
M_{12}.2 | Atlas of Group Representations: G ≤ Sym(24), generators are M12d2G1-p24B0.m1, M12d2G1-p24B0.m2 | M12.2 | 0.100 |
2.M_{12} | Atlas of Group Representations: G ≤ Sym(24), generators are 2M12G1-p24aB0.m1, 2M12G1-p24aB0.m2 | 2.M12 | 0.100 |
2.M_{12}.2 | Atlas of Group Representations: G ≤ Sym(48), generators are 2M12d2G1-p48B0.m1, 2M12d2G1-p48B0.m2 | 2.M12.2 | 0.180 |
U_{3}(5) | Atlas of Group Representations: G ≤ Sym(50), generators are U35G1-p50B0.m1, U35G1-p50B0.m2 | U3(5) | 0.080 |
U_{3}(5).2 | Atlas of Group Representations: G ≤ Sym(50), generators are U35d2G1-p50B0.m1, U35d2G1-p50B0.m2 | U3(5).2 | 0.090 |
U_{3}(5).3 | GroupForTom( "U3(5).3" ): G ≤ Sym(126), generators are magmaoutput/U3(5).3-p126.m1, magmaoutput/U3(5).3-p126.m2 | U3(5).3 | 0.140 |
3.U_{3}(5) | Atlas of Group Representations: restriction from 3.M^{c}L to its 4th maximal subgroup, G ≤ Sym(66825), generators of 3.M^{c}L are 3McLG1-p66825B0.m1, 3McLG1-p66825B0.m2, the script for restricting is McLG1-max4W1 | 3.U3(5) | 8.340 |
3.U_{3}(5).2 | Multiplicity-free permutation representations: restriction from 3.M^{c}L.2 to its 3rd maximal subgroup, G ≤ Sym(66825), generators of 3.M^{c}L.2 are 3McLd2G1-p66825bB0.m1, 3McLd2G1-p66825bB0.m2, the script for restricting is McLd2G1-max3W1 | 3.U3(5).2 | 5.940 |
3.U_{3}(5).3 | index 2 subgroup of GU(3,8): G ≤ GL(3,25), generators are magmaoutput/3.U3(5).3-r3f25.m1, magmaoutput/3.U3(5).3-r3f25.m2, magmaoutput/3.U3(5).3-r3f25.m3 | 3.U3(5).3 | 0.480 |
J_{1} | Atlas of Group Representations: G ≤ Sym(266), generators are J1G1-p266B0.m1, J1G1-p266B0.m2 | J1 | 0.080 |
A_{9} | Atlas of Group Representations: G ≤ Sym(9), generators are A9G1-p9B0.m1, A9G1-p9B0.m2 | A9 | 0.060 |
A_{9}.2 | Atlas of Group Representations: G ≤ Sym(9), generators are S9G1-p9B0.m1, S9G1-p9B0.m2 | A9.2 | 0.050 |
2.A_{9} | Atlas of Group Representations: G ≤ GL(8,3), generators are 2A9G1-f3r8B0.m1, 2A9G1-f3r8B0.m2 | 2.A9 | 0.250 |
2.A_{9}.2 | SchurCoverOfSymmetricGroup( 9, 3, -1 ): G ≤ GL(8,9), generators are magmaoutput/2.A9.2-r8f9.m1, magmaoutput/2.A9.2-r8f9.m2 | 2.A9.2 | 0.640 |
L_{3}(5) | Atlas of Group Representations: G ≤ Sym(31), generators are L35G1-p31aB0.m1, L35G1-p31aB0.m2 | L3(5) | 0.090 |
L_{3}(5).2 | Atlas of Group Representations: G ≤ Sym(62), generators are L35d2G1-p62B0.m1, L35d2G1-p62B0.m2 | L3(5).2 | 0.110 |
M_{22} | Atlas of Group Representations: G ≤ Sym(22), generators are M22G1-p22B0.m1, M22G1-p22B0.m2 | M22 | 0.090 |
M_{22}.2 | Atlas of Group Representations: G ≤ Sym(22), generators are M22d2G1-p22B0.m1, M22d2G1-p22B0.m2 | M22.2 | 0.120 |
2.M_{22} | Atlas of Group Representations: G ≤ Sym(352), generators are 2M22G1-p352aB0.m1, 2M22G1-p352aB0.m2 | 2.M22 | 0.180 |
2.M_{22}.2 | Multiplicity-free permutation representations: G ≤ Sym(660), generators are 2M22d2G1-p660aB0.m1, 2M22d2G1-p660aB0.m2 | 2.M22.2 | 0.280 |
3.M_{22} | Atlas of Group Representations: G ≤ Sym(693), generators are 3M22G1-p693B0.m1, 3M22G1-p693B0.m2 | 3.M22 | 0.260 |
3.M_{22}.2 | Multiplicity-free permutation representations: G ≤ Sym(693), generators are 3M22d2G1-p693B0.m1, 3M22d2G1-p693B0.m2 | 3.M22.2 | 0.270 |
4.M_{22} | Atlas of Group Representations: G ≤ Sym(4928), generators are 4M22G1-p4928aB0.m1, 4M22G1-p4928aB0.m2 | 4.M22 | 0.590 |
4.M_{22}.2 | Atlas of Group Representations: G ≤ GL(32,7), generators are 4M22d2G1-f7r32B0.m1, 4M22d2G1-f7r32B0.m2 | 4.M22.2 | 12.210 |
6.M_{22} | Atlas of Group Representations: G ≤ Sym(1980), generators are 6M22G1-p1980B0.m1, 6M22G1-p1980B0.m2 | 6.M22 | 0.590 |
6.M_{22}.2 | Multiplicity-free permutation representations: G ≤ Sym(1980), generators are 6M22d2G1-p1980aB0.m1, 6M22d2G1-p1980aB0.m2 | 6.M22.2 | 0.640 |
12.M_{22} | Atlas of Group Representations: G ≤ Sym(31680), generators are 12M22G1-p31680aB0.m1, 12M22G1-p31680aB0.m2 | 12.M22 | 12.260 |
12.M_{22}.2 | Atlas of Group Representations: G ≤ GL(48,11), generators are 12M22d2G1-f11r48B0.m1, 12M22d2G1-f11r48B0.m2 | 12.M22.2 | 362.040 |
J_{2} | Atlas of Group Representations: G ≤ Sym(100), generators are J2G1-p100B0.m1, J2G1-p100B0.m2 | J2 | 0.120 |
J_{2}.2 | Atlas of Group Representations: G ≤ Sym(100), generators are J2d2G1-p100B0.m1, J2d2G1-p100B0.m2 | J2.2 | 0.140 |
2.J_{2} | Atlas of Group Representations: G ≤ Sym(200), generators are 2J2G1-p200B0.m1, 2J2G1-p200B0.m2 | 2.J2 | 0.210 |
2.J_{2}.2 | Multiplicity-free permutation representations: G ≤ Sym(400), generators are 2J2d2G1-p400B0.m1, 2J2d2G1-p400B0.m2 | 2.J2.2 | 0.310 |
S_{4}(4) | Atlas of Group Representations: G ≤ Sym(85), generators are S44G1-p85aB0.m1, S44G1-p85aB0.m2 | S4(4) | 0.190 |
S_{4}(4).2 | Atlas of Group Representations: G ≤ GL(8,2), generators are S44d2G1-f2r8aB0.m1, S44d2G1-f2r8aB0.m2 | S4(4).2 | 0.330 |
S_{4}(4).4 | Atlas of Group Representations: G ≤ Sym(170), generators are S44d4G1-p170B0.m1, S44d4G1-p170B0.m2 | S4(4).4 | 0.200 |
S_{6}(2) | Atlas of Group Representations: G ≤ Sym(28), generators are S62G1-p28B0.m1, S62G1-p28B0.m2 | S6(2) | 0.110 |
2.S_{6}(2) | Atlas of Group Representations: G ≤ Sym(240), generators are 2S62G1-p240aB0.m1, 2S62G1-p240aB0.m2 | 2.S6(2) | 0.310 |
A_{10} | Atlas of Group Representations: G ≤ Sym(10), generators are A10G1-p10B0.m1, A10G1-p10B0.m2 | A10 | 0.080 |
A_{10}.2 | Atlas of Group Representations: G ≤ Sym(10), generators are S10G1-p10B0.m1, S10G1-p10B0.m2 | A10.2 | 0.120 |
2.A_{10} | Atlas of Group Representations: G ≤ GL(16,3), generators are 2A10G1-f3r16B0.m1, 2A10G1-f3r16B0.m2 | 2.A10 | 0.460 |
2.A_{10}.2 | SchurCoverOfSymmetricGroup( 10, 3, -1 ): G ≤ GL(16,9), generators are magmaoutput/2.A10.2-r16f9.m1, magmaoutput/2.A10.2-r16f9.m2 | 2.A10.2 | 15.900 |
L_{3}(7) | Atlas of Group Representations: G ≤ Sym(57), generators are L37G1-p57B0.m1, L37G1-p57B0.m2 | L3(7) | 0.090 |
L_{3}(7).2 | Atlas of Group Representations: G ≤ GL(8,7), generators are L37d2G1-f7r8B0.m1, L37d2G1-f7r8B0.m2 | L3(7).2 | 0.370 |
L_{3}(7).3 | PrimitiveGroup( 57, 3 ): G ≤ Sym(57), generators are magmaoutput/L3(7).3-p57.m1, magmaoutput/L3(7).3-p57.m2 | L3(7).3 | 0.180 |
3.L_{3}(7) | Atlas of Group Representations: G ≤ GL(3,7), generators are 3L37G1-f7r3B0.m1, 3L37G1-f7r3B0.m2 | 3.L3(7) | 0.330 |
3.L_{3}(7).2 | Extension of the Atlas of Group Representations: G ≤ GL(6,7), generators are 3L37d2G1-f7r6aB0.m1, 3L37d2G1-f7r6aB0.m2 | 3.L3(7).2 | 0.380 |
3.L_{3}(7).3 | index 2 subgroup in GL(3,7): G ≤ GL(3,7), generators are magmaoutput/3.L3(7).3-r3f7.m1, magmaoutput/3.L3(7).3-r3f7.m2, magmaoutput/3.L3(7).3-r3f7.m3 | 3.L3(7).3 | 0.970 |
U_{4}(3) | Atlas of Group Representations: restriction from M^{c}L to its 1st maximal subgroup, G ≤ Sym(275), generators of M^{c}L are McLG1-p275B0.m1, McLG1-p275B0.m2, the script for restricting is McLG1-max1W1 | U4(3) | 0.270 |
U_{4}(3).2_{1} | GroupForTom( "U4(3).2^2_133", 1788 ): G ≤ Sym(112), generators are magmaoutput/U4(3).2_1-p112.m1, magmaoutput/U4(3).2_1-p112.m2 | U4(3).2_1 | 0.250 |
U_{4}(3).2_{2} | Atlas of Group Representations: restriction from U_{6}(2) to its 4th maximal subgroup, G ≤ Sym(672), generators of U_{6}(2) are U62G1-p672B0.m1, U62G1-p672B0.m2, the script for restricting is U62G1-max4W1 | U4(3).2_2 | 0.370 |
U_{4}(3).2_{3} | Atlas of Group Representations: restriction from M^{c}L.2 to its 2nd maximal subgroup, G ≤ Sym(275), generators of M^{c}L.2 are McLd2G1-p275B0.m1, McLd2G1-p275B0.m2, the script for restricting is McLd2G1-max2W1 | U4(3).2_3 | 0.280 |
U_{4}(3).4 | PrimitiveGroup( 112, 6 ): G ≤ Sym(112), generators are magmaoutput/U4(3).4-p112.m1, magmaoutput/U4(3).4-p112.m2 | U4(3).4 | 0.330 |
2.U_{4}(3) | a factor group of SU(4,3): G ≤ Sym(224), generators are magmaoutput/2.U4(3)-p224.m1, magmaoutput/2.U4(3)-p224.m2 | 2.U4(3) | 0.320 |
2.U_{4}(3).2_{1} | isoclinic variant of SO(-1,6,3): G ≤ GL(6,9), generators are magmaoutput/2.U4(3).2_1-r6f9.m1, magmaoutput/2.U4(3).2_1-r6f9.m2, magmaoutput/2.U4(3).2_1-r6f9.m3 | 2.U4(3).2_1 | 0.770 |
2.U_{4}(3).2_{2} | Atlas of Group Representations: restriction from 2.U_{6}(2) to its 5th maximal subgroup, G ≤ Sym(1344), generators of 2.U_{6}(2) are 2U62G1-p1344B0.m1, 2U62G1-p1344B0.m2, the script for restricting is U62G1-max5W1 | 2.U4(3).2_2 | 1.170 |
2.U_{4}(3).2_{3} | isoclinic variant of a subgroup of 2.U_{4}(3).D_{8}: G ≤ Sym(504), generators are magmaoutput/2.U4(3).2_3-p504.m1, magmaoutput/2.U4(3).2_3-p504.m2 | 2.U4(3).2_3 | 0.430 |
2.U_{4}(3).4 | a factor group of GU(4,3): G ≤ Sym(1120), generators are magmaoutput/2.U4(3).4-p1120.m1, magmaoutput/2.U4(3).4-p1120.m2 | 2.U4(3).4 | 1.210 |
3_{1}.U_{4}(3) | derived subgroup of the fourth maximal subgroup of 3.U_{6}(2): G ≤ Sym(378), generators are magmaoutput/3_1.U4(3)-p378.m1, magmaoutput/3_1.U4(3)-p378.m2 | 3_1.U4(3) | 0.490 |
3_{1}.U_{4}(3).2_{1} | factor group of the derived subgroup of 3^{2}.U_{4}(3).D_{8}: G ≤ Sym(378), generators are magmaoutput/3_1.U4(3).2_1-p378.m1, magmaoutput/3_1.U4(3).2_1-p378.m2 | 3_1.U4(3).2_1 | 0.550 |
3_{1}.U_{4}(3).2_{2} | Atlas of Group Representations: restriction from 3.U_{6}(2) to its 4th maximal subgroup, G ≤ Sym(2016), generators of 3.U_{6}(2) are 3U62G1-p2016B0.m1, 3U62G1-p2016B0.m2, the script for restricting is U62G1-max4W1 | 3_1.U4(3).2_2 | 1.870 |
3_{1}.U_{4}(3).2_{2}' | factor group of an index 4 subgroup of 3^{2}.U_{4}(3).D_{8}: G ≤ Sym(378), generators are magmaoutput/3_1.U4(3).2_2'-p378.m1, magmaoutput/3_1.U4(3).2_2'-p378.m2 | 3_1.U4(3).2_2' | 0.570 |
3_{2}.U_{4}(3) | Atlas of Group Representations: restriction from 3.M^{c}L to its 1st maximal subgroup, G ≤ Sym(66825), generators of 3.M^{c}L are 3McLG1-p66825B0.m1, 3McLG1-p66825B0.m2, the script for restricting is McLG1-max1W1 | 3_2.U4(3) | 32.300 |
3_{2}.U_{4}(3).2_{1} | index 2 subgroup of the third maximal subgroup of Suz.2: G ≤ Sym(486), generators are magmaoutput/3_2.U4(3).2_1-p486.m1, magmaoutput/3_2.U4(3).2_1-p486.m2 | 3_2.U4(3).2_1 | 0.570 |
3_{2}.U_{4}(3).2_{3} | index 2 subgroup of the third maximal subgroup of Suz.2: G ≤ Sym(1620), generators are magmaoutput/3_2.U4(3).2_3-p1620.m1, magmaoutput/3_2.U4(3).2_3-p1620.m2 | 3_2.U4(3).2_3 | 0.990 |
3_{2}.U_{4}(3).2_{3}' | Multiplicity-free permutation representations: restriction from 3.M^{c}L.2 to its 2nd maximal subgroup, G ≤ Sym(66825), generators of 3.M^{c}L.2 are 3McLd2G1-p66825bB0.m1, 3McLd2G1-p66825bB0.m2, the script for restricting is McLd2G1-max2W1 | 3_2.U4(3).2_3' | 21.570 |
4.U_{4}(3) | SU( 4, 3 ): G ≤ GL(4,9), generators are magmaoutput/4.U4(3)-r4f9.m1, magmaoutput/4.U4(3)-r4f9.m2 | 4.U4(3) | 0.830 |
4.U_{4}(3).2_{1} | index 2 subgroup of GU(4,3): G ≤ GL(4,9), generators are magmaoutput/4.U4(3).2_1-r4f9.m1, magmaoutput/4.U4(3).2_1-r4f9.m2 | 4.U4(3).2_1 | 1.240 |
4.U_{4}(3).2_{2} | semidirect product of 4.U_{4}(3) with an outer automorphism: G ≤ Sym(2240), generators are magmaoutput/4.U4(3).2_2-p2240.m1, magmaoutput/4.U4(3).2_2-p2240.m2 | 4.U4(3).2_2 | 2.690 |
4.U_{4}(3).2_{3} | semidirect product of 4.U_{4}(3) with an outer automorphism: G ≤ Sym(2160), generators are magmaoutput/4.U4(3).2_3-p2160.m1, magmaoutput/4.U4(3).2_3-p2160.m2, magmaoutput/4.U4(3).2_3-p2160.m3 | 4.U4(3).2_3 | 1.000 |
4.U_{4}(3).4 | GU( 4, 3 ): G ≤ GL(4,9), generators are magmaoutput/4.U4(3).4-r4f9.m1, magmaoutput/4.U4(3).4-r4f9.m2 | 4.U4(3).4 | 1.930 |
6_{1}.U_{4}(3) | derived subgroup of the 5th maximal subgroup of 6.U_{6}(2): G ≤ Sym(2240), generators are magmaoutput/6_1.U4(3)-p2240.m1, magmaoutput/6_1.U4(3)-p2240.m2 | 6_1.U4(3) | 1.770 |
6_{1}.U_{4}(3).2_{1} | subdirect product of 3_{1}.U_{4}(3).2_{1} and 2.U_{4}(3).2_{1}: G ≤ Sym(826), generators are magmaoutput/6_1.U4(3).2_1-p826.m1, magmaoutput/6_1.U4(3).2_1-p826.m2 | 6_1.U4(3).2_1 | 1.760 |
6_{1}.U_{4}(3).2_{2} | Atlas of Group Representations: restriction from 6.U_{6}(2) to its 5th maximal subgroup, G ≤ Sym(4032), generators of 6.U_{6}(2) are 6U62G1-p4032B0.m1, 6U62G1-p4032B0.m2, the script for restricting is U62G1-max5W1 | 6_1.U4(3).2_2 | 8.150 |
6_{1}.U_{4}(3).2_{2}' | subdirect product of 3_{1}.U_{4}(3).2_{2}' and 2.U_{4}(3).2_{2}: G ≤ Sym(602), generators are magmaoutput/6_1.U4(3).2_2'-p602.m1, magmaoutput/6_1.U4(3).2_2'-p602.m2 | 6_1.U4(3).2_2' | 1.340 |
6_{2}.U_{4}(3) | derived subgroup of the second maximal subgroup of 2.Suz: G ≤ Sym(630), generators are magmaoutput/6_2.U4(3)-p630.m1, magmaoutput/6_2.U4(3)-p630.m2 | 6_2.U4(3) | 0.880 |
6_{2}.U_{4}(3).2_{1} | subdirect product of 3_{2}.U_{4}(3).2_{1} and 2.U_{4}(3).2_{1}: G ≤ Sym(934), generators are magmaoutput/6_2.U4(3).2_1-p934.m1, magmaoutput/6_2.U4(3).2_1-p934.m2 | 6_2.U4(3).2_1 | 1.660 |
6_{2}.U_{4}(3).2_{3} | subdirect product of 3_{2}.U_{4}(3).2_{3} and 2.U_{4}(3).2_{3}: G ≤ Sym(2124), generators are magmaoutput/6_2.U4(3).2_3-p2124.m1, magmaoutput/6_2.U4(3).2_3-p2124.m2 | 6_2.U4(3).2_3 | 2.420 |
6_{2}.U_{4}(3).2_{3}' | isoclinic variant of the second maximal subgroup of 2.Suz: G ≤ Sym(1260), generators are magmaoutput/6_2.U4(3).2_3'-p1260.m1, magmaoutput/6_2.U4(3).2_3'-p1260.m2 | 6_2.U4(3).2_3' | 1.040 |
12_{1}.U_{4}(3) | subdirect product of 3_{1}.U_{4}(3) and 4.U_{4}(3): G ≤ Sym(2618), generators are magmaoutput/12_1.U4(3)-p2618.m1, magmaoutput/12_1.U4(3)-p2618.m2 | 12_1.U4(3) | 4.300 |
12_{1}.U_{4}(3).2_{1} | subdirect product of 3_{1}.U_{4}(3).2_{1} and 4.U_{4}(3).2_{1}: G ≤ Sym(2618), generators are magmaoutput/12_1.U4(3).2_1-p2618.m1, magmaoutput/12_1.U4(3).2_1-p2618.m2 | 12_1.U4(3).2_1 | 4.370 |
12_{1}.U_{4}(3).2_{2} | subdirect product of 3_{1}.U_{4}(3).2_{2} and 4.U_{4}(3).2_{2}: G ≤ Sym(2996), generators are magmaoutput/12_1.U4(3).2_2-p2996.m1, magmaoutput/12_1.U4(3).2_2-p2996.m2 | 12_1.U4(3).2_2 | 9.910 |
12_{1}.U_{4}(3).2_{2}' | subdirect product of 3_{1}.U_{4}(3).2_{2}' and 4.U_{4}(3).2_{2}: G ≤ Sym(2618), generators are magmaoutput/12_1.U4(3).2_2'-p2618.m1, magmaoutput/12_1.U4(3).2_2'-p2618.m2 | 12_1.U4(3).2_2' | 4.130 |
12_{2}.U_{4}(3) | subdirect product of 3_{2}.U_{4}(3) and 4.U_{4}(3): G ≤ Sym(10745), generators are magmaoutput/12_2.U4(3)-p10745.m1, magmaoutput/12_2.U4(3)-p10745.m2 | 12_2.U4(3) | 12.440 |
12_{2}.U_{4}(3).2_{1} | subdirect product of 3_{2}.U_{4}(3).2_{1} and 4.U_{4}(3).2_{1}: G ≤ Sym(2726), generators are magmaoutput/12_2.U4(3).2_1-p2726.m1, magmaoutput/12_2.U4(3).2_1-p2726.m2 | 12_2.U4(3).2_1 | 6.080 |
12_{2}.U_{4}(3).2_{3} | subdirect product of 3_{2}.U_{4}(3).2_{3} and 4.U_{4}(3).2_{3}: G ≤ Sym(6100), generators are magmaoutput/12_2.U4(3).2_3-p6100.m1, magmaoutput/12_2.U4(3).2_3-p6100.m2 | 12_2.U4(3).2_3 | 8.690 |
12_{2}.U_{4}(3).2_{3}' | subdirect product of 3_{2}.U_{4}(3).2_{3}' and 4.U_{4}(3).2_{3}: G ≤ Sym(3780), generators are magmaoutput/12_2.U4(3).2_3'-p3780.m1, magmaoutput/12_2.U4(3).2_3'-p3780.m2 | 12_2.U4(3).2_3' | 3.170 |
G_{2}(3) | Atlas of Group Representations: G ≤ GL(14,2), generators are G23G1-f2r14B0.m1, G23G1-f2r14B0.m2 | G2(3) | 0.880 |
G_{2}(3).2 | Atlas of Group Representations: G ≤ Sym(756), generators are G23d2G1-p756B0.m1, G23d2G1-p756B0.m2 | G2(3).2 | 0.300 |
3.G_{2}(3) | Atlas of Group Representations: G ≤ Sym(1134), generators are 3G23G1-p1134B0.m1, 3G23G1-p1134B0.m2 | 3.G2(3) | 0.700 |
3.G_{2}(3).2 | Atlas of Group Representations: G ≤ GL(54,2), generators are 3G23d2G1-f2r54B0.m1, 3G23d2G1-f2r54B0.m2 | 3.G2(3).2 | 8271.650 |
S_{4}(5) | Atlas of Group Representations: G ≤ Sym(156), generators are S45G1-p156aB0.m1, S45G1-p156aB0.m2 | S4(5) | 0.230 |
S_{4}(5).2 | Atlas of Group Representations: G ≤ GL(24,2), generators are S45d2G1-f2r24B0.m1, S45d2G1-f2r24B0.m2 | S4(5).2 | 0.820 |
2.S_{4}(5) | Atlas of Group Representations: G ≤ Sym(624), generators are 2S45G1-p624B0.m1, 2S45G1-p624B0.m2 | 2.S4(5) | 0.440 |
2.S_{4}(5).2 | semidirect product of 2.S_{4}(5) with an outer automorphism: G ≤ Sym(1248), generators are magmaoutput/2.S4(5).2-p1248.m1, magmaoutput/2.S4(5).2-p1248.m2, magmaoutput/2.S4(5).2-p1248.m3 | 2.S4(5).2 | 0.790 |
U_{3}(8) | Atlas of Group Representations: G ≤ Sym(513), generators are U38G1-p513B0.m1, U38G1-p513B0.m2 | U3(8) | 0.170 |
U_{3}(8).2 | Atlas of Group Representations: G ≤ Sym(513), generators are U38d2G1-p513B0.m1, U38d2G1-p513B0.m2 | U3(8).2 | 0.200 |
U_{3}(8).3_{1} | Atlas of Group Representations: G ≤ Sym(513), generators are U38d3aG1-p513B0.m1, U38d3aG1-p513B0.m2 | U3(8).3_1 | 0.370 |
U_{3}(8).3_{2} | Atlas of Group Representations: G ≤ Sym(513), generators are U38d3bG1-p513B0.m1, U38d3bG1-p513B0.m2 | U3(8).3_2 | 0.330 |
U_{3}(8).3_{3} | Atlas of Group Representations: G ≤ Sym(513), generators are U38d3cG1-p513B0.m1, U38d3cG1-p513B0.m2 | U3(8).3_3 | 0.210 |
U_{3}(8).6 | Atlas of Group Representations: G ≤ Sym(513), generators are U38d6G1-p513B0.m1, U38d6G1-p513B0.m2 | U3(8).6 | 0.370 |
3.U_{3}(8) | Atlas of Group Representations: G ≤ Sym(4617), generators are 3U38G1-p4617B0.m1, 3U38G1-p4617B0.m2 | 3.U3(8) | 1.310 |
3.U_{3}(8).2 | semidirect product of 3.U_{3}(8) with an outer automorphism: G ≤ Sym(9234), generators are magmaoutput/3.U3(8).2-p9234.m1, magmaoutput/3.U3(8).2-p9234.m2 | 3.U3(8).2 | 1.810 |
3.U_{3}(8).3_{1} | semidirect product of 3.U_{3}(8) with an outer automorphism: G ≤ Sym(13851), generators are magmaoutput/3.U3(8).3_1-p13851.m1, magmaoutput/3.U3(8).3_1-p13851.m2 | 3.U3(8).3_1 | 7.730 |
3.U_{3}(8).3_{2} | isoclinic variant of a semidirect product of 3.U_{3}(8) with an outer automorphism: G ≤ Sym(13851), generators are magmaoutput/3.U3(8).3_2-p13851.m1, magmaoutput/3.U3(8).3_2-p13851.m2 | 3.U3(8).3_2 | 13.580 |
3.U_{3}(8).6 | semidirect product of 3.U_{3}(8) with an outer automorphism: G ≤ Sym(27702), generators are magmaoutput/3.U3(8).6-p27702.m1, magmaoutput/3.U3(8).6-p27702.m2 | 3.U3(8).6 | 8.180 |
9.U_{3}(8).3_{3} | subgroup of GammaU(3,8): G ≤ Sym(4617), generators are magmaoutput/9.U3(8).3_3-p4617.m1, magmaoutput/9.U3(8).3_3-p4617.m2 | 9.U3(8).3_3 | 29.600 |
U_{3}(7) | Atlas of Group Representations: G ≤ Sym(344), generators are U37G1-p344B0.m1, U37G1-p344B0.m2 | U3(7) | 0.210 |
U_{3}(7).2 | PrimitiveGroup( 344, 2 ): G ≤ Sym(344), generators are magmaoutput/U3(7).2-p344.m1, magmaoutput/U3(7).2-p344.m2 | U3(7).2 | 0.240 |
L_{4}(3) | GroupForTom( "L4(3)" ): G ≤ Sym(40), generators are magmaoutput/L4(3)-p40.m1, magmaoutput/L4(3)-p40.m2 | L4(3) | 0.190 |
L_{4}(3).2_{1} | PrimitiveGroup( 40, 6 ): G ≤ Sym(40), generators are magmaoutput/L4(3).2_1-p40.m1, magmaoutput/L4(3).2_1-p40.m2, magmaoutput/L4(3).2_1-p40.m3 | L4(3).2_1 | 0.210 |
L_{4}(3).2_{2} | Atlas of Group Representations: point stabilizer in O_{7}(3), G ≤ Sym(378), generators of O_{7}(3) are O73G1-p378B0.m1, O73G1-p378B0.m2 | L4(3).2_2 | 0.550 |
L_{4}(3).2_{3} | PrimitiveGroup( 130, 4 ): G ≤ Sym(130), generators are magmaoutput/L4(3).2_3-p130.m1, magmaoutput/L4(3).2_3-p130.m2 | L4(3).2_3 | 0.220 |
2.L_{4}(3) | SL( 4, 3 ): G ≤ GL(4,3), generators are magmaoutput/2.L4(3)-r4f3.m1, magmaoutput/2.L4(3)-r4f3.m2 | 2.L4(3) | 0.330 |
2.L_{4}(3).2_{1} | GL( 4, 3 ): G ≤ GL(4,3), generators are magmaoutput/2.L4(3).2_1-r4f3.m1, magmaoutput/2.L4(3).2_1-r4f3.m2 | 2.L4(3).2_1 | 0.350 |
2.L_{4}(3).2_{2} | semidirect product of 2.L_{4}(3) with an outer automorphism: G ≤ Sym(160), generators are magmaoutput/2.L4(3).2_2-p160.m1, magmaoutput/2.L4(3).2_2-p160.m2 | 2.L4(3).2_2 | 0.720 |
2.L_{4}(3).2_{3} | semidirect product of 2.L_{4}(3) with an outer automorphism: G ≤ Sym(160), generators are magmaoutput/2.L4(3).2_3-p160.m1, magmaoutput/2.L4(3).2_3-p160.m2 | 2.L4(3).2_3 | 0.420 |
L_{5}(2) | Atlas of Group Representations: G ≤ Sym(31), generators are L52G1-p31aB0.m1, L52G1-p31aB0.m2 | L5(2) | 0.170 |
L_{5}(2).2 | Atlas of Group Representations: G ≤ Sym(62), generators are L52d2G1-p62B0.m1, L52d2G1-p62B0.m2 | L5(2).2 | 0.230 |
M_{23} | Atlas of Group Representations: G ≤ Sym(23), generators are M23G1-p23B0.m1, M23G1-p23B0.m2 | M23 | 0.090 |
U_{5}(2) | Atlas of Group Representations: G ≤ Sym(165), generators are U52G1-p165B0.m1, U52G1-p165B0.m2 | U5(2) | 0.370 |
U_{5}(2).2 | Atlas of Group Representations: G ≤ Sym(165), generators are U52d2G1-p165B0.m1, U52d2G1-p165B0.m2 | U5(2).2 | 0.320 |
L_{3}(8) | Atlas of Group Representations: G ≤ Sym(73), generators are L38G1-p73aB0.m1, L38G1-p73aB0.m2 | L3(8) | 0.240 |
L_{3}(8).2 | Atlas of Group Representations: G ≤ Sym(146), generators are L38d2G1-p146B0.m1, L38d2G1-p146B0.m2 | L3(8).2 | 0.230 |
L_{3}(8).3 | Atlas of Group Representations: G ≤ Sym(73), generators are L38d3G1-p73aB0.m1, L38d3G1-p73aB0.m2 | L3(8).3 | 0.210 |
L_{3}(8).6 | Atlas of Group Representations: G ≤ Sym(438), generators are L38d6G1-p438B0.m1, L38d6G1-p438B0.m2 | L3(8).6 | 0.280 |
^{2}F_{4}(2)' | Atlas of Group Representations: G ≤ Sym(1600), generators are TF42G1-p1600B0.m1, TF42G1-p1600B0.m2 | 2F4(2)' | 0.350 |
^{2}F_{4}(2)'.2 | Atlas of Group Representations: G ≤ Sym(1755), generators are TF42d2G1-p1755B0.m1, TF42d2G1-p1755B0.m2 | 2F4(2)'.2 | 0.480 |
A_{11} | Atlas of Group Representations: G ≤ Sym(11), generators are A11G1-p11B0.m1, A11G1-p11B0.m2 | A11 | 0.110 |
A_{11}.2 | Atlas of Group Representations: G ≤ Sym(11), generators are S11G1-p11B0.m1, S11G1-p11B0.m2 | A11.2 | 0.230 |
2.A_{11} | Atlas of Group Representations: G ≤ Sym(5040), generators are 2A11G1-p5040B0.m1, 2A11G1-p5040B0.m2 | 2.A11 | 1.110 |
2.A_{11}.2 | Atlas of Group Representations: G ≤ GL(16,11), generators are 2S11G1-f11r16B0.m1, 2S11G1-f11r16B0.m2 | 2.A11.2 | 664.100 |
Sz(32) | Atlas of Group Representations: G ≤ Sym(1025), generators are Sz32G1-p1025B0.m1, Sz32G1-p1025B0.m2 | Sz(32) | 0.240 |
Sz(32).5 | Atlas of Group Representations: G ≤ Sym(1025), generators are Sz32d5G1-p1025B0.m1, Sz32d5G1-p1025B0.m2 | Sz(32).5 | 0.290 |
L_{3}(9) | GroupForTom( "L3(9)" ): G ≤ Sym(91), generators are magmaoutput/L3(9)-p91.m1, magmaoutput/L3(9)-p91.m2 | L3(9) | 0.320 |
L_{3}(9).2_{1} | PrimitiveGroup( 910, 1 ): G ≤ Sym(910), generators are magmaoutput/L3(9).2_1-p910.m1, magmaoutput/L3(9).2_1-p910.m2 | L3(9).2_1 | 0.460 |
L_{3}(9).2_{2} | PrimitiveGroup( 91, 8 ): G ≤ Sym(91), generators are magmaoutput/L3(9).2_2-p91.m1, magmaoutput/L3(9).2_2-p91.m2 | L3(9).2_2 | 0.270 |
L_{3}(9).2_{3} | PrimitiveGroup( 910, 2 ): G ≤ Sym(910), generators are magmaoutput/L3(9).2_3-p910.m1, magmaoutput/L3(9).2_3-p910.m2 | L3(9).2_3 | 0.460 |
U_{3}(9) | Atlas of Group Representations: G ≤ Sym(730), generators are U39G1-p730B0.m1, U39G1-p730B0.m2 | U3(9) | 0.520 |
U_{3}(9).2 | PrimitiveGroup( 730, 2 ): G ≤ Sym(730), generators are magmaoutput/U3(9).2-p730.m1, magmaoutput/U3(9).2-p730.m2 | U3(9).2 | 0.470 |
U_{3}(9).4 | PrimitiveGroup( 730, 3 ): G ≤ Sym(730), generators are magmaoutput/U3(9).4-p730.m1, magmaoutput/U3(9).4-p730.m2 | U3(9).4 | 0.440 |
HS | Atlas of Group Representations: G ≤ Sym(100), generators are HSG1-p100B0.m1, HSG1-p100B0.m2 | HS | 0.180 |
HS.2 | Atlas of Group Representations: G ≤ Sym(100), generators are HSd2G1-p100B0.m1, HSd2G1-p100B0.m2 | HS.2 | 0.250 |
2.HS | Atlas of Group Representations: G ≤ Sym(704), generators are 2HSG1-p704B0.m1, 2HSG1-p704B0.m2 | 2.HS | 0.420 |
2.HS.2 | Atlas of Group Representations: G ≤ Sym(1408), generators are 2HSd2G1-p1408B0.m1, 2HSd2G1-p1408B0.m2 | 2.HS.2 | 1.120 |
J_{3} | Atlas of Group Representations: G ≤ Sym(6156), generators are J3G1-p6156B0.m1, J3G1-p6156B0.m2 | J3 | 0.410 |
J_{3}.2 | Atlas of Group Representations: G ≤ Sym(6156), generators are J3d2G1-p6156B0.m1, J3d2G1-p6156B0.m2 | J3.2 | 0.640 |
3.J_{3} | Atlas of Group Representations: G ≤ GL(9,4), generators are 3J3G1-f4r9aB0.m1, 3J3G1-f4r9aB0.m2 | 3.J3 | 113.600 |
3.J_{3}.2 | Atlas of Group Representations: G ≤ GL(18,2), generators are 3J3d2G1-f2r18B0.m1, 3J3d2G1-f2r18B0.m2 | 3.J3.2 | 15.890 |
U_{3}(11) | Atlas of Group Representations: G ≤ Sym(1332), generators are U311G1-p1332B0.m1, U311G1-p1332B0.m2 | U3(11) | 0.300 |
U_{3}(11).2 | Atlas of Group Representations: G ≤ Sym(1332), generators are U311d2G1-p1332B0.m1, U311d2G1-p1332B0.m2 | U3(11).2 | 0.360 |
U_{3}(11).3 | PrimitiveGroup( 1332, 3 ): G ≤ Sym(1332), generators are magmaoutput/U3(11).3-p1332.m1, magmaoutput/U3(11).3-p1332.m2 | U3(11).3 | 0.900 |
3.U_{3}(11) | Atlas of Group Representations: G ≤ GL(3,121), generators are 3U311G1-f121r3aB0.m1, 3U311G1-f121r3aB0.m2 | 3.U3(11) | 1.370 |
3.U_{3}(11).2 | Atlas of Group Representations: G ≤ GL(6,11), generators are 3U311d2G1-f11r6B0.m1, 3U311d2G1-f11r6B0.m2 | 3.U3(11).2 | 8.950 |
3.U_{3}(11).3 | index 4 subgroup in GU(3,11): G ≤ GL(3,121), generators are magmaoutput/3.U3(11).3-r3f121.m1, magmaoutput/3.U3(11).3-r3f121.m2, magmaoutput/3.U3(11).3-r3f121.m3 | 3.U3(11).3 | 7.800 |
O_{8}^{+}(2) | Atlas of Group Representations: restriction from O_{8}^{+}(3) to its 10th maximal subgroup, G ≤ Sym(1080), generators of O_{8}^{+}(3) are O8p3G1-p1080aB0.m1, O8p3G1-p1080aB0.m2, the script for restricting is O8p3G1-max10W1 | O8+(2) | 1.270 |
O_{8}^{+}(2).2 | Atlas of Group Representations: point stabilizer in S_{8}(2), G ≤ Sym(136), generators of S_{8}(2) are S82G1-p136B0.m1, S82G1-p136B0.m2 | O8+(2).2 | 0.740 |
O_{8}^{+}(2).3 | PrimitiveGroup( 1575, 3 ): G ≤ Sym(1575), generators are magmaoutput/O8+(2).3-p1575.m1, magmaoutput/O8+(2).3-p1575.m2 | O8+(2).3 | 1.260 |
2.O_{8}^{+}(2) | derived subgroup of the Weyl group of type E_{8}: G ≤ Sym(2160), generators are magmaoutput/2.O8+(2)-p2160.m1, magmaoutput/2.O8+(2)-p2160.m2 | 2.O8+(2) | 2.210 |
2.O_{8}^{+}(2).2 | Weyl group of type E_{8}: G ≤ Sym(2160), generators are magmaoutput/2.O8+(2).2-p2160.m1, magmaoutput/2.O8+(2).2-p2160.m2 | 2.O8+(2).2 | 2.860 |
O_{8}^{−}(2) | Atlas of Group Representations: G ≤ Sym(119), generators are O8m2G1-p119B0.m1, O8m2G1-p119B0.m2 | O8-(2) | 0.410 |
O_{8}^{−}(2).2 | Atlas of Group Representations: G ≤ Sym(119), generators are O8m2d2G1-p119B0.m1, O8m2d2G1-p119B0.m2 | O8-(2).2 | 0.530 |
^{3}D_{4}(2) | Atlas of Group Representations: G ≤ Sym(819), generators are TD42G1-p819B0.m1, TD42G1-p819B0.m2 | 3D4(2) | 0.460 |
^{3}D_{4}(2).3 | Atlas of Group Representations: G ≤ GL(24,2), generators are TD42d3G1-f2r24B0.m1, TD42d3G1-f2r24B0.m2 | 3D4(2).3 | 9248.800 |
A_{12} | Atlas of Group Representations: G ≤ Sym(12), generators are A12G1-p12B0.m1, A12G1-p12B0.m2 | A12 | 0.210 |
A_{12}.2 | Atlas of Group Representations: G ≤ Sym(12), generators are S12G1-p12B0.m1, S12G1-p12B0.m2 | A12.2 | 0.460 |
2.A_{12} | Atlas of Group Representations: G ≤ GL(16,3), generators are 2A12G1-f3r16aB0.m1, 2A12G1-f3r16aB0.m2 | 2.A12 | 22.570 |
2.A_{12}.2 | SchurCoverOfSymmetricGroup( 12, 3, -1 ): G ≤ GL(32,9), generators are magmaoutput/2.A12.2-r32f9.m1, magmaoutput/2.A12.2-r32f9.m2 | 2.A12.2 | 72.060 |
M_{24} | Atlas of Group Representations: G ≤ Sym(24), generators are M24G1-p24B0.m1, M24G1-p24B0.m2 | M24 | 0.180 |
G_{2}(4) | Atlas of Group Representations: G ≤ Sym(416), generators are G24G1-p416B0.m1, G24G1-p416B0.m2 | G2(4) | 0.460 |
G_{2}(4).2 | Atlas of Group Representations: G ≤ GL(12,2), generators are G24d2G1-f2r12B0.m1, G24d2G1-f2r12B0.m2 | G2(4).2 | 2.200 |
2.G_{2}(4) | Atlas of Group Representations: G ≤ GL(12,3), generators are 2G24G1-f3r12B0.m1, 2G24G1-f3r12B0.m2 | 2.G2(4) | 79.620 |
2.G_{2}(4).2 | Atlas of Group Representations: G ≤ GL(12,7), generators are 2G24d2G1-f7r12B0.m1, 2G24d2G1-f7r12B0.m2 | 2.G2(4).2 | 705.400 |
M^{c}L | Atlas of Group Representations: G ≤ Sym(275), generators are McLG1-p275B0.m1, McLG1-p275B0.m2 | McL | 0.220 |
M^{c}L.2 | Atlas of Group Representations: G ≤ Sym(275), generators are McLd2G1-p275B0.m1, McLd2G1-p275B0.m2 | McL.2 | 0.260 |
3.M^{c}L | Atlas of Group Representations: G ≤ Sym(66825), generators are 3McLG1-p66825B0.m1, 3McLG1-p66825B0.m2 | 3.McL | 40.010 |
3.M^{c}L.2 | Multiplicity-free permutation representations: G ≤ Sym(66825), generators are 3McLd2G1-p66825bB0.m1, 3McLd2G1-p66825bB0.m2 | 3.McL.2 | 25.370 |
A_{13} | Atlas of Group Representations: G ≤ Sym(13), generators are A13G1-p13B0.m1, A13G1-p13B0.m2 | A13 | 0.360 |
A_{13}.2 | Atlas of Group Representations: G ≤ Sym(13), generators are S13G1-p13B0.m1, S13G1-p13B0.m2 | A13.2 | 1.140 |
2.A_{13} | Atlas of Group Representations: G ≤ GL(32,3), generators are 2A13G1-f3r32aB0.m1, 2A13G1-f3r32aB0.m2 | 2.A13 | 26.600 |
2.A_{13}.2 | SchurCoverOfSymmetricGroup( 13, 3, -1 ): G ≤ GL(64,9), generators are magmaoutput/2.A13.2-r64f9.m1, magmaoutput/2.A13.2-r64f9.m2 | 2.A13.2 | 340.370 |
He | Atlas of Group Representations: G ≤ Sym(2058), generators are HeG1-p2058B0.m1, HeG1-p2058B0.m2 | He | 0.710 |
He.2 | Atlas of Group Representations: G ≤ Sym(2058), generators are Hed2G1-p2058B0.m1, Hed2G1-p2058B0.m2 | He.2 | 0.790 |
O_{7}(3) | Atlas of Group Representations: G ≤ Sym(351), generators are O73G1-p351B0.m1, O73G1-p351B0.m2 | O7(3) | 1.140 |
O_{7}(3).2 | Atlas of Group Representations: G ≤ Sym(351), generators are O73d2G1-p351B0.m1, O73d2G1-p351B0.m2 | O7(3).2 | 2.500 |
2.O_{7}(3) | Atlas of Group Representations: G ≤ Sym(2160), generators are 2O73G1-p2160B0.m1, 2O73G1-p2160B0.m2 | 2.O7(3) | 3.020 |
2.O_{7}(3).2 | Extension of the Atlas of Group Representations: G ≤ GL(8,9), generators are 2O73d2G1-f9r8B0.m1, 2O73d2G1-f9r8B0.m2 | 2.O7(3).2 | 16.640 |
3.O_{7}(3) | Atlas of Group Representations: G ≤ GL(27,4), generators are 3O73G1-f4r27aB0.m1, 3O73G1-f4r27aB0.m2 | 3.O7(3) | 51.340 |
3.O_{7}(3).2 | Atlas of Group Representations: G ≤ GL(54,2), generators are 3O73d2G1-f2r54B0.m1, 3O73d2G1-f2r54B0.m2 | 3.O7(3).2 | 8.810 |
6.O_{7}(3) | Extension of the Atlas of Group Representations: G ≤ Sym(3374), generators are 6O73G1-p3374B0.m1, 6O73G1-p3374B0.m2 | 6.O7(3) | 227.790 |
6.O_{7}(3).2 | Extension of the Atlas of Group Representations: G ≤ Sym(5614), generators are 6O73d2G1-p5614B0.m1, 6O73d2G1-p5614B0.m2 | 6.O7(3).2 | 11.120 |
S_{6}(3) | Atlas of Group Representations: G ≤ Sym(364), generators are S63G1-p364B0.m1, S63G1-p364B0.m2 | S6(3) | 1.390 |
S_{6}(3).2 | Atlas of Group Representations: G ≤ Sym(364), generators are S63d2G1-p364B0.m1, S63d2G1-p364B0.m2 | S6(3).2 | 1.290 |
2.S_{6}(3) | Atlas of Group Representations: G ≤ GL(6,3), generators are 2S63G1-f3r6B0.m1, 2S63G1-f3r6B0.m2 | 2.S6(3) | 4.230 |
2.S_{6}(3).2 | Atlas of Group Representations: G ≤ Sym(728), generators are 2S63d2G1-p728B0.m1, 2S63d2G1-p728B0.m2 | 2.S6(3).2 | 2.830 |
G_{2}(5) | Atlas of Group Representations: G ≤ Sym(3906), generators are G25G1-p3906aB0.m1, G25G1-p3906aB0.m2 | G2(5) | 1.170 |
U_{6}(2) | Atlas of Group Representations: G ≤ Sym(672), generators are U62G1-p672B0.m1, U62G1-p672B0.m2 | U6(2) | 1.230 |
U_{6}(2).2 | Atlas of Group Representations: G ≤ Sym(672), generators are U62d2G1-p672B0.m1, U62d2G1-p672B0.m2 | U6(2).2 | 1.240 |
U_{6}(2).3 | PrimitiveGroup( 672, 3 ): G ≤ Sym(672), generators are magmaoutput/U6(2).3-p672.m1, magmaoutput/U6(2).3-p672.m2 | U6(2).3 | 3.470 |
2.U_{6}(2) | Atlas of Group Representations: G ≤ Sym(1344), generators are 2U62G1-p1344B0.m1, 2U62G1-p1344B0.m2 | 2.U6(2) | 2.740 |
2.U_{6}(2).2 | Atlas of Group Representations: restriction from Fi_{22}.2 to its 2nd maximal subgroup, G ≤ Sym(3510), generators of Fi_{22}.2 are F22d2G1-p3510B0.m1, F22d2G1-p3510B0.m2, the script for restricting is F22d2G1-max2W1 | 2.U6(2).2 | 6.730 |
3.U_{6}(2) | Atlas of Group Representations: G ≤ Sym(2016), generators are 3U62G1-p2016B0.m1, 3U62G1-p2016B0.m2 | 3.U6(2) | 5.410 |
3.U_{6}(2).2 | factor group of the second maximal subgroup of 3.Fi_{22}.2: G ≤ Sym(19008), generators are magmaoutput/3.U6(2).2-p19008.m1, magmaoutput/3.U6(2).2-p19008.m2 | 3.U6(2).2 | 32.160 |
3.U_{6}(2).3 | GU( 6, 2 ): G ≤ GL(6,4), generators are magmaoutput/3.U6(2).3-r6f4.m1, magmaoutput/3.U6(2).3-r6f4.m2 | 3.U6(2).3 | 12.670 |
6.U_{6}(2) | Atlas of Group Representations: G ≤ Sym(4032), generators are 6U62G1-p4032B0.m1, 6U62G1-p4032B0.m2 | 6.U6(2) | 18.050 |
6.U_{6}(2).2 | Atlas of Group Representations: restriction from 3.Fi_{22}.2 to its 2nd maximal subgroup, G ≤ Sym(185328), generators of 3.Fi_{22}.2 are 3F22d2G1-p185328B0.m1, 3F22d2G1-p185328B0.m2, the script for restricting is F22d2G1-max2W1 | 6.U6(2).2 | 1537.710 |
R(27) | Atlas of Group Representations: G ≤ Sym(19684), generators are R27G1-p19684B0.m1, R27G1-p19684B0.m2 | R(27) | 2.830 |
R(27).3 | Atlas of Group Representations: G ≤ Sym(19684), generators are R27d3G1-p19684B0.m1, R27d3G1-p19684B0.m2 | R(27).3 | 3.310 |
S_{8}(2) | Atlas of Group Representations: G ≤ Sym(120), generators are S82G1-p120B0.m1, S82G1-p120B0.m2 | S8(2) | 1.490 |
Ru | Atlas of Group Representations: G ≤ Sym(4060), generators are RuG1-p4060B0.m1, RuG1-p4060B0.m2 | Ru | 1.040 |
2.Ru | Atlas of Group Representations: G ≤ Sym(16240), generators are 2RuG1-p16240B0.m1, 2RuG1-p16240B0.m2 | 2.Ru | 5.470 |
Suz | Atlas of Group Representations: G ≤ Sym(1782), generators are SuzG1-p1782B0.m1, SuzG1-p1782B0.m2 | Suz | 1.240 |
Suz.2 | Atlas of Group Representations: G ≤ Sym(1782), generators are Suzd2G1-p1782B0.m1, Suzd2G1-p1782B0.m2 | Suz.2 | 1.630 |
2.Suz | Atlas of Group Representations: G ≤ Sym(65520), generators are 2SuzG1-p65520B0.m1, 2SuzG1-p65520B0.m2 | 2.Suz | 38.240 |
2.Suz.2 | Multiplicity-free permutation representations: G ≤ Sym(65520), generators are 2Suzd2G1-p65520aB0.m1, 2Suzd2G1-p65520aB0.m2 | 2.Suz.2 | 94.910 |
3.Suz | Atlas of Group Representations: G ≤ Sym(5346), generators are 3SuzG1-p5346B0.m1, 3SuzG1-p5346B0.m2 | 3.Suz | 12.260 |
3.Suz.2 | Atlas of Group Representations: G ≤ Sym(5346), generators are 3Suzd2G1-p5346B0.m1, 3Suzd2G1-p5346B0.m2 | 3.Suz.2 | 9.640 |
6.Suz | Atlas of Group Representations: G ≤ GL(12,7), generators are 6SuzG1-f7r12aB0.m1, 6SuzG1-f7r12aB0.m2 | 6.Suz | 41.320 |
6.Suz.2 | Atlas of Group Representations: G ≤ GL(24,3), generators are 6Suzd2G1-f3r24B0.m1, 6Suzd2G1-f3r24B0.m2 | 6.Suz.2 | 73.450 |
ON | Atlas of Group Representations: G ≤ Sym(122760), generators are ONG1-p122760aB0.m1, ONG1-p122760aB0.m2 | ON | 62.030 |
ON.2 | Atlas of Group Representations: G ≤ Sym(245520), generators are ONd2G1-p245520B0.m1, ONd2G1-p245520B0.m2 | ON.2 | 185.360 |
3.ON | Atlas of Group Representations: G ≤ Sym(368280), generators are 3ONG1-p368280B0.m1, 3ONG1-p368280B0.m2 | 3.ON | 599.890 |
3.ON.2 | Atlas of Group Representations: G ≤ Sym(736560), generators are 3ONd2G1-p736560B0.m1, 3ONd2G1-p736560B0.m2 | 3.ON.2 | 1308.730 |
Co_{3} | Atlas of Group Representations: G ≤ Sym(276), generators are Co3G1-p276B0.m1, Co3G1-p276B0.m2 | Co3 | 0.500 |
O_{8}^{+}(3) | Atlas of Group Representations: G ≤ Sym(1080), generators are O8p3G1-p1080aB0.m1, O8p3G1-p1080aB0.m2 | O8+(3) | 8.120 |
O_{10}^{+}(2) | Atlas of Group Representations: G ≤ Sym(496), generators are O10p2G1-p496B0.m1, O10p2G1-p496B0.m2 | O10+(2) | 3.510 |
O_{10}^{+}(2).2 | Atlas of Group Representations: G ≤ Sym(496), generators are O10p2d2G1-p496B0.m1, O10p2d2G1-p496B0.m2 | O10+(2).2 | 7.930 |
O_{10}^{−}(2) | Atlas of Group Representations: G ≤ Sym(495), generators are O10m2G1-p495B0.m1, O10m2G1-p495B0.m2 | O10-(2) | 5.070 |
O_{10}^{−}(2).2 | Atlas of Group Representations: G ≤ Sym(495), generators are O10m2d2G1-p495B0.m1, O10m2d2G1-p495B0.m2 | O10-(2).2 | 10.050 |
Co_{2} | Atlas of Group Representations: G ≤ Sym(2300), generators are Co2G1-p2300B0.m1, Co2G1-p2300B0.m2 | Co2 | 2.990 |
Fi_{22} | Atlas of Group Representations: G ≤ Sym(3510), generators are F22G1-p3510B0.m1, F22G1-p3510B0.m2 | Fi22 | 4.380 |
Fi_{22}.2 | Atlas of Group Representations: G ≤ Sym(3510), generators are F22d2G1-p3510B0.m1, F22d2G1-p3510B0.m2 | Fi22.2 | 8.690 |
2.Fi_{22} | Atlas of Group Representations: G ≤ Sym(28160), generators are 2F22G1-p28160B0.m1, 2F22G1-p28160B0.m2 | 2.Fi22 | 59.920 |
2.Fi_{22}.2 | Atlas of Group Representations: G ≤ Sym(56320), generators are 2F22d2G1-p56320B0.m1, 2F22d2G1-p56320B0.m2 | 2.Fi22.2 | 313.540 |
3.Fi_{22} | Atlas of Group Representations: G ≤ GL(27,4), generators are 3F22G1-f4r27aB0.m1, 3F22G1-f4r27aB0.m2 | 3.Fi22 | 45.780 |
3.Fi_{22}.2 | Atlas of Group Representations: G ≤ Sym(185328), generators are 3F22d2G1-p185328B0.m1, 3F22d2G1-p185328B0.m2 | 3.Fi22.2 | 1427.120 |
6.Fi_{22} | Multiplicity-free permutation representations: G ≤ Sym(370656), generators are 6F22G1-p370656aB0.m1, 6F22G1-p370656aB0.m2 | 6.Fi22 | 8605.640 |
6.Fi_{22}.2 | Multiplicity-free permutation representations: G ≤ Sym(741312), generators are 6F22d2G1-p741312aB0.m1, 6F22d2G1-p741312aB0.m2 | 6.Fi22.2 | 26723.800 |
HN | Atlas of Group Representations: G ≤ Sym(1140000), generators are HNG1-p1140000B0.m1, HNG1-p1140000B0.m2 | HN | 7844.900 |
HN.2 | Multiplicity-free permutation representations: G ≤ Sym(1140000), generators are HNd2G1-p1140000B0.m1, HNd2G1-p1140000B0.m2 | HN.2 | 5526.680 |
F_{4}(2) | Atlas of Group Representations: G ≤ Sym(69888), generators are F42G1-p69888aB0.m1, F42G1-p69888aB0.m2 | F4(2) | 1889.540 |
F_{4}(2).2 | Atlas of Group Representations: G ≤ GL(52,2), generators are F42d2G1-f2r52B0.m1, F42d2G1-f2r52B0.m2 | F4(2).2 | 844.430 |
2.F_{4}(2) | Atlas of Group Representations: G ≤ Sym(139776), generators are 2F42G1-p139776B0.m1, 2F42G1-p139776B0.m2 | 2.F4(2) | 4142.350 |
2.F_{4}(2).2 | Atlas of Group Representations: G ≤ GL(52,25), generators are 2F42d2G1-f25r52B0.m1, 2F42d2G1-f25r52B0.m2 | 2.F4(2).2 | 4695.120 |
Ly | Multiplicity-free permutation representations: G ≤ Sym(8835156), generators are LyG1-p8835156B0.m1, LyG1-p8835156B0.m2 | Ly | 47398.820 |
Th | Atlas of Group Representations: G ≤ GL(248,2), generators are ThG1-f2r248B0.m1, ThG1-f2r248B0.m2 | Th* | 988923.560 |
Fi_{23} | Atlas of Group Representations: G ≤ Sym(31671), generators are F23G1-p31671B0.m1, F23G1-p31671B0.m2 | Fi23 | 85.990 |
Co_{1} | Atlas of Group Representations: G ≤ Sym(98280), generators are Co1G1-p98280B0.m1, Co1G1-p98280B0.m2 | Co1 | 499.630 |
2.Co_{1} | Atlas of Group Representations: G ≤ GL(24,3), generators are 2Co1G1-f3r24B0.m1, 2Co1G1-f3r24B0.m2 | 2.Co1 | 1503.160 |
J_{4} | Atlas of Group Representations: G ≤ GL(112,2), generators are J4G1-f2r112B0.m1, J4G1-f2r112B0.m2 | J4 | — |
2.^{2}E_{6}(2) | Atlas of Group Representations: G ≤ GL(1704,2), generators are 2TE62G1-f2r1704B0.m1, 2TE62G1-f2r1704B0.m2 | 2.2E6(2) | — |
2.^{2}E_{6}(2).2 | Atlas of Group Representations: G ≤ GL(1705,2), generators are 2TE62d2G1-f2r1705B0.m1, 2TE62d2G1-f2r1705B0.m2 | 2.2E6(2).2 | — |
^{2}E_{6}(2) | Atlas of Group Representations: G ≤ GL(78,2), generators are TE62G1-f2r78B0.m1, TE62G1-f2r78B0.m2 | 2E6(2)* | 754034.830 |
^{2}E_{6}(2).2 | Atlas of Group Representations: G ≤ GL(78,2), generators are TE62d2G1-f2r78B0.m1, TE62d2G1-f2r78B0.m2 | 2E6(2).2* | 773379.750 |
F_{3+} | Atlas of Group Representations: G ≤ Sym(306936), generators are F24G1-p306936B0.m1, F24G1-p306936B0.m2 | F3+ | 7529.770 |
F_{3+}.2 | Atlas of Group Representations: G ≤ Sym(306936), generators are F24d2G1-p306936B0.m1, F24d2G1-p306936B0.m2 | F3+.2 | 12867.060 |
3.F_{3+} | Atlas of Group Representations: G ≤ Sym(920808), generators are 3F24G1-p920808B0.m1, 3F24G1-p920808B0.m2 | 3.F3+ | 169418.100 |
3.F_{3+}.2 | Atlas of Group Representations: G ≤ Sym(920808), generators are 3F24d2G1-p920808B0.m1, 3F24d2G1-p920808B0.m2 | 3.F3+.2 | 485227.130 |
B | Atlas of Group Representations: G ≤ GL(4370,2), generators are BG1-f2r4370B0.m1, BG1-f2r4370B0.m2 | B | — |
2.B | (no representation available) | — | — |
M | (no representation available) | — | — |
File created automatically by GAP on 18-Mar-2017.