ATLAS verification

ATLAS Groups and the Representations used

(The rows for Th, 2E6(2), 2E6(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
A5 Atlas of Group Representations: G ≤ Sym(5), generators are A5G1-p5B0.m1, A5G1-p5B0.m2 A5 0.020
A5.2 Atlas of Group Representations: G ≤ Sym(5), generators are S5G1-p5B0.m1, S5G1-p5B0.m2 A5.2 0.010
2.A5 Atlas of Group Representations: G ≤ Sym(24), generators are 2A5G1-p24B0.m1, 2A5G1-p24B0.m2 2.A5 0.010
2.A5.2 Atlas of Group Representations: G ≤ Sym(40), generators are 2S5G1-p40aB0.m1, 2S5G1-p40aB0.m2 2.A5.2 0.030
L3(2) Atlas of Group Representations: G ≤ Sym(7), generators are L27G1-p7aB0.m1, L27G1-p7aB0.m2 L3(2) 0.020
L3(2).2 Atlas of Group Representations: G ≤ Sym(8), generators are L27d2G1-p8B0.m1, L27d2G1-p8B0.m2 L3(2).2 0.020
2.L3(2) Atlas of Group Representations: G ≤ Sym(16), generators are 2L27G1-p16B0.m1, 2L27G1-p16B0.m2 2.L3(2) 0.020
2.L3(2).2 Atlas of Group Representations: G ≤ Sym(32), generators are 2L27d2G1-p32B0.m1, 2L27d2G1-p32B0.m2 2.L3(2).2 0.030
A6 Atlas of Group Representations: G ≤ Sym(6), generators are A6G1-p6aB0.m1, A6G1-p6aB0.m2 A6 0.020
A6.21 Atlas of Group Representations: G ≤ Sym(6), generators are S6G1-p6aB0.m1, S6G1-p6aB0.m2 A6.2_1 0.020
A6.22 Atlas of Group Representations: G ≤ Sym(10), generators are PGL29G1-p10B0.m1, PGL29G1-p10B0.m2 A6.2_2 0.030
A6.23 Atlas of Group Representations: G ≤ Sym(10), generators are M10G1-p10B0.m1, M10G1-p10B0.m2 A6.2_3 0.020
2.A6 Atlas of Group Representations: G ≤ Sym(80), generators are 2A6G1-p80B0.m1, 2A6G1-p80B0.m2 2.A6 0.020
2.A6.21 Atlas of Group Representations: G ≤ Sym(80), generators are 2S6G1-p80B0.m1, 2S6G1-p80B0.m2 2.A6.2_1 0.020
2.A6.22 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.A6 Atlas of Group Representations: G ≤ Sym(18), generators are 3A6G1-p18aB0.m1, 3A6G1-p18aB0.m2 3.A6 0.020
3.A6.21 Atlas of Group Representations: G ≤ Sym(18), generators are 3S6G1-p18aB0.m1, 3S6G1-p18aB0.m2 3.A6.2_1 0.030
3.A6.22 Atlas of Group Representations: restriction from J2 to its 2nd maximal subgroup, G ≤ Sym(100), generators of J2 are J2G1-p100B0.m1, J2G1-p100B0.m2, the script for restricting is J2G1-max2W1 3.A6.2_2 0.030
3.A6.23 Atlas of Group Representations: restriction from 3.M22 to its 7th maximal subgroup, G ≤ Sym(693), generators of 3.M22 are 3M22G1-p693B0.m1, 3M22G1-p693B0.m2, the script for restricting is M22G1-max7W1 3.A6.2_3 0.040
4.A6.23 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.A6 Atlas of Group Representations: G ≤ Sym(432), generators are 6A6G1-p432B0.m1, 6A6G1-p432B0.m2 6.A6 0.050
6.A6.21 Atlas of Group Representations: G ≤ Sym(720), generators are 6S6G1-p720aB0.m1, 6S6G1-p720aB0.m2 6.A6.2_1 0.070
6.A6.22 subdirect product of 2.A6.22 and 3.A6.22: 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.A6.23 subdirect product of 3.A6.23 and 4.A6.23: 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
L2(8) Atlas of Group Representations: G ≤ Sym(9), generators are L28G1-p9B0.m1, L28G1-p9B0.m2 L2(8) 0.020
L2(8).3 Atlas of Group Representations: G ≤ Sym(9), generators are L28d3G1-p9B0.m1, L28d3G1-p9B0.m2 L2(8).3 0.030
L2(11) Atlas of Group Representations: G ≤ Sym(11), generators are L211G1-p11aB0.m1, L211G1-p11aB0.m2 L2(11) 0.020
L2(11).2 Atlas of Group Representations: G ≤ Sym(12), generators are L211d2G1-p12B0.m1, L211d2G1-p12B0.m2 L2(11).2 0.030
2.L2(11) Atlas of Group Representations: G ≤ GL(2,11), generators are 2L211G1-f11r2B0.m1, 2L211G1-f11r2B0.m2 2.L2(11) 0.100
2.L2(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
L2(13) Atlas of Group Representations: G ≤ Sym(14), generators are L213G1-p14B0.m1, L213G1-p14B0.m2 L2(13) 0.020
L2(13).2 Atlas of Group Representations: G ≤ Sym(14), generators are L213d2G1-p14B0.m1, L213d2G1-p14B0.m2 L2(13).2 0.020
2.L2(13) Atlas of Group Representations: G ≤ GL(6,3), generators are 2L213G1-f3r6aB0.m1, 2L213G1-f3r6aB0.m2 2.L2(13) 0.230
2.L2(13).2 Atlas of Group Representations: G ≤ GL(12,3), generators are 2L213d2G1-f3r12aB0.m1, 2L213d2G1-f3r12aB0.m2 2.L2(13).2 1.040
L2(17) Atlas of Group Representations: G ≤ Sym(18), generators are L217G1-p18B0.m1, L217G1-p18B0.m2 L2(17) 0.020
L2(17).2 Atlas of Group Representations: G ≤ Sym(18), generators are L217d2G1-p18B0.m1, L217d2G1-p18B0.m2 L2(17).2 0.040
2.L2(17) Atlas of Group Representations: G ≤ GL(8,9), generators are 2L217G1-f9r8aB0.m1, 2L217G1-f9r8aB0.m2 2.L2(17) 1.090
2.L2(17).2 Atlas of Group Representations: G ≤ GL(16,3), generators are 2L217d2G1-f3r16B0.m1, 2L217d2G1-f3r16B0.m2 2.L2(17).2 0.780
A7 Atlas of Group Representations: G ≤ Sym(7), generators are A7G1-p7B0.m1, A7G1-p7B0.m2 A7 0.020
A7.2 Atlas of Group Representations: G ≤ Sym(7), generators are S7G1-p7B0.m1, S7G1-p7B0.m2 A7.2 0.050
2.A7 Atlas of Group Representations: G ≤ Sym(240), generators are 2A7G1-p240B0.m1, 2A7G1-p240B0.m2 2.A7 0.060
2.A7.2 Atlas of Group Representations: G ≤ GL(8,7), generators are 2S7G1-f7r8B0.m1, 2S7G1-f7r8B0.m2 2.A7.2 0.210
3.A7 Atlas of Group Representations: G ≤ Sym(45), generators are 3A7G1-p45aB0.m1, 3A7G1-p45aB0.m2 3.A7 0.080
3.A7.2 Atlas of Group Representations: G ≤ Sym(63), generators are 3S7G1-p63B0.m1, 3S7G1-p63B0.m2 3.A7.2 0.100
6.A7 Atlas of Group Representations: G ≤ Sym(720), generators are 6A7G1-p720B0.m1, 6A7G1-p720B0.m2 6.A7 0.200
6.A7.2 Atlas of Group Representations: G ≤ GL(12,7), generators are 6S7G1-f7r12B0.m1, 6S7G1-f7r12B0.m2 6.A7.2 0.700
L2(19) Atlas of Group Representations: G ≤ Sym(20), generators are L219G1-p20B0.m1, L219G1-p20B0.m2 L2(19) 0.020
L2(19).2 Atlas of Group Representations: G ≤ Sym(20), generators are L219d2G1-p20B0.m1, L219d2G1-p20B0.m2 L2(19).2 0.060
2.L2(19) Atlas of Group Representations: G ≤ Sym(40), generators are 2L219G1-p40B0.m1, 2L219G1-p40B0.m2 2.L2(19) 0.070
2.L2(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
L2(16) Atlas of Group Representations: G ≤ Sym(17), generators are L216G1-p17B0.m1, L216G1-p17B0.m2 L2(16) 0.030
L2(16).2 Atlas of Group Representations: G ≤ GL(4,4), generators are L216d2G1-f4r4aB0.m1, L216d2G1-f4r4aB0.m2 L2(16).2 0.140
L2(16).4 Atlas of Group Representations: G ≤ GL(8,2), generators are L216d4G1-f2r8aB0.m1, L216d4G1-f2r8aB0.m2 L2(16).4 0.140
L3(3) Atlas of Group Representations: G ≤ Sym(13), generators are L33G1-p13aB0.m1, L33G1-p13aB0.m2 L3(3) 0.060
L3(3).2 Atlas of Group Representations: G ≤ Sym(26), generators are L33d2G1-p26B0.m1, L33d2G1-p26B0.m2 L3(3).2 0.090
U3(3) Atlas of Group Representations: G ≤ Sym(28), generators are U33G1-p28B0.m1, U33G1-p28B0.m2 U3(3) 0.080
U3(3).2 Atlas of Group Representations: G ≤ Sym(63), generators are U33d2G1-p63bB0.m1, U33d2G1-p63bB0.m2 U3(3).2 0.100
L2(23) Atlas of Group Representations: G ≤ Sym(24), generators are L223G1-p24B0.m1, L223G1-p24B0.m2 L2(23) 0.040
L2(23).2 Atlas of Group Representations: G ≤ GL(22,2), generators are L223d2G1-f2r22aB0.m1, L223d2G1-f2r22aB0.m2 L2(23).2 0.190
2.L2(23) Atlas of Group Representations: G ≤ GL(2,23), generators are 2L223G1-f23r2B0.m1, 2L223G1-f23r2B0.m2 2.L2(23) 0.120
2.L2(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
L2(25) Atlas of Group Representations: restriction from 2F4(2)' to its 4th maximal subgroup, G ≤ Sym(1600), generators of 2F4(2)' are TF42G1-p1600B0.m1, TF42G1-p1600B0.m2, the script for restricting is TF42G1-max4W1 L2(25) 0.200
L2(25).21 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
L2(25).22 Atlas of Group Representations: restriction from S4(5) to its 3rd maximal subgroup, G ≤ Sym(156), generators of S4(5) are S45G1-p156aB0.m1, S45G1-p156aB0.m2, the script for restricting is S45G1-max3W1 L2(25).2_2 0.130
L2(25).23 Atlas of Group Representations: point stabilizer in 2F4(2)'.2, G ≤ Sym(2304), generators of 2F4(2)'.2 are TF42d2G1-p2304B0.m1, TF42d2G1-p2304B0.m2 L2(25).2_3 0.400
2.L2(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.L2(25).21 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.L2(25).22 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.L2(25).23 a central extension of (2 × L2(25)).23: 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
M11 Atlas of Group Representations: G ≤ Sym(11), generators are M11G1-p11B0.m1, M11G1-p11B0.m2 M11 0.060
L2(27) Atlas of Group Representations: G ≤ Sym(28), generators are L227G1-p28B0.m1, L227G1-p28B0.m2 L2(27) 0.080
L2(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
L2(27).3 Atlas of Group Representations: restriction from S6(3) to its 6th maximal subgroup, G ≤ Sym(364), generators of S6(3) are S63G1-p364B0.m1, S63G1-p364B0.m2, the script for restricting is S63G1-max6W1 L2(27).3 0.140
L2(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.L2(27) Atlas of Group Representations: G ≤ GL(2,27), generators are 2L227G1-f27r2aB0.m1, 2L227G1-f27r2aB0.m2 2.L2(27) 0.200
2.L2(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.L2(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.L2(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
L2(29) Atlas of Group Representations: G ≤ Sym(30), generators are L229G1-p30B0.m1, L229G1-p30B0.m2 L2(29) 0.060
L2(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.L2(29) Atlas of Group Representations: G ≤ GL(2,29), generators are 2L229G1-f29r2B0.m1, 2L229G1-f29r2B0.m2 2.L2(29) 0.150
2.L2(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
L2(31) Atlas of Group Representations: G ≤ Sym(32), generators are L231G1-p32B0.m1, L231G1-p32B0.m2 L2(31) 0.060
L2(31).2 Atlas of Group Representations: G ≤ GL(30,2), generators are L231d2G1-f2r30B0.m1, L231d2G1-f2r30B0.m2 L2(31).2 1.080
2.L2(31) Atlas of Group Representations: G ≤ GL(16,5), generators are 2L231G1-f5r16aB0.m1, 2L231G1-f5r16aB0.m2 2.L2(31) 0.330
2.L2(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
A8 Atlas of Group Representations: G ≤ Sym(8), generators are A8G1-p8B0.m1, A8G1-p8B0.m2 A8 0.080
A8.2 Atlas of Group Representations: G ≤ Sym(8), generators are S8G1-p8B0.m1, S8G1-p8B0.m2 A8.2 0.080
2.A8 Atlas of Group Representations: G ≤ Sym(240), generators are 2A8G1-p240aB0.m1, 2A8G1-p240aB0.m2 2.A8 0.220
2.A8.2 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
L3(4) Atlas of Group Representations: G ≤ Sym(21), generators are L34G1-p21aB0.m1, L34G1-p21aB0.m2 L3(4) 0.090
L3(4).21 Atlas of Group Representations: G ≤ GL(16,2), generators are L34d2aG1-f2r16aB0.m1, L34d2aG1-f2r16aB0.m2 L3(4).2_1 0.290
L3(4).22 Atlas of Group Representations: restriction from M22.2 to its 2nd maximal subgroup, G ≤ Sym(22), generators of M22.2 are M22d2G1-p22B0.m1, M22d2G1-p22B0.m2, the script for restricting is M22d2G1-max2W1 L3(4).2_2 0.130
L3(4).23 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
L3(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
L3(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.L3(4) Atlas of Group Representations: G ≤ Sym(112), generators are 2L34G1-p112aB0.m1, 2L34G1-p112aB0.m2 2.L3(4) 0.160
2.L3(4).21 Atlas of Group Representations: G ≤ GL(20,3), generators are 2L34d2aG1-f3r20aB0.m1, 2L34d2aG1-f3r20aB0.m2 2.L3(4).2_1 0.360
2.L3(4).22 Multiplicity-free permutation representations: restriction from 2.M22.2 to its 2nd maximal subgroup, G ≤ Sym(660), generators of 2.M22.2 are 2M22d2G1-p660aB0.m1, 2M22d2G1-p660aB0.m2, the script for restricting is M22d2G1-max2W1 2.L3(4).2_2 0.200
2.L3(4).23 factor group of 41.L3(4).23: 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.L3(4) Atlas of Group Representations: G ≤ Sym(63), generators are 3L34G1-p63aB0.m1, 3L34G1-p63aB0.m2 3.L3(4) 0.130
3.L3(4).21 Atlas of Group Representations: G ≤ GL(6,4), generators are 3L34d2aG1-f4r6aB0.m1, 3L34d2aG1-f4r6aB0.m2 3.L3(4).2_1 0.310
3.L3(4).22 Multiplicity-free permutation representations: restriction from 3.M22.2 to its 2nd maximal subgroup, G ≤ Sym(693), generators of 3.M22.2 are 3M22d2G1-p693B0.m1, 3M22d2G1-p693B0.m2, the script for restricting is M22d2G1-max2W1 3.L3(4).2_2 0.180
3.L3(4).23 Atlas of Group Representations: restriction from G2(4) to its 5th maximal subgroup, G ≤ Sym(416), generators of G2(4) are G24G1-p416B0.m1, G24G1-p416B0.m2, the script for restricting is G24G1-max5W1 3.L3(4).2_3 0.190
3.L3(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.L3(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
41.L3(4) Atlas of Group Representations: G ≤ Sym(224), generators are 4aL34G1-p224B0.m1, 4aL34G1-p224B0.m2 4_1.L3(4) 0.140
41.L3(4).21 Atlas of Group Representations: G ≤ GL(16,3), generators are 4aL34d2aG1-f3r16aB0.m1, 4aL34d2aG1-f3r16aB0.m2 4_1.L3(4).2_1 0.580
41.L3(4).22 semidirect product of 41.L3(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
41.L3(4).23 semidirect product of 41.L3(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
42.L3(4) Atlas of Group Representations: G ≤ Sym(224), generators are 4bL34G1-p224B0.m1, 4bL34G1-p224B0.m2 4_2.L3(4) 0.150
42.L3(4).21 Atlas of Group Representations: G ≤ GL(8,3), generators are 4bL34d2aG1-f3r8aB0.m1, 4bL34d2aG1-f3r8aB0.m2 4_2.L3(4).2_1 0.460
42.L3(4).22 semidirect product of 42.L3(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
42.L3(4).23 semidirect product of 42.L3(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.L3(4) Atlas of Group Representations: G ≤ Sym(720), generators are 6L34G1-p720aB0.m1, 6L34G1-p720aB0.m2 6.L3(4) 0.240
6.L3(4).21 Atlas of Group Representations: G ≤ GL(6,7), generators are 6L34d2aG1-f7r6aB0.m1, 6L34d2aG1-f7r6aB0.m2 6.L3(4).2_1 0.680
6.L3(4).22 Multiplicity-free permutation representations: restriction from 6.M22.2 to its 2nd maximal subgroup, G ≤ Sym(1980), generators of 6.M22.2 are 6M22d2G1-p1980aB0.m1, 6M22d2G1-p1980aB0.m2, the script for restricting is M22d2G1-max2W1 6.L3(4).2_2 0.460
6.L3(4).23 subdirect product of 2.L3(4).23 and 3.L3(4).23: 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
121.L3(4) Atlas of Group Representations: G ≤ Sym(1440), generators are 12aL34G1-p1440B0.m1, 12aL34G1-p1440B0.m2 12_1.L3(4) 0.560
121.L3(4).21 Atlas of Group Representations: G ≤ GL(48,7), generators are 12aL34d2aG1-f7r48aB0.m1, 12aL34d2aG1-f7r48aB0.m2 12_1.L3(4).2_1 6.890
121.L3(4).22 subdirect product of 41.L3(4).22 and 3.L3(4).22: 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
121.L3(4).23 subdirect product of 41.L3(4).23 and 3.L3(4).23: 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
122.L3(4) Atlas of Group Representations: G ≤ Sym(1440), generators are 12bL34G1-p1440B0.m1, 12bL34G1-p1440B0.m2 12_2.L3(4) 0.590
122.L3(4).21 Atlas of Group Representations: G ≤ GL(24,7), generators are 12bL34d2aG1-f7r24aB0.m1, 12bL34d2aG1-f7r24aB0.m2 12_2.L3(4).2_1 3.360
122.L3(4).22 subdirect product of 42.L3(4).22 and 3.L3(4).22: 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
122.L3(4).23 subdirect product of 42.L3(4).23 and 3.L3(4).23: 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
U4(2) Atlas of Group Representations: G ≤ Sym(27), generators are U42G1-p27B0.m1, U42G1-p27B0.m2 U4(2) 0.120
U4(2).2 Atlas of Group Representations: G ≤ Sym(27), generators are U42d2G1-p27B0.m1, U42d2G1-p27B0.m2 U4(2).2 0.100
2.U4(2) Atlas of Group Representations: G ≤ Sym(80), generators are 2U42G1-p80B0.m1, 2U42G1-p80B0.m2 2.U4(2) 0.170
2.U4(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
L2(32) Atlas of Group Representations: G ≤ Sym(33), generators are L232G1-p33B0.m1, L232G1-p33B0.m2 L2(32) 0.120
L2(32).5 Atlas of Group Representations: G ≤ Sym(33), generators are L232d5G1-p33B0.m1, L232d5G1-p33B0.m2 L2(32).5 0.070
U3(4) Atlas of Group Representations: G ≤ Sym(65), generators are U34G1-p65B0.m1, U34G1-p65B0.m2 U3(4) 0.090
U3(4).2 Atlas of Group Representations: G ≤ Sym(65), generators are U34d2G1-p65B0.m1, U34d2G1-p65B0.m2 U3(4).2 0.090
U3(4).4 Atlas of Group Representations: G ≤ Sym(65), generators are U34d4G1-p65B0.m1, U34d4G1-p65B0.m2 U3(4).4 0.090
M12 Atlas of Group Representations: G ≤ Sym(12), generators are M12G1-p12aB0.m1, M12G1-p12aB0.m2 M12 0.080
M12.2 Atlas of Group Representations: G ≤ Sym(24), generators are M12d2G1-p24B0.m1, M12d2G1-p24B0.m2 M12.2 0.100
2.M12 Atlas of Group Representations: G ≤ Sym(24), generators are 2M12G1-p24aB0.m1, 2M12G1-p24aB0.m2 2.M12 0.100
2.M12.2 Atlas of Group Representations: G ≤ Sym(48), generators are 2M12d2G1-p48B0.m1, 2M12d2G1-p48B0.m2 2.M12.2 0.180
U3(5) Atlas of Group Representations: G ≤ Sym(50), generators are U35G1-p50B0.m1, U35G1-p50B0.m2 U3(5) 0.080
U3(5).2 Atlas of Group Representations: G ≤ Sym(50), generators are U35d2G1-p50B0.m1, U35d2G1-p50B0.m2 U3(5).2 0.090
U3(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.U3(5) Atlas of Group Representations: restriction from 3.McL to its 4th maximal subgroup, G ≤ Sym(66825), generators of 3.McL are 3McLG1-p66825B0.m1, 3McLG1-p66825B0.m2, the script for restricting is McLG1-max4W1 3.U3(5) 8.340
3.U3(5).2 Multiplicity-free permutation representations: restriction from 3.McL.2 to its 3rd maximal subgroup, G ≤ Sym(66825), generators of 3.McL.2 are 3McLd2G1-p66825bB0.m1, 3McLd2G1-p66825bB0.m2, the script for restricting is McLd2G1-max3W1 3.U3(5).2 5.940
3.U3(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
J1 Atlas of Group Representations: G ≤ Sym(266), generators are J1G1-p266B0.m1, J1G1-p266B0.m2 J1 0.080
A9 Atlas of Group Representations: G ≤ Sym(9), generators are A9G1-p9B0.m1, A9G1-p9B0.m2 A9 0.060
A9.2 Atlas of Group Representations: G ≤ Sym(9), generators are S9G1-p9B0.m1, S9G1-p9B0.m2 A9.2 0.050
2.A9 Atlas of Group Representations: G ≤ GL(8,3), generators are 2A9G1-f3r8B0.m1, 2A9G1-f3r8B0.m2 2.A9 0.250
2.A9.2 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
L3(5) Atlas of Group Representations: G ≤ Sym(31), generators are L35G1-p31aB0.m1, L35G1-p31aB0.m2 L3(5) 0.090
L3(5).2 Atlas of Group Representations: G ≤ Sym(62), generators are L35d2G1-p62B0.m1, L35d2G1-p62B0.m2 L3(5).2 0.110
M22 Atlas of Group Representations: G ≤ Sym(22), generators are M22G1-p22B0.m1, M22G1-p22B0.m2 M22 0.090
M22.2 Atlas of Group Representations: G ≤ Sym(22), generators are M22d2G1-p22B0.m1, M22d2G1-p22B0.m2 M22.2 0.120
2.M22 Atlas of Group Representations: G ≤ Sym(352), generators are 2M22G1-p352aB0.m1, 2M22G1-p352aB0.m2 2.M22 0.180
2.M22.2 Multiplicity-free permutation representations: G ≤ Sym(660), generators are 2M22d2G1-p660aB0.m1, 2M22d2G1-p660aB0.m2 2.M22.2 0.280
3.M22 Atlas of Group Representations: G ≤ Sym(693), generators are 3M22G1-p693B0.m1, 3M22G1-p693B0.m2 3.M22 0.260
3.M22.2 Multiplicity-free permutation representations: G ≤ Sym(693), generators are 3M22d2G1-p693B0.m1, 3M22d2G1-p693B0.m2 3.M22.2 0.270
4.M22 Atlas of Group Representations: G ≤ Sym(4928), generators are 4M22G1-p4928aB0.m1, 4M22G1-p4928aB0.m2 4.M22 0.590
4.M22.2 Atlas of Group Representations: G ≤ GL(32,7), generators are 4M22d2G1-f7r32B0.m1, 4M22d2G1-f7r32B0.m2 4.M22.2 12.210
6.M22 Atlas of Group Representations: G ≤ Sym(1980), generators are 6M22G1-p1980B0.m1, 6M22G1-p1980B0.m2 6.M22 0.590
6.M22.2 Multiplicity-free permutation representations: G ≤ Sym(1980), generators are 6M22d2G1-p1980aB0.m1, 6M22d2G1-p1980aB0.m2 6.M22.2 0.640
12.M22 Atlas of Group Representations: G ≤ Sym(31680), generators are 12M22G1-p31680aB0.m1, 12M22G1-p31680aB0.m2 12.M22 12.260
12.M22.2 Atlas of Group Representations: G ≤ GL(48,11), generators are 12M22d2G1-f11r48B0.m1, 12M22d2G1-f11r48B0.m2 12.M22.2 362.040
J2 Atlas of Group Representations: G ≤ Sym(100), generators are J2G1-p100B0.m1, J2G1-p100B0.m2 J2 0.120
J2.2 Atlas of Group Representations: G ≤ Sym(100), generators are J2d2G1-p100B0.m1, J2d2G1-p100B0.m2 J2.2 0.140
2.J2 Atlas of Group Representations: G ≤ Sym(200), generators are 2J2G1-p200B0.m1, 2J2G1-p200B0.m2 2.J2 0.210
2.J2.2 Multiplicity-free permutation representations: G ≤ Sym(400), generators are 2J2d2G1-p400B0.m1, 2J2d2G1-p400B0.m2 2.J2.2 0.310
S4(4) Atlas of Group Representations: G ≤ Sym(85), generators are S44G1-p85aB0.m1, S44G1-p85aB0.m2 S4(4) 0.190
S4(4).2 Atlas of Group Representations: G ≤ GL(8,2), generators are S44d2G1-f2r8aB0.m1, S44d2G1-f2r8aB0.m2 S4(4).2 0.330
S4(4).4 Atlas of Group Representations: G ≤ Sym(170), generators are S44d4G1-p170B0.m1, S44d4G1-p170B0.m2 S4(4).4 0.200
S6(2) Atlas of Group Representations: G ≤ Sym(28), generators are S62G1-p28B0.m1, S62G1-p28B0.m2 S6(2) 0.110
2.S6(2) Atlas of Group Representations: G ≤ Sym(240), generators are 2S62G1-p240aB0.m1, 2S62G1-p240aB0.m2 2.S6(2) 0.310
A10 Atlas of Group Representations: G ≤ Sym(10), generators are A10G1-p10B0.m1, A10G1-p10B0.m2 A10 0.080
A10.2 Atlas of Group Representations: G ≤ Sym(10), generators are S10G1-p10B0.m1, S10G1-p10B0.m2 A10.2 0.120
2.A10 Atlas of Group Representations: G ≤ GL(16,3), generators are 2A10G1-f3r16B0.m1, 2A10G1-f3r16B0.m2 2.A10 0.460
2.A10.2 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
L3(7) Atlas of Group Representations: G ≤ Sym(57), generators are L37G1-p57B0.m1, L37G1-p57B0.m2 L3(7) 0.090
L3(7).2 Atlas of Group Representations: G ≤ GL(8,7), generators are L37d2G1-f7r8B0.m1, L37d2G1-f7r8B0.m2 L3(7).2 0.370
L3(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.L3(7) Atlas of Group Representations: G ≤ GL(3,7), generators are 3L37G1-f7r3B0.m1, 3L37G1-f7r3B0.m2 3.L3(7) 0.330
3.L3(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.L3(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
U4(3) Atlas of Group Representations: restriction from McL to its 1st maximal subgroup, G ≤ Sym(275), generators of McL are McLG1-p275B0.m1, McLG1-p275B0.m2, the script for restricting is McLG1-max1W1 U4(3) 0.270
U4(3).21 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
U4(3).22 Atlas of Group Representations: restriction from U6(2) to its 4th maximal subgroup, G ≤ Sym(672), generators of U6(2) are U62G1-p672B0.m1, U62G1-p672B0.m2, the script for restricting is U62G1-max4W1 U4(3).2_2 0.370
U4(3).23 Atlas of Group Representations: restriction from McL.2 to its 2nd maximal subgroup, G ≤ Sym(275), generators of McL.2 are McLd2G1-p275B0.m1, McLd2G1-p275B0.m2, the script for restricting is McLd2G1-max2W1 U4(3).2_3 0.280
U4(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.U4(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.U4(3).21 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.U4(3).22 Atlas of Group Representations: restriction from 2.U6(2) to its 5th maximal subgroup, G ≤ Sym(1344), generators of 2.U6(2) are 2U62G1-p1344B0.m1, 2U62G1-p1344B0.m2, the script for restricting is U62G1-max5W1 2.U4(3).2_2 1.170
2.U4(3).23 isoclinic variant of a subgroup of 2.U4(3).D8: 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.U4(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
31.U4(3) derived subgroup of the fourth maximal subgroup of 3.U6(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
31.U4(3).21 factor group of the derived subgroup of 32.U4(3).D8: 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
31.U4(3).22 Atlas of Group Representations: restriction from 3.U6(2) to its 4th maximal subgroup, G ≤ Sym(2016), generators of 3.U6(2) are 3U62G1-p2016B0.m1, 3U62G1-p2016B0.m2, the script for restricting is U62G1-max4W1 3_1.U4(3).2_2 1.870
31.U4(3).22' factor group of an index 4 subgroup of 32.U4(3).D8: 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
32.U4(3) Atlas of Group Representations: restriction from 3.McL to its 1st maximal subgroup, G ≤ Sym(66825), generators of 3.McL are 3McLG1-p66825B0.m1, 3McLG1-p66825B0.m2, the script for restricting is McLG1-max1W1 3_2.U4(3) 32.300
32.U4(3).21 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
32.U4(3).23 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
32.U4(3).23' Multiplicity-free permutation representations: restriction from 3.McL.2 to its 2nd maximal subgroup, G ≤ Sym(66825), generators of 3.McL.2 are 3McLd2G1-p66825bB0.m1, 3McLd2G1-p66825bB0.m2, the script for restricting is McLd2G1-max2W1 3_2.U4(3).2_3' 21.570
4.U4(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.U4(3).21 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.U4(3).22 semidirect product of 4.U4(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.U4(3).23 semidirect product of 4.U4(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.U4(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
61.U4(3) derived subgroup of the 5th maximal subgroup of 6.U6(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
61.U4(3).21 subdirect product of 31.U4(3).21 and 2.U4(3).21: 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
61.U4(3).22 Atlas of Group Representations: restriction from 6.U6(2) to its 5th maximal subgroup, G ≤ Sym(4032), generators of 6.U6(2) are 6U62G1-p4032B0.m1, 6U62G1-p4032B0.m2, the script for restricting is U62G1-max5W1 6_1.U4(3).2_2 8.150
61.U4(3).22' subdirect product of 31.U4(3).22' and 2.U4(3).22: 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
62.U4(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
62.U4(3).21 subdirect product of 32.U4(3).21 and 2.U4(3).21: 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
62.U4(3).23 subdirect product of 32.U4(3).23 and 2.U4(3).23: 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
62.U4(3).23' 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
121.U4(3) subdirect product of 31.U4(3) and 4.U4(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
121.U4(3).21 subdirect product of 31.U4(3).21 and 4.U4(3).21: 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
121.U4(3).22 subdirect product of 31.U4(3).22 and 4.U4(3).22: 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
121.U4(3).22' subdirect product of 31.U4(3).22' and 4.U4(3).22: 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
122.U4(3) subdirect product of 32.U4(3) and 4.U4(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
122.U4(3).21 subdirect product of 32.U4(3).21 and 4.U4(3).21: 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
122.U4(3).23 subdirect product of 32.U4(3).23 and 4.U4(3).23: 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
122.U4(3).23' subdirect product of 32.U4(3).23' and 4.U4(3).23: 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
G2(3) Atlas of Group Representations: G ≤ GL(14,2), generators are G23G1-f2r14B0.m1, G23G1-f2r14B0.m2 G2(3) 0.880
G2(3).2 Atlas of Group Representations: G ≤ Sym(756), generators are G23d2G1-p756B0.m1, G23d2G1-p756B0.m2 G2(3).2 0.300
3.G2(3) Atlas of Group Representations: G ≤ Sym(1134), generators are 3G23G1-p1134B0.m1, 3G23G1-p1134B0.m2 3.G2(3) 0.700
3.G2(3).2 Atlas of Group Representations: G ≤ GL(54,2), generators are 3G23d2G1-f2r54B0.m1, 3G23d2G1-f2r54B0.m2 3.G2(3).2 8271.650
S4(5) Atlas of Group Representations: G ≤ Sym(156), generators are S45G1-p156aB0.m1, S45G1-p156aB0.m2 S4(5) 0.230
S4(5).2 Atlas of Group Representations: G ≤ GL(24,2), generators are S45d2G1-f2r24B0.m1, S45d2G1-f2r24B0.m2 S4(5).2 0.820
2.S4(5) Atlas of Group Representations: G ≤ Sym(624), generators are 2S45G1-p624B0.m1, 2S45G1-p624B0.m2 2.S4(5) 0.440
2.S4(5).2 semidirect product of 2.S4(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
U3(8) Atlas of Group Representations: G ≤ Sym(513), generators are U38G1-p513B0.m1, U38G1-p513B0.m2 U3(8) 0.170
U3(8).2 Atlas of Group Representations: G ≤ Sym(513), generators are U38d2G1-p513B0.m1, U38d2G1-p513B0.m2 U3(8).2 0.200
U3(8).31 Atlas of Group Representations: G ≤ Sym(513), generators are U38d3aG1-p513B0.m1, U38d3aG1-p513B0.m2 U3(8).3_1 0.370
U3(8).32 Atlas of Group Representations: G ≤ Sym(513), generators are U38d3bG1-p513B0.m1, U38d3bG1-p513B0.m2 U3(8).3_2 0.330
U3(8).33 Atlas of Group Representations: G ≤ Sym(513), generators are U38d3cG1-p513B0.m1, U38d3cG1-p513B0.m2 U3(8).3_3 0.210
U3(8).6 Atlas of Group Representations: G ≤ Sym(513), generators are U38d6G1-p513B0.m1, U38d6G1-p513B0.m2 U3(8).6 0.370
3.U3(8) Atlas of Group Representations: G ≤ Sym(4617), generators are 3U38G1-p4617B0.m1, 3U38G1-p4617B0.m2 3.U3(8) 1.310
3.U3(8).2 semidirect product of 3.U3(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.U3(8).31 semidirect product of 3.U3(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.U3(8).32 isoclinic variant of a semidirect product of 3.U3(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.U3(8).6 semidirect product of 3.U3(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.U3(8).33 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
U3(7) Atlas of Group Representations: G ≤ Sym(344), generators are U37G1-p344B0.m1, U37G1-p344B0.m2 U3(7) 0.210
U3(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
L4(3) GroupForTom( "L4(3)" ): G ≤ Sym(40), generators are magmaoutput/L4(3)-p40.m1, magmaoutput/L4(3)-p40.m2 L4(3) 0.190
L4(3).21 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
L4(3).22 Atlas of Group Representations: point stabilizer in O7(3), G ≤ Sym(378), generators of O7(3) are O73G1-p378B0.m1, O73G1-p378B0.m2 L4(3).2_2 0.550
L4(3).23 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.L4(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.L4(3).21 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.L4(3).22 semidirect product of 2.L4(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.L4(3).23 semidirect product of 2.L4(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
L5(2) Atlas of Group Representations: G ≤ Sym(31), generators are L52G1-p31aB0.m1, L52G1-p31aB0.m2 L5(2) 0.170
L5(2).2 Atlas of Group Representations: G ≤ Sym(62), generators are L52d2G1-p62B0.m1, L52d2G1-p62B0.m2 L5(2).2 0.230
M23 Atlas of Group Representations: G ≤ Sym(23), generators are M23G1-p23B0.m1, M23G1-p23B0.m2 M23 0.090
U5(2) Atlas of Group Representations: G ≤ Sym(165), generators are U52G1-p165B0.m1, U52G1-p165B0.m2 U5(2) 0.370
U5(2).2 Atlas of Group Representations: G ≤ Sym(165), generators are U52d2G1-p165B0.m1, U52d2G1-p165B0.m2 U5(2).2 0.320
L3(8) Atlas of Group Representations: G ≤ Sym(73), generators are L38G1-p73aB0.m1, L38G1-p73aB0.m2 L3(8) 0.240
L3(8).2 Atlas of Group Representations: G ≤ Sym(146), generators are L38d2G1-p146B0.m1, L38d2G1-p146B0.m2 L3(8).2 0.230
L3(8).3 Atlas of Group Representations: G ≤ Sym(73), generators are L38d3G1-p73aB0.m1, L38d3G1-p73aB0.m2 L3(8).3 0.210
L3(8).6 Atlas of Group Representations: G ≤ Sym(438), generators are L38d6G1-p438B0.m1, L38d6G1-p438B0.m2 L3(8).6 0.280
2F4(2)' Atlas of Group Representations: G ≤ Sym(1600), generators are TF42G1-p1600B0.m1, TF42G1-p1600B0.m2 2F4(2)' 0.350
2F4(2)'.2 Atlas of Group Representations: G ≤ Sym(1755), generators are TF42d2G1-p1755B0.m1, TF42d2G1-p1755B0.m2 2F4(2)'.2 0.480
A11 Atlas of Group Representations: G ≤ Sym(11), generators are A11G1-p11B0.m1, A11G1-p11B0.m2 A11 0.110
A11.2 Atlas of Group Representations: G ≤ Sym(11), generators are S11G1-p11B0.m1, S11G1-p11B0.m2 A11.2 0.230
2.A11 Atlas of Group Representations: G ≤ Sym(5040), generators are 2A11G1-p5040B0.m1, 2A11G1-p5040B0.m2 2.A11 1.110
2.A11.2 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
L3(9) GroupForTom( "L3(9)" ): G ≤ Sym(91), generators are magmaoutput/L3(9)-p91.m1, magmaoutput/L3(9)-p91.m2 L3(9) 0.320
L3(9).21 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
L3(9).22 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
L3(9).23 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
U3(9) Atlas of Group Representations: G ≤ Sym(730), generators are U39G1-p730B0.m1, U39G1-p730B0.m2 U3(9) 0.520
U3(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
U3(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
J3 Atlas of Group Representations: G ≤ Sym(6156), generators are J3G1-p6156B0.m1, J3G1-p6156B0.m2 J3 0.410
J3.2 Atlas of Group Representations: G ≤ Sym(6156), generators are J3d2G1-p6156B0.m1, J3d2G1-p6156B0.m2 J3.2 0.640
3.J3 Atlas of Group Representations: G ≤ GL(9,4), generators are 3J3G1-f4r9aB0.m1, 3J3G1-f4r9aB0.m2 3.J3 113.600
3.J3.2 Atlas of Group Representations: G ≤ GL(18,2), generators are 3J3d2G1-f2r18B0.m1, 3J3d2G1-f2r18B0.m2 3.J3.2 15.890
U3(11) Atlas of Group Representations: G ≤ Sym(1332), generators are U311G1-p1332B0.m1, U311G1-p1332B0.m2 U3(11) 0.300
U3(11).2 Atlas of Group Representations: G ≤ Sym(1332), generators are U311d2G1-p1332B0.m1, U311d2G1-p1332B0.m2 U3(11).2 0.360
U3(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.U3(11) Atlas of Group Representations: G ≤ GL(3,121), generators are 3U311G1-f121r3aB0.m1, 3U311G1-f121r3aB0.m2 3.U3(11) 1.370
3.U3(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.U3(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
O8+(2) Atlas of Group Representations: restriction from O8+(3) to its 10th maximal subgroup, G ≤ Sym(1080), generators of O8+(3) are O8p3G1-p1080aB0.m1, O8p3G1-p1080aB0.m2, the script for restricting is O8p3G1-max10W1 O8+(2) 1.270
O8+(2).2 Atlas of Group Representations: point stabilizer in S8(2), G ≤ Sym(136), generators of S8(2) are S82G1-p136B0.m1, S82G1-p136B0.m2 O8+(2).2 0.740
O8+(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.O8+(2) derived subgroup of the Weyl group of type E8: G ≤ Sym(2160), generators are magmaoutput/2.O8+(2)-p2160.m1, magmaoutput/2.O8+(2)-p2160.m2 2.O8+(2) 2.210
2.O8+(2).2 Weyl group of type E8: 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
O8(2) Atlas of Group Representations: G ≤ Sym(119), generators are O8m2G1-p119B0.m1, O8m2G1-p119B0.m2 O8-(2) 0.410
O8(2).2 Atlas of Group Representations: G ≤ Sym(119), generators are O8m2d2G1-p119B0.m1, O8m2d2G1-p119B0.m2 O8-(2).2 0.530
3D4(2) Atlas of Group Representations: G ≤ Sym(819), generators are TD42G1-p819B0.m1, TD42G1-p819B0.m2 3D4(2) 0.460
3D4(2).3 Atlas of Group Representations: G ≤ GL(24,2), generators are TD42d3G1-f2r24B0.m1, TD42d3G1-f2r24B0.m2 3D4(2).3 9248.800
A12 Atlas of Group Representations: G ≤ Sym(12), generators are A12G1-p12B0.m1, A12G1-p12B0.m2 A12 0.210
A12.2 Atlas of Group Representations: G ≤ Sym(12), generators are S12G1-p12B0.m1, S12G1-p12B0.m2 A12.2 0.460
2.A12 Atlas of Group Representations: G ≤ GL(16,3), generators are 2A12G1-f3r16aB0.m1, 2A12G1-f3r16aB0.m2 2.A12 22.570
2.A12.2 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
M24 Atlas of Group Representations: G ≤ Sym(24), generators are M24G1-p24B0.m1, M24G1-p24B0.m2 M24 0.180
G2(4) Atlas of Group Representations: G ≤ Sym(416), generators are G24G1-p416B0.m1, G24G1-p416B0.m2 G2(4) 0.460
G2(4).2 Atlas of Group Representations: G ≤ GL(12,2), generators are G24d2G1-f2r12B0.m1, G24d2G1-f2r12B0.m2 G2(4).2 2.200
2.G2(4) Atlas of Group Representations: G ≤ GL(12,3), generators are 2G24G1-f3r12B0.m1, 2G24G1-f3r12B0.m2 2.G2(4) 79.620
2.G2(4).2 Atlas of Group Representations: G ≤ GL(12,7), generators are 2G24d2G1-f7r12B0.m1, 2G24d2G1-f7r12B0.m2 2.G2(4).2 705.400
McL Atlas of Group Representations: G ≤ Sym(275), generators are McLG1-p275B0.m1, McLG1-p275B0.m2 McL 0.220
McL.2 Atlas of Group Representations: G ≤ Sym(275), generators are McLd2G1-p275B0.m1, McLd2G1-p275B0.m2 McL.2 0.260
3.McL Atlas of Group Representations: G ≤ Sym(66825), generators are 3McLG1-p66825B0.m1, 3McLG1-p66825B0.m2 3.McL 40.010
3.McL.2 Multiplicity-free permutation representations: G ≤ Sym(66825), generators are 3McLd2G1-p66825bB0.m1, 3McLd2G1-p66825bB0.m2 3.McL.2 25.370
A13 Atlas of Group Representations: G ≤ Sym(13), generators are A13G1-p13B0.m1, A13G1-p13B0.m2 A13 0.360
A13.2 Atlas of Group Representations: G ≤ Sym(13), generators are S13G1-p13B0.m1, S13G1-p13B0.m2 A13.2 1.140
2.A13 Atlas of Group Representations: G ≤ GL(32,3), generators are 2A13G1-f3r32aB0.m1, 2A13G1-f3r32aB0.m2 2.A13 26.600
2.A13.2 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
O7(3) Atlas of Group Representations: G ≤ Sym(351), generators are O73G1-p351B0.m1, O73G1-p351B0.m2 O7(3) 1.140
O7(3).2 Atlas of Group Representations: G ≤ Sym(351), generators are O73d2G1-p351B0.m1, O73d2G1-p351B0.m2 O7(3).2 2.500
2.O7(3) Atlas of Group Representations: G ≤ Sym(2160), generators are 2O73G1-p2160B0.m1, 2O73G1-p2160B0.m2 2.O7(3) 3.020
2.O7(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.O7(3) Atlas of Group Representations: G ≤ GL(27,4), generators are 3O73G1-f4r27aB0.m1, 3O73G1-f4r27aB0.m2 3.O7(3) 51.340
3.O7(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.O7(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.O7(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
S6(3) Atlas of Group Representations: G ≤ Sym(364), generators are S63G1-p364B0.m1, S63G1-p364B0.m2 S6(3) 1.390
S6(3).2 Atlas of Group Representations: G ≤ Sym(364), generators are S63d2G1-p364B0.m1, S63d2G1-p364B0.m2 S6(3).2 1.290
2.S6(3) Atlas of Group Representations: G ≤ GL(6,3), generators are 2S63G1-f3r6B0.m1, 2S63G1-f3r6B0.m2 2.S6(3) 4.230
2.S6(3).2 Atlas of Group Representations: G ≤ Sym(728), generators are 2S63d2G1-p728B0.m1, 2S63d2G1-p728B0.m2 2.S6(3).2 2.830
G2(5) Atlas of Group Representations: G ≤ Sym(3906), generators are G25G1-p3906aB0.m1, G25G1-p3906aB0.m2 G2(5) 1.170
U6(2) Atlas of Group Representations: G ≤ Sym(672), generators are U62G1-p672B0.m1, U62G1-p672B0.m2 U6(2) 1.230
U6(2).2 Atlas of Group Representations: G ≤ Sym(672), generators are U62d2G1-p672B0.m1, U62d2G1-p672B0.m2 U6(2).2 1.240
U6(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.U6(2) Atlas of Group Representations: G ≤ Sym(1344), generators are 2U62G1-p1344B0.m1, 2U62G1-p1344B0.m2 2.U6(2) 2.740
2.U6(2).2 Atlas of Group Representations: restriction from Fi22.2 to its 2nd maximal subgroup, G ≤ Sym(3510), generators of Fi22.2 are F22d2G1-p3510B0.m1, F22d2G1-p3510B0.m2, the script for restricting is F22d2G1-max2W1 2.U6(2).2 6.730
3.U6(2) Atlas of Group Representations: G ≤ Sym(2016), generators are 3U62G1-p2016B0.m1, 3U62G1-p2016B0.m2 3.U6(2) 5.410
3.U6(2).2 factor group of the second maximal subgroup of 3.Fi22.2: 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.U6(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.U6(2) Atlas of Group Representations: G ≤ Sym(4032), generators are 6U62G1-p4032B0.m1, 6U62G1-p4032B0.m2 6.U6(2) 18.050
6.U6(2).2 Atlas of Group Representations: restriction from 3.Fi22.2 to its 2nd maximal subgroup, G ≤ Sym(185328), generators of 3.Fi22.2 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
S8(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
Co3 Atlas of Group Representations: G ≤ Sym(276), generators are Co3G1-p276B0.m1, Co3G1-p276B0.m2 Co3 0.500
O8+(3) Atlas of Group Representations: G ≤ Sym(1080), generators are O8p3G1-p1080aB0.m1, O8p3G1-p1080aB0.m2 O8+(3) 8.120
O10+(2) Atlas of Group Representations: G ≤ Sym(496), generators are O10p2G1-p496B0.m1, O10p2G1-p496B0.m2 O10+(2) 3.510
O10+(2).2 Atlas of Group Representations: G ≤ Sym(496), generators are O10p2d2G1-p496B0.m1, O10p2d2G1-p496B0.m2 O10+(2).2 7.930
O10(2) Atlas of Group Representations: G ≤ Sym(495), generators are O10m2G1-p495B0.m1, O10m2G1-p495B0.m2 O10-(2) 5.070
O10(2).2 Atlas of Group Representations: G ≤ Sym(495), generators are O10m2d2G1-p495B0.m1, O10m2d2G1-p495B0.m2 O10-(2).2 10.050
Co2 Atlas of Group Representations: G ≤ Sym(2300), generators are Co2G1-p2300B0.m1, Co2G1-p2300B0.m2 Co2 2.990
Fi22 Atlas of Group Representations: G ≤ Sym(3510), generators are F22G1-p3510B0.m1, F22G1-p3510B0.m2 Fi22 4.380
Fi22.2 Atlas of Group Representations: G ≤ Sym(3510), generators are F22d2G1-p3510B0.m1, F22d2G1-p3510B0.m2 Fi22.2 8.690
2.Fi22 Atlas of Group Representations: G ≤ Sym(28160), generators are 2F22G1-p28160B0.m1, 2F22G1-p28160B0.m2 2.Fi22 59.920
2.Fi22.2 Atlas of Group Representations: G ≤ Sym(56320), generators are 2F22d2G1-p56320B0.m1, 2F22d2G1-p56320B0.m2 2.Fi22.2 313.540
3.Fi22 Atlas of Group Representations: G ≤ GL(27,4), generators are 3F22G1-f4r27aB0.m1, 3F22G1-f4r27aB0.m2 3.Fi22 45.780
3.Fi22.2 Atlas of Group Representations: G ≤ Sym(185328), generators are 3F22d2G1-p185328B0.m1, 3F22d2G1-p185328B0.m2 3.Fi22.2 1427.120
6.Fi22 Multiplicity-free permutation representations: G ≤ Sym(370656), generators are 6F22G1-p370656aB0.m1, 6F22G1-p370656aB0.m2 6.Fi22 8605.640
6.Fi22.2 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
F4(2) Atlas of Group Representations: G ≤ Sym(69888), generators are F42G1-p69888aB0.m1, F42G1-p69888aB0.m2 F4(2) 1889.540
F4(2).2 Atlas of Group Representations: G ≤ GL(52,2), generators are F42d2G1-f2r52B0.m1, F42d2G1-f2r52B0.m2 F4(2).2 844.430
2.F4(2) Atlas of Group Representations: G ≤ Sym(139776), generators are 2F42G1-p139776B0.m1, 2F42G1-p139776B0.m2 2.F4(2) 4142.350
2.F4(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
Fi23 Atlas of Group Representations: G ≤ Sym(31671), generators are F23G1-p31671B0.m1, F23G1-p31671B0.m2 Fi23 85.990
Co1 Atlas of Group Representations: G ≤ Sym(98280), generators are Co1G1-p98280B0.m1, Co1G1-p98280B0.m2 Co1 499.630
2.Co1 Atlas of Group Representations: G ≤ GL(24,3), generators are 2Co1G1-f3r24B0.m1, 2Co1G1-f3r24B0.m2 2.Co1 1503.160
J4 Atlas of Group Representations: G ≤ GL(112,2), generators are J4G1-f2r112B0.m1, J4G1-f2r112B0.m2 J4
2.2E6(2) Atlas of Group Representations: G ≤ GL(1704,2), generators are 2TE62G1-f2r1704B0.m1, 2TE62G1-f2r1704B0.m2 2.2E6(2)
2.2E6(2).2 Atlas of Group Representations: G ≤ GL(1705,2), generators are 2TE62d2G1-f2r1705B0.m1, 2TE62d2G1-f2r1705B0.m2 2.2E6(2).2
2E6(2) Atlas of Group Representations: G ≤ GL(78,2), generators are TE62G1-f2r78B0.m1, TE62G1-f2r78B0.m2 2E6(2)* 754034.830
2E6(2).2 Atlas of Group Representations: G ≤ GL(78,2), generators are TE62d2G1-f2r78B0.m1, TE62d2G1-f2r78B0.m2 2E6(2).2* 773379.750
F3+ Atlas of Group Representations: G ≤ Sym(306936), generators are F24G1-p306936B0.m1, F24G1-p306936B0.m2 F3+ 7529.770
F3+.2 Atlas of Group Representations: G ≤ Sym(306936), generators are F24d2G1-p306936B0.m1, F24d2G1-p306936B0.m2 F3+.2 12867.060
3.F3+ Atlas of Group Representations: G ≤ Sym(920808), generators are 3F24G1-p920808B0.m1, 3F24G1-p920808B0.m2 3.F3+ 169418.100
3.F3+.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.