Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for 6.Suz

Name:

6.Suz

Group order:

2690072985600 = 2¹⁴ ⋅ 3⁸ ⋅ 5² ⋅ 7 ⋅ 11 ⋅ 13

Number of classes:

210

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13]

Maximal subgroups:

	Order	Index	Structure	Name
1	1509580800	1782	3 × 2.G2(4)	3x2.G2(4)
2	117573120	22880	Isoclinic((32 × 2).U4(3).23')	Isoclinic((3^2x2).U4(3).2_3')
3	82114560	32760	6 × U5(2)	6xU5(2)
4	19906560	135135	3 × 2.21+6−.U4(2)	3x2.SuzM4
5	11547360	232960	2 × 36.M11	2x3^6.M11
6	7257600	370656	3 × 2.J2.2	3x2.J2.2
7	6635520	405405	3 × (2.24.26):3A6	3x2.SuzM7
8	2903040	926640	2.(A4 × 3.L3(4)).2	6.SuzM8
9	2211840	1216215	3 × 2.(22+8:(A5 × S3))	3x2.SuzM9
10	1140480	2358720	3 × Isoclinic(2.M12.2)	3xIsoclinic(2.M12.2)
11	839808	3203200	6.(32+4:2(A4 × 22).2)	6.SuzM11
12	259200	10378368	(3.A6 × 2.A5).2	(3.A6x2.A5).2
13	155520	17297280	(31+2:4 × 2.A6).2	(3^(1+2):4x2.A6).2
14	67392	39916800	3 × (2 × L3(3)).2	3x(2xL3(3)).2
15	67392	39916800	3 × (2 × L3(3)).2	3x(2xL3(3)).2
16	46800	57480192	3 × 2.L2(25)	3x2.L2(25)
17	15120	177914880	6.A7	6.A7

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	147456	18243225	3 × 2.SuzN2	3x2.SuzN2
3	209952	12812800	2 × 3.35:(32:SD16)	2x3.3^5:(3^2:SD16)
5	3600	747242496	3 × 2.J2.2N5	3x2.J2.2N5
7	3024	889574400	3 × (SL(2, 3) × 7:3).2	3x(SL(2,3)x7:3).2
11	660	4075868160	3 × 11:20	3x11:20
13	468	5748019200	3 × (2 × 13).6	3x(2x13).6

Available Brauer tables:

p
2	dec. matrix (PDF)
3	dec. matrix (PDF)
5	dec. matrix (PDF)
7	dec. matrix (PDF)
11	dec. matrix (PDF)
13	dec. matrix (PDF)

Atlas representations:

4 available

Group constructions in GAP:

AtlasGroup( "6.Suz" ), AtlasSubgroup( "6.Suz.2", 1 )

Stored class fusions from this table:

2.Suz, 3.Suz, 6.Suz.2, Suz

Stored class fusions to this table:

2.(D₈ × 3¹⁺²₊:Q₈), 2 × 3.3⁵:(3²:SD₁₆), 2 × 3⁶.M₁₁, 3 × 2.G₂(4), 3 × 2.J₂.2, 3 × 2.J₂.2N5, 3 × 2.L₂(25), 3 × 2.2¹⁺⁶₋.U₄(2), 3 × (2.2⁴.2⁶):3A₆, 3 × 2.(2²⁺⁸:(A₅ × S₃)), 3 × 2.SuzN2, 3 × 11:20, 3 × (2.A₅ × D₁₀).2, 3 × (2 × 13).6, 3 × (2 × L₃(3)).2, 3 × (SL(2, 3) × 7:3).2, 3 × Isoclinic(2.M₁₂.2), 6.A₇, 2.(A₄ × 3.L₃(4)).2, 6.(3²⁺⁴:2(A₄ × 2²).2), 6 × U₅(2), (2.D₁₀ × 3.A₆).2₃, (3.A₆ × 2.A₅).2, (3¹⁺²:4 × 2.A₆).2, Isoclinic((3² × 2).U₄(3).2₃')

File created automatically by GAP on 20-May-2025.