Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for S₆(3)

Name:

S6(3)

Group order:

4585351680 = 2⁹ ⋅ 3⁹ ⋅ 5 ⋅ 7 ⋅ 13

Number of classes:

74

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r.

Maximal subgroups:

	Order	Index	Structure	Name
1	12597120	364	31+4+.2U4(2)	3^(1+4).2U4(2)
2	4094064	1120	36:L3(3)	3^6:L3(3)
3	1259712	3640	33+4:2(S4 × A4)	3^(3+4):2(S4xA4)
4	622080	7371	2.(A4 × U4(2))	2.(A4xU4(2))
5	41472	110565	22+6:33:S3	2^(2+6):3^3:S3
6	29484	155520	L2(27).3	L2(27).3
7	24192	189540	2 × U3(3).2	2xU3(3).2
8	11232	408240	L3(3).2	L3(3).2
9	1092	4199040	L2(13)	L2(13)
10	1092	4199040	L2(13)	L2(13)
11	60	76422528	A5	A5

Available Brauer tables:

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

Atlas representations:

16 available

Group constructions in GAP:

AtlasGroup( "S6(3)" ), PSp( 6, 3 ), PrimitiveGroup( 364, 1 ), PrimitiveGroup( 1120, 3 ), PrimitiveGroup( 3640, 1 )

Stored class fusions from this table:

S₆(3).2

Stored class fusions to this table:

2.(A₄ × U₄(2)), 2.S₆(3), 2²⁺⁶:3³:S₃, 2 × U₃(3).2, 3⁶:L₃(3), 3¹⁺⁴₊.2U₄(2), 3³⁺⁴:2(S₄ × A₄), A₅, L₂(13), L₂(27).3, L₃(3).2

File created automatically by GAP on 13-Mar-2024.