Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for S₆(2)

Name:

S6(2)

Group order:

1451520 = 2⁹ ⋅ 3⁴ ⋅ 5 ⋅ 7

Number of classes:

30

InfoText value:

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

Duplicates:

O7(3)M8, O8+(2)M2, O8+(2)M3, U6(2)M10, U6(2)M9

Maximal subgroups:

	Order	Index	Structure	Name
1	51840	28	U4(2).2	U4(2).2
2	40320	36	S8	A8.2
3	23040	63	25:S6	2^5:S6
4	12096	120	U3(3).2	U3(3).2
5	10752	135	26:L3(2)	2^6:L3(2)
6	4608	315	2.[26]:(S3 × S3)	2.[2^6]:(S3xS3)
7	4320	336	S3 × S6	S3xS6
8	1512	960	L2(8).3	L2(8).3

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	512	2835	S6(2)N2	S6(2)N2
3	324	4480	33:(S3 × 2)	3^3:(S3x2)
5	120	12096	S3 × 5:4	S3x5:4
7	42	34560	7:6	7:6

Available Brauer tables:

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

Atlas representations:

57 available

Group constructions in GAP:

AtlasGroup( "S6(2)" ), AtlasStabilizer( "O8-(2)", "O8m2G1-p136B0" ), AtlasStabilizer( "U6(2)", "U62G1-p6336aB0" ), AtlasStabilizer( "U6(2)", "U62G1-p6336bB0" ), AtlasStabilizer( "U6(2)", "U62G1-p6336cB0" ), AtlasSubgroup( "O7(3)", 7 ), AtlasSubgroup( "U6(2)", 8 ), AtlasSubgroup( "U6(2)", 9 ), AtlasSubgroup( "U6(2)", 10 ), POmega( 7, 2 ), PSp( 6, 2 ), PerfectGroup( 1451520, 1 ), PrimitiveGroup( 28, 6 ), PrimitiveGroup( 36, 10 ), PrimitiveGroup( 63, 5 ), PrimitiveGroup( 120, 14 ), PrimitiveGroup( 135, 1 ), PrimitiveGroup( 315, 1 ), PrimitiveGroup( 336, 7 ), PrimitiveGroup( 960, 6 ), TransitiveGroup( 28, 1256 )

Stored class fusions from this table:

2⁶:S₆(2), 2⁸:S₆(2), L₆(2), O₇(3), O₇(5), O₈⁺(2), O₈⁻(2), U₆(2)

Stored class fusions to this table:

2.F₄(2)M1, 2.S₆(2), 2.[2⁶].(2 × S₃), 2.[2⁶]:(S₃ × S₃), 2¹⁺⁸₊:S₆(2), 2⁵:S₆, 2⁶:L₃(2), 2⁶:S₄a, 2⁶:S₄b, 2⁶:S₆(2), 2⁷:S₆(2), 2⁸:S₆(2), 2 × 2.S₆(2), 3³:(S₃ × 2), 3⁽¹⁺²⁾⁺:2S₄, 3 × 2.S₆(2), 7:6, (2⁶ × 2⁸):S₆(2), (2¹⁺⁸ × 2⁶):S₆(2), S₈, L₂(8).3, S₃ × 5:4, S₃ × S₆, S₆(2)N2, 2⁷:S₆(2), U₃(3).2, U₄(2).2, 3³:(S₄ × 2)

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