Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for S₄(4).2

Name:

S4(4).2

Group order:

1958400 = 2⁹ ⋅ 3² ⋅ 5² ⋅ 17

Number of classes:

30

InfoText value:

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

Maximal subgroups:

	Order	Index	Structure	Name
1	979200	2	S4(4)	S4(4)
2	23040	85	26:(3 × A5):2	2^6:(3xA5):2
3	23040	85	26:(3 × A5):2	S4(4).2M3
4	16320	120	L2(16).4	L2(16).4
5	16320	120	L2(16).4	S4(4).2M5
6	14400	136	(A5 × A5):22	(A5xA5):2^2
7	14400	136	(A5 × A5):22	S4(4).2M7
8	1440	1360	S6 × 2	S6x2

Available Brauer tables:

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

Atlas representations:

1 available

Group constructions in GAP:

AtlasGroup( "S4(4).2" ), AtlasStabilizer( "He", "HeG1-p2058B0" ), AtlasSubgroup( "He", 1 ), PrimitiveGroup( 85, 2 ), PrimitiveGroup( 120, 13 ), PrimitiveGroup( 136, 8 ), PrimitiveGroup( 1360, 2 )

Stored class fusions from this table:

He, S₄(4).4, S₈(2)

Stored class fusions to this table:

2⁶:(3 × A₅):2, (A₅ × A₅):2², L₂(16).4, S₄(4), 2⁶:(3 × A₅):2, L₂(16).4, (A₅ × A₅):2², S₆ × 2

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