Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for S₄(4)

Name:

S4(4)

Group order:

979200 = 2⁸ ⋅ 3² ⋅ 5² ⋅ 17

Number of classes:

27

InfoText value:

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

Maximal subgroups:

	Order	Index	Structure	Name
1	11520	85	26:(3 × A5)	2^6:(3xA5)
2	11520	85	26:(3 × A5)	S4(4)M2
3	8160	120	L2(16).2	L2(16).2
4	8160	120	L2(16).2	S4(4)M4
5	7200	136	(A5 × A5):2	a5wc2
6	7200	136	(A5 × A5):2	S4(4)M6
7	720	1360	S6	A6.2_1

Available Brauer tables:

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

Atlas representations:

26 available

Group constructions in GAP:

AtlasGroup( "S4(4)" ), POmega( 5, 4 ), PSp( 4, 4 ), PerfectGroup( 979200, 1 ), PrimitiveGroup( 85, 1 ), PrimitiveGroup( 120, 12 ), PrimitiveGroup( 136, 7 ), PrimitiveGroup( 1360, 1 )

Stored class fusions from this table:

S₄(4).2, S₄(4).4, U₄(4)

Stored class fusions to this table:

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

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