Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for ²F₄(2)'.2

Name:

2F4(2)'.2

Group order:

35942400 = 2¹² ⋅ 3³ ⋅ 5² ⋅ 13

Number of classes:

29

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., constructions: Aut(2F4(2)')

Maximal subgroups:

	Order	Index	Structure	Name
1	17971200	2	2F4(2)'	2F4(2)'
2	20480	1755	2.[29]:5:4	2.[2^9]:5:4
3	15600	2304	L2(25).23	L2(25).2_3
4	12288	2925	22.[29]:S3	2^2.[2^9]:S3
5	2400	14976	52:4S4	Fi22N5
6	432	83200	31+2:SD16	3^(1+2):SD16
7	156	230400	13:12	13:12

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	4096	8775	2F4(2)'.2N2	2F4(2)'.2N2
5	2400	14976	52:4S4	Fi22N5

Available Brauer tables:

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

Atlas representations:

21 available

Group constructions in GAP:

AtlasGroup( "2F4(2)'.2" ), AtlasStabilizer( "Fi22.2", "F22d2G1-p3592512B0" ), AtlasStabilizer( "Ru", "RuG1-p4060B0" ), AtlasSubgroup( "Fi22.2", 8 ), AtlasSubgroup( "Ru", 1 ), AutomorphismGroup( AtlasGroup( "2F4(2)'" ) ), PrimitiveGroup( 1755, 2 ), PrimitiveGroup( 2304, 10 ), PrimitiveGroup( 2925, 2 )

Stored class fusions from this table:

F₄(2), Fi₂₂.2, Ru

Stored class fusions to this table:

(2 × ²F₄(2)').2, 2.[2⁹]:5:4, ²F₄(2)', ²F₄(2)'.2N2, 2².[2⁹]:S₃, 3¹⁺²:SD₁₆, 13:12, 5²:4S₄, L₂(25).2₃

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