Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for 3.O₇(3)

Name:

3.O7(3)

Group order:

13756055040 = 2⁹ ⋅ 3¹⁰ ⋅ 5 ⋅ 7 ⋅ 13

Number of classes:

126

InfoText value:

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

Duplicates:

3.Fi22M3

Maximal subgroups:

	Order	Index	Structure	Name
1	39191040	351	61.U4(3).22	6_1.U4(3).2_2
2	37791360	364	3.35:U4(2):2	3.3^5:U4(2):2
3	36391680	378	3 × L4(3).22	3xL4(3).2_2
4	12737088	1080	3.G2(3)	3.G2(3)
5	12737088	1080	3.G2(3)	3.O7(3)M5
6	12282192	1120	3.(33+3:L3(3))	3.(3^(3+3):L3(3))
7	4354560	3159	3 × S6(2)	3xS6(2)
8	4354560	3159	3 × S6(2)	3.O7(3)M8
9	3779136	3640	3.31+6+.(2A4 × A4).2	3.O7(3)M9
10	1088640	12636	3 × S9	3xS9
11	1088640	12636	3 × S9	3.O7(3)M11
12	622080	22113	3 × (22 × U4(2)):2	3x(2^2xU4(2)):2
13	483840	28431	26:3A7	2^6:3A7
14	51840	265356	3 × S6 × S4	3xS6xS4
15	41472	331695	3.(A4 × 2(A4 × A4).2).2	3.(A4x2(A4xA4).2).2

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:

2 available

Group constructions in GAP:

AtlasGroup( "3.O7(3)" ), AtlasSubgroup( "3.Fi22", 2 ), AtlasSubgroup( "3.Fi22", 3 )

Stored class fusions from this table:

3.Fi₂₂, 3.O₇(3).2, O₇(3)

Stored class fusions to this table:

2⁶:3A₇, 3.3⁵:U₄(2):2, 3.(3³⁺³:L₃(3)), 3.(A₄ × 2(A₄ × A₄).2).2, 3.G₂(3), 3.G₂(3), 3 × S₆(2), 3.3¹⁺⁶₊.(2A₄ × A₄).2, 3 × S₉, 3 × (2² × U₄(2)):2, 3 × L₄(3).2₂, 3 × S₆(2), 3 × S₆ × S₄, 3 × S₉, 6.O₇(3), 6₁.U₄(3).2₂

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