Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for O₇(3)

Name:

O7(3)

Group order:

4585351680 = 2⁹ ⋅ 3⁹ ⋅ 5 ⋅ 7 ⋅ 13

Number of classes:

58

InfoText value:

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

Duplicates:

Fi22M3, O8+(3)M2, O8+(3)M3, O8+(3)M4, O8+(3)M5, O8+(3)M6

Maximal subgroups:

	Order	Index	Structure	Name
1	13063680	351	2.U4(3).22	2.U4(3).2_2
2	12597120	364	35:U4(2):2	3^5:U4(2):2
3	12130560	378	L4(3).22	L4(3).2_2
4	4245696	1080	G2(3)	G2(3)
5	4245696	1080	G2(3)	O7(3)M5
6	4094064	1120	33+3:L3(3)	3^(3+3):L3(3)
7	1451520	3159	S6(2)	S6(2)
8	1451520	3159	S6(2)	O7(3)M8
9	1259712	3640	31+6+:(2A4 × A4).2	O7(3)N3A
10	362880	12636	S9	A9.2
11	362880	12636	S9	O7(3)M11
12	207360	22113	(22 × U4(2)):2	(2^2xU4(2)):2
13	161280	28431	26:A7	2^6:A7
14	17280	265356	S6 × S4	S6xS4
15	13824	331695	(A4 × 2(A4 × A4).2).2	(A4x2(A4xA4).2).2

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	512	8955765	S6(2)N2	S6(2)N2
3	78732	58240	Fi22N3	Fi22N3
5	480	9552816	5:4 × S4	5:4xS4
7	84	54587520	2 × 7:6	2x7:6
13	78	58786560	13:6	13:6

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:

28 available

Group constructions in GAP:

AtlasGroup( "O7(3)" ), AtlasStabilizer( "Fi22", "F22G1-p14080aB0" ), AtlasStabilizer( "Fi22", "F22G1-p14080bB0" ), AtlasStabilizer( "O8+(3)", "O8p3G1-p1080aB0" ), AtlasStabilizer( "O8+(3)", "O8p3G1-p1080bB0" ), AtlasStabilizer( "O8+(3)", "O8p3G1-p1080cB0" ), AtlasStabilizer( "O8+(3)", "O8p3G1-p1080dB0" ), AtlasStabilizer( "O8+(3)", "O8p3G1-p1080eB0" ), AtlasStabilizer( "O8+(3)", "O8p3G1-p1080fB0" ), AtlasSubgroup( "Fi22", 2 ), AtlasSubgroup( "Fi22", 3 ), AtlasSubgroup( "O7(3).2", 1 ), AtlasSubgroup( "O8+(3)", 1 ), AtlasSubgroup( "O8+(3)", 2 ), POmega( 7, 3 ), PrimitiveGroup( 351, 5 ), PrimitiveGroup( 364, 3 ), PrimitiveGroup( 378, 5 ), PrimitiveGroup( 1080, 4 ), PrimitiveGroup( 1120, 4 ), PrimitiveGroup( 3159, 3 ), PrimitiveGroup( 3640, 2 )

Stored class fusions from this table:

3⁷:O₇(3), Fi₂₂, O₇(3).2, O₈⁺(3)

Stored class fusions to this table:

2.O₇(3), 2.U₄(3).2₂, 2.[2⁶].(2 × S₃), 2⁵:S₆, 2⁶:A₇, 2⁶:S₄b, 2 × 7:6, 3.O₇(3), 3⁵.3³.(2 × S₄), 3⁵.3¹⁺².2.S₄, 3⁵:U₄(2), 3⁵:U₄(2):2, 3⁷.O₇(3), 3⁷:O₇(3), 3³⁺³:L₃(3), 5:4 × S₄, 6.O₇(3), 13:6, (2² × U₄(2)):2, (2⁴:A₄ × A₄).2, (3¹⁺⁶.3)a.2.S₄, (A₄ × 2(A₄ × A₄).2).2, S₉, Fi₂₂N3, G₂(3), L₄(3).2₂, G₂(3), S₆(2), S₉, 3¹⁺⁶₊:(2A₄ × A₄).2, S₆(2), S₆(2)N2, S₆ × D₈, S₆ × S₄

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