Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for O₈⁺(2)

Name:

O8+(2)

Group order:

174182400 = 2¹² ⋅ 3⁵ ⋅ 5² ⋅ 7

Number of classes:

53

InfoText value:

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

Duplicates:

O8+(3)M11, O8+(3)M12, O8+(3)M13

Maximal subgroups:

	Order	Index	Structure	Name
1	1451520	120	S6(2)	S6(2)
2	1451520	120	S6(2)	O8+(2)M2
3	1451520	120	S6(2)	O8+(2)M3
4	1290240	135	26:A8	2^6:A8
5	1290240	135	26:A8	O8+(2)M5
6	1290240	135	26:A8	O8+(2)M6
7	181440	960	A9	A9
8	181440	960	A9	O8+(2)M8
9	181440	960	A9	O8+(2)M9
10	155520	1120	(3 × U4(2)):2	(3xU4(2)):2
11	155520	1120	(3 × U4(2)):2	O8+(2)M11
12	155520	1120	(3 × U4(2)):2	O8+(2)M12
13	110592	1575	21+8+:(S3 × S3 × S3)	2^(1+8)_+:(S3xS3xS3)
14	15552	11200	34:23.S4	3^4:2^3.S4(a)
15	14400	12096	(A5 × A5):22	(A5xA5):2^2
16	14400	12096	(A5 × A5):22	O8+(2)M16
17	14400	12096	(A5 × A5):22	O8+(2)M17

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	4096	42525	O8+(2)N2	O8+(2)N2
5	400	435456	(D10 × D10).22	(D10xD10).2^2
7	42	4147200	7:6	7:6

Available Brauer tables:

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

Atlas representations:

13 available

Group constructions in GAP:

AtlasGroup( "O8+(2)" ), AtlasStabilizer( "O8+(3)", "O8p3G1-p28431aB0" ), AtlasStabilizer( "O8+(3)", "O8p3G1-p28431bB0" ), AtlasStabilizer( "O8+(3)", "O8p3G1-p28431cB0" ), AtlasStabilizer( "O8+(3)", "O8p3G1-p28431dB0" ), AtlasSubgroup( "O8+(3)", 10 ), AtlasSubgroup( "O8+(3)", 11 ), AtlasSubgroup( "O8+(3)", 12 ), AtlasSubgroup( "O8+(3)", 13 ), POmega( 1, 8, 2 ), PrimitiveGroup( 120, 16 ), PrimitiveGroup( 135, 2 ), PrimitiveGroup( 960, 7 ), PrimitiveGroup( 1120, 1 ), PrimitiveGroup( 1575, 1 )

Stored class fusions from this table:

2⁸:O₈⁺(2), O₈⁺(2).2, O₈⁺(2).3, O₈⁺(3)

Stored class fusions to this table:

2.O₈⁺(2), 2².O₈⁺(2), 2⁶:A₈, 2⁸:O₈⁺(2), 2⁽¹⁺⁸⁾⁺.O₈⁺(2), 2¹⁺⁸₊:(S₃ × S₃ × S₃), 2³⁺³⁺³.L₃(2), 3⁴:2³.S₄, 7:6, (3 × 3³:S₃):2, (3 × 3⁽¹⁺²⁾⁺:2A₄).2, (3 × U₄(2)):2, (A₅ × A₅):2², (A₅ × D₁₀).2, (D₁₀ × A₅).2, (D₁₀ × D₁₀).2², A₉, NRS(O₈⁺(2), 2³⁺³⁺³_a), NRS(O₈⁺(2), 2³⁺³⁺³_b), S₆(2), S₆(2), 2⁶:A₈, 2⁶:A₈, A₉, A₉, (3 × U₄(2)):2, (3 × U₄(2)):2, (A₅ × A₅):2², (A₅ × A₅):2², O₈⁺(2)N2, O₈⁺(2)N5C, S₆(2)

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