Character Table info for O7(3)
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Name:
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O7(3)
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Group order:
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4585351680 = 29 ⋅ 39 ⋅ 5 ⋅ 7 ⋅ 13
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Number of classes:
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58
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InfoText value:
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origin: ATLAS of finite groups, tests: 1.o.r.
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Duplicates:
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Fi22M3,
O8+(3)M2,
O8+(3)M3,
O8+(3)M4,
O8+(3)M5,
O8+(3)M6
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Maximal subgroups:
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Stored Sylow p normalizers:
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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 |
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Available Brauer tables:
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Atlas representations:
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28 available
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Group constructions in GAP:
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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" )
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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 )
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Stored class fusions from this table:
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37:O7(3),
Fi22,
O7(3).2,
O8+(3)
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Stored class fusions to this table:
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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