Character Table info for McL
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Name:
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McL
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Group order:
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898128000 = 27 ⋅ 36 ⋅ 53 ⋅ 7 ⋅ 11
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Number of classes:
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24
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InfoText value:
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origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]
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Maximal subgroups:
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|
Order |
Index |
Structure |
Name |
1 |
3265920 |
275 |
U4(3) |
U4(3) |
2 |
443520 |
2025 |
M22 |
M22 |
3 |
443520 |
2025 |
M22 |
McLM3 |
4 |
126000 |
7128 |
U3(5) |
U3(5) |
5 |
58320 |
15400 |
31+4+:2S5 |
3^(1+4):2S5 |
6 |
58320 |
15400 |
34:M10 |
3^4:m10 |
7 |
40320 |
22275 |
L3(4).22 |
L3(4).2_2 |
8 |
40320 |
22275 |
2.A8 |
2.A8 |
9 |
40320 |
22275 |
24:A7 |
2^4:a7 |
10 |
40320 |
22275 |
24:A7 |
McLM10 |
11 |
7920 |
113400 |
M11 |
M11 |
12 |
3000 |
299376 |
51+2+:3:8 |
5^(1+2):3:8 |
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Stored Sylow p normalizers:
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p |
Order |
Index |
Structure |
Name |
2 |
128 |
7016625 |
McLN2 |
McLN2 |
3 |
5832 |
154000 |
34:(32:Q8) |
3^4:(3^2:Q8) |
5 |
3000 |
299376 |
51+2+:3:8 |
5^(1+2):3:8 |
7 |
42 |
21384000 |
2 × 7:3 |
2x7:3 |
11 |
55 |
16329600 |
11:5 |
11:5 |
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Available Brauer tables:
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Atlas representations:
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46 available
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Group constructions in GAP:
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AtlasGroup( "McL" )
,
AtlasStabilizer( "Co2", "Co2G1-p47104B0" )
,
AtlasSubgroup( "Co2", 3 )
,
AtlasSubgroup( "McL.2", 1 )
,
PrimitiveGroup( 275, 1 )
,
PrimitiveGroup( 2025, 34 )
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Stored class fusions from this table:
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Co2,
Co3,
McL.2
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Stored class fusions to this table:
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2(A4 × A4).22,
2.A8,
24:A7,
21+1+2+2:S3,
21+3:L3(2),
22+4.S3,
22+4:(3 × 3):2,
2 × 7:3,
3.McL,
34.32.Q8,
34:(32:Q8),
34:M10,
31+4+:2S5,
31+4+.2S4,
51+2+:3:8,
11:5,
L3(4).22,
M11,
M22,
M22C2A,
M22,
24:A7,
McLN2,
U3(5),
U4(3)