Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for S12

Name:
A12.2
Group order:
479001600 = 210 ⋅ 35 ⋅ 52 ⋅ 7 ⋅ 11
Number of classes:
77
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11], constructions: Aut(A12)
Maximal subgroups:
  Order Index Structure Name
1 239500800 2 A12 A12
2 39916800 12 S11 A11.2
3 7257600 66 S10 × 2 S10x2
4 2177280 220 S9 × S3 S9xS3
5 1036800 462 (S6 × S6):2 (S6xS6):2
6 967680 495 S8 × S4 S8xS4
7 604800 792 S7 × S5 S7xS5
8 82944 5775 S4 ≀ S3 S4wrS3
9 46080 10395 26:S6 2^6:S6
10 31104 15400 S3 ≀ S4 S3wrS4
11 1320 362880 L2(11).2 L2(11).2
Stored Sylow p normalizers:
p Order Index Structure Name
7 5040 95040 7:6 × A5.2 7:6xA5.2
Available Brauer tables:
p  
2 dec. matrix (PDF)
3 dec. matrix (PDF)
5 dec. matrix (PDF)
7 dec. matrix (PDF)
11 dec. matrix (PDF)
Atlas representations:
10 available
Group constructions in GAP:
AtlasGroup( "A12.2" ), AtlasStabilizer( "A13.2", "S13G1-p13B0" ), AtlasStabilizer( "A14", "A14G1-p91B0" ), AtlasStabilizer( "HN.2", "HNd2G1-p1140000B0" ), AtlasSubgroup( "Fi23", 9 ), AtlasSubgroup( "HN.2", 2 ), AutomorphismGroup( AlternatingGroup( 12 ) ), PrimitiveGroup( 12, 6 ), PrimitiveGroup( 66, 5 ), PrimitiveGroup( 220, 3 ), PrimitiveGroup( 462, 2 ), PrimitiveGroup( 495, 8 ), PrimitiveGroup( 792, 2 ), SymmetricGroup( 12 ), TransitiveGroup( 12, 301 ), TransitiveGroup( 24, 24748 )
Stored class fusions from this table:
A13.2, A14, Fi23, HN.2
Stored class fusions to this table:
2.A12.2, 26:S6, 7:6 × A5.2, (A5 × A12):2, (S6 × S6):2, S11, A12, Isoclinic(2.A12.2), L2(11).2, S3 ≀ S4, S4 ≀ S3, S7 × S5, S8 × S4, S9 × S3, S10 × 2

File created automatically by GAP on 13-Mar-2024.