Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for L3(2)

Name:
L3(2)
Group order:
168 = 23 ⋅ 3 ⋅ 7
Number of classes:
6
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,7]
Duplicates:
L3(4)M7, L3(4)M8
Maximal subgroups:
  Order Index Structure Name
1 24 7 S4 Symm(4)
2 24 7 S4 Symm(4)
3 21 8 7:3 7:3
Stored Sylow p normalizers:
p Order Index Structure Name
2 8 21 D8 D8
3 6 28 S3 S3
7 21 8 7:3 7:3
Available Brauer tables:
p  
2 dec. matrix (PDF)
3 dec. matrix (PDF)
7 dec. matrix (PDF)
Atlas representations:
31 available
Group constructions in GAP:
AtlasGroup( "L3(2)" ), AtlasStabilizer( "L3(4)", "L34G1-p120aB0" ), AtlasStabilizer( "L3(4)", "L34G1-p120bB0" ), AtlasStabilizer( "L3(4)", "L34G1-p120cB0" ), AtlasStabilizer( "L3(8)", "L38G1-p98112B0" ), AtlasStabilizer( "U3(3)", "U33G1-p36B0" ), AtlasSubgroup( "A7", 2 ), AtlasSubgroup( "L3(2).2", 1 ), AtlasSubgroup( "L3(4)", 6 ), AtlasSubgroup( "L3(4)", 7 ), AtlasSubgroup( "L3(4)", 8 ), AtlasSubgroup( "L3(8)", 5 ), AtlasSubgroup( "M24", 9 ), AtlasSubgroup( "U3(3)", 2 ), POmega( 3, 7 ), PSL( 2, 7 ), PSL( 3, 2 ), PSU( 2, 7 ), PSp( 2, 7 ), PerfectGroup( 168, 1 ), PrimitiveGroup( 7, 5 ), PrimitiveGroup( 8, 4 ), SmallGroup( 168, 42 ), TransitiveGroup( 7, 5 ), TransitiveGroup( 8, 37 ), TransitiveGroup( 14, 10 ), TransitiveGroup( 21, 14 ), TransitiveGroup( 24, 284 ), TransitiveGroup( 28, 32 )
Stored class fusions from this table:
23:L3(2), A7, L3(2).2, L3(4), L3(8), L3(11), M24, O8−(2), U3(3)
Stored class fusions to this table:
2.23+8:L3(2), 2.43.L3(2), 2.L3(2), 21+6+.L3(2), 23+8:L3(2), 23.L3(2), 23:L3(2), 26:L3(2), 21+3:L3(2), 23+1+3.L3(2), 2 × 23:L3(2), 3 × 2.L3(2), 2.(2 × 23:L3(2)), 43.L3(2), 43:(L3(2) × 2), 43:L3(2), 7:3, D8, M23C2A, M24C2A, P11/G1/L1/V1/ext2, P11/G1/L1/V1/ext3, P11/G1/L1/V1/ext4, P11/G1/L1/V2/ext2, P11/G1/L1/V2/ext4, P11/G1/L1/V3/ext2, P11/G1/L1/V3/ext4, P11/G2/L1/V1/ext2, P11/G2/L1/V1/ext3, P11/G2/L1/V2/ext2, P11/G3/L1/V1/ext2, P11/G3/L1/V1/ext3, P11/G3/L1/V2/ext3, P11/G3/L3/V1/ext2, P11/G3/L3/V2/ext3, P11/G3/L4/V2/ext2, P11/G3/L4/V2/ext3, P11/G3/L4/V3/ext2, P11/G4/L1/V1/ext2, P11/G4/L1/V1/ext3, P12/G1/L2/V1/ext2, P13/G1/L2/V1/ext2, P13/G1/L6/V1/ext2, S3, S4, ons1, S4

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