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Cayley diagramAliases
Subgroups
445 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 12 points:
(1,2);(3,4);(5,6)(7,10)(8,9)(11,12);(6,9)(10,12);(5,7,8,11)(6,10,9,12)
Conjugacy classes & character table
40 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #144362, #144365, #144369, … |
| Frattini subgroup of | #7305, #7306, #7309, … |
| Fitting subgroup of | C22×#41⋊C3, A4×#41, #5948, … |
| maximal subgroup of | #1780, #1782, #1785, … |
| maximal normal subgroup of | #1780, #1782, #1785, … |
| maximal quotient of | C22×#117, C22×C4×D4, C22×C4×Q8, … |
| automorphism group of | C2×C3×C16, C3×M32 |
| outer automorphism group of | C2×C3×C16, #1367, #1370, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(64, 263);
Finite Group Databasebeta