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Cayley diagramAliases
Subgroups
2272 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 12 points:
(3,4);(1,2)(3,4);(6,8)(10,12);(9,10)(11,12);(5,6)(7,8)(9,10)(11,12)
Conjugacy classes & character table
56 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #72227479, #72227568, #72227707, … |
| Frattini subgroup of | #93099, #93100, #93144, … |
| Fitting subgroup of | C22×#120⋊C3, A4×#120, #85645, … |
| maximal subgroup of | #8541, #8547, #10965, … |
| maximal normal subgroup of | #8541, #8547, #10965, … |
| maximal quotient of | C22×#379, C22×#385, C22×#386, … |
| automorphism group of | C4×D4, #121, C22⋊Q8, … |
| outer automorphism group of | #385, #386, #394, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 2163);
Finite Group Databasebeta