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Cayley diagramAliases
Subgroups
1264 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)
Conjugacy classes & character table
56 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #72227678, #72227681, #72227686, … |
| Frattini subgroup of | #93103, #93104, #93105, … |
| Fitting subgroup of | A4×#121, #11711019, #11713209, … |
| maximal subgroup of | #8307, #8328, #8542, … |
| maximal normal subgroup of | #8307, #8328, #8542, … |
| maximal quotient of | C22×#380, C22×#386, C22×#388, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 2164);
Finite Group Databasebeta