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Cayley diagramAliases
Subgroups
984 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 16 points:
(3,4);(1,2)(3,4);(6,8)(10,13)(11,15);(9,10)(11,14)(12,13)(15,16);(5,6)(7,8)(9,11,12,15)(10,14,13,16)
Conjugacy classes & character table
56 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #72227720, #72227721, #72227725, … |
| Frattini subgroup of | #93101, #93102, #93119, … |
| Fitting subgroup of | A4×#123, #11711502, #11713203, … |
| maximal subgroup of | #8304, #8543, #8548, … |
| maximal normal subgroup of | #8304, #8543, #8548, … |
| maximal quotient of | C22×#381, C22×#385, C22×#386, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 2166);
Finite Group Databasebeta