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Cayley diagramAliases
Subgroups
920 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)(9,10,12,14)(11,15,16,13);(9,11,12,16)(10,13,14,15);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)
Conjugacy classes & character table
56 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #72268090, #72268118, #72268228, … |
| Frattini subgroup of | #93106, #93107, #93108, … |
| Fitting subgroup of | A4×C22⋊Q8, #11711020, #11713210, … |
| maximal subgroup of | #8308, #8329, #8550, … |
| maximal normal subgroup of | #8308, #8329, #8550, … |
| maximal quotient of | C22×#380, C22×#385, C22×#387, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 2165);
Finite Group Databasebeta