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Cayley diagramAliases
Subgroups
812 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)(9,10,13,16)(11,15,12,14);(9,11,13,12)(10,14,16,15);(5,6,7,8)(9,12,13,11)(10,15,16,14)
Conjugacy classes & character table
56 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #72266350, #72266412, #72268194, … |
| Frattini subgroup of | #93114, #93116, #93117, … |
| Fitting subgroup of | A4×C4⋊Q8, #11711024, #11711025, … |
| maximal subgroup of | #8340, #8342, #8551, … |
| maximal normal subgroup of | #8340, #8342, #8551, … |
| maximal quotient of | C22×#384, C22×#389, C22×#391, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 2173);
Finite Group Databasebeta