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Cayley diagramAliases
Subgroups
940 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 16 points:
(3,4);(1,2)(3,4);(6,7)(11,15)(13,16);(5,6,8,7)(9,10,12,14)(11,13,15,16);(5,7,8,6)(9,11)(10,13)(12,15)(14,16)
Conjugacy classes & character table
56 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #72227934, #72227935, #72227938, … |
| Frattini subgroup of | #93115, #93120, #93124, … |
| Fitting subgroup of | A4×#124, #11711021, #11711505, … |
| maximal subgroup of | #8305, #8334, #8544, … |
| maximal normal subgroup of | #8305, #8334, #8544, … |
| maximal quotient of | C22×#382, C22×#388, C22×#390, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 2168);
Finite Group Databasebeta