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Cayley diagramAliases
Subgroups
2316 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 14 points:
(3,4);(5,6);(1,2)(3,4)(5,6);(8,10)(11,12,13,14);(7,8)(9,10)(11,12)(13,14)
Conjugacy classes & character table
80 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #72227598, #72227689, #72227748, … |
| Frattini subgroup of | #93464, #93470, #93488, … |
| Fitting subgroup of | C2×A4×C22⋊C4, #11711009, #11711294, … |
| maximal subgroup of | #7555, #8298, #10725, … |
| maximal normal subgroup of | #7555, #8298, #10725, … |
| maximal quotient of | C23×#95, C22×C4×C22⋊C4, C22×#379, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(128, 2151);
Finite Group Databasebeta