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Cayley diagramAliases
Subgroups
449 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 10 points:
(1,2);(3,4)(5,9)(6,7)(8,10);(4,7)(8,9);(3,4)(5,8)(6,7)(9,10);(3,5)(4,8)(6,10)(7,9)
Conjugacy classes & character table
34 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #32898⋊C3, #32899⋊C3, #32900⋊C3, … |
| Frattini subgroup of | #72232878, #72233665, #72258948, … |
| Fitting subgroup of | C2×#994, C2×#997, #73152, … |
| maximal subgroup of | #1790, #1792, #1795, … |
| maximal normal subgroup of | #1790, #1792, #1795, … |
| maximal quotient of | C2×#518, C2×#520, C4×H(5,𝔽2), … |
| outer automorphism group of | #1510, #1511, #1514, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(64, 264);
Finite Group Databasebeta