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Cayley diagramAliases
Subgroups
681 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 generators on 10 points:
(3,4);(5,6);(1,2)(3,4)(5,6);(8,10);(7,8)(9,10)
Conjugacy classes & character table
40 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #144364, #144366, #144367, … |
| Frattini subgroup of | #7304, #7307, #7310, … |
| Fitting subgroup of | C2×D4×A4, #73143, #73144, … |
| maximal subgroup of | #1438, #1781, #1783, … |
| maximal normal subgroup of | #1438, #1781, #1783, … |
| maximal quotient of | C23×C22⋊C4, C23×C4⋊C4, C22×C4×D4, … |
| automorphism group of | #102, #103, C3×#104 |
| outer automorphism group of | #408, #424, C8×D4, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(64, 261);
Finite Group Databasebeta