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Cayley diagramC26 #586
Aliases
Subgroups
2825 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 6 generators on 12 points:
(1,2);(3,4);(5,6);(7,8);(9,10);(11,12)
Conjugacy classes & character table
64 conjugacy classes — view the full character table.
Relationships
| center of | C23×#95, C24×C22⋊C4, C24×C4⋊C4, … |
| derived subgroup of | C22⋊(C22⋊A4), #85645, C2×C22⋊(C22⋊A4), … |
| Frattini subgroup of | #94849, #97550, #97551, … |
| Fitting subgroup of | C24×A4, C22×C22⋊A4, C22⋊(C22⋊A4), … |
| socle of | C25×C4, C24×A4, C22×C22⋊A4, … |
| maximal subgroup of | C2×#379, #2846, C23×C22⋊C4, … |
| maximal normal subgroup of | C2×#379, #2846, C23×C22⋊C4, … |
| maximal quotient of | C25×C4, C24×D4, C24×Q8, … |
| outer automorphism group of | #387, #388, #432, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(64, 267);
Finite Group Databasebeta