← Prev (#578) Next (#580) →
Cayley diagramAliases
Subgroups
681 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 5 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 | C2×C4×#95, C22×#336, C22×#376, … |
| derived subgroup of | #102873, #102874, #102875, … |
| Frattini subgroup of | #7032, #7035, #7047, … |
| Fitting subgroup of | C22×C4×A4, C4×C22⋊A4, C4×C24⋊C5, … |
| socle of | C24×#585, C4×#15258, #72258449, … |
| maximal subgroup of | C22⋊#95, #1779, C22×#95, … |
| maximal normal subgroup of | C22⋊#95, #1779, C22×#95, … |
| maximal quotient of | C23×C42, C23×C22⋊C4, C23×C4⋊C4, … |
| outer automorphism group of | #2169, C4×SD32, #2183, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(64, 260);
Finite Group Databasebeta