← Prev (#580) Next (#582) →
Cayley diagramAliases
Subgroups
425 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);(7,8,10,12)(9,13,14,11);(7,9,10,14)(8,11,12,13)
Conjugacy classes & character table
40 conjugacy classes — view the full character table.
Relationships
| derived subgroup of | #144363, #144372, #144373, … |
| Frattini subgroup of | #7308, #7315, #7317, … |
| Fitting subgroup of | C23×SL(2,𝔽3), C2×Q8×A4, C2×C22⋊SL(2,𝔽3), … |
| maximal subgroup of | #1446, #1784, #1787, … |
| maximal normal subgroup of | #1446, #1784, #1787, … |
| maximal quotient of | C23×C4⋊C4, C22×C4×Q8, C22×C22⋊Q8, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(64, 262);
Finite Group Databasebeta