Finite Group DatabasebetaFinite Group Databasebeta| order | 7264 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×C227⋊C8 |
| derived, Sylow | C227 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D227 |
| commutator, hypocenter | C227 | C4×C8 |
| Frattini | C2×C4 | C2×D227 |
| Fitting | C42×C227 | C2 |
| socle | C22×C227 | C2×C4 |
| LCS | G ▷ C227 | |
| UCS | C1 ◁ C42 | |
44 conjugacy classes of subgroups.
1840 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×C227⋊C8, #28408753, #28408754, … |
| maximal normal subgroup of | C8×C227⋊C8, #28408753, #28408754, … |
| maximal quotient of | C8×C227⋊C8, #28408753, #28408787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7264, 55);