Finite Group DatabasebetaFinite Group Databasebeta| order | 7264 |
| isoclinism | isoclinic class of D227 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C24×D227 |
| unambiguous semidirect product | C227⋊C25 |
| unambiguous semidirect product | (C2×C227)⋊C24 |
| Fitting, socle | C24×C227 ⋊ C2 |
| derived, Sylow | C227 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D227 |
| commutator, hypocenter | C227 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C24×C227 | C2 |
| LCS | G ▷ C227 | |
| UCS | C1 ◁ C24 | |
748 conjugacy classes of subgroups.
1840 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28408887, C2×C22⋊C4×D227, C22×(C2×D227)⋊C4, … |
| maximal normal subgroup of | #28408887, C2×C22⋊C4×D227, C22×(C2×D227)⋊C4, … |
| maximal quotient of | C23×C4×D227, C24×Dic227, C22×D4×D227, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7264, 195);