Finite Group DatabasebetaFinite Group Databasebeta| order | 7264 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×Q8×D227 |
| Fitting | C2×Q8×C227 ⋊ C2 |
| Sylow | C227 ⋊ C22×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D227 |
| commutator | C2×C227 | C24 |
| Frattini | C2 | C23×D227 |
| Fitting | C2×Q8×C227 | C2 |
| socle | C22×C227 | C23 |
| hypercenter | C2×Q8 | D227 |
| hypocenter | C227 | C22×Q8 |
| LCS | G ▷ C2×C227 ▷ C227 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
156 conjugacy classes of subgroups.
1150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #101×D227, #103×D227, #28409039, … |
| maximal normal subgroup of | #101×D227, #103×D227, #28409039, … |
| maximal quotient of | C2×C4⋊C4×D227, C4×Q8×D227, C2×#20300253, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7264, 185);