Finite Group DatabasebetaFinite Group Databasebeta| order | 7264 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C4×Dic454 |
| Sylow | C227 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D227 |
| commutator | C2×C227 | C22×C4 |
| Frattini | C22 | C22×D227 |
| Fitting | C42×C227 | C2 |
| socle | C22×C227 | C23 |
| hypercenter | C42 | D227 |
| hypocenter | C227 | C4×Q8 |
| LCS | G ▷ C2×C227 ▷ C227 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
70 conjugacy classes of subgroups.
1828 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28408762, #28408764, C4×#16813872, … |
| maximal normal subgroup of | #28408762, #28408764, C4×#16813872, … |
| maximal quotient of | C4×C4⋊Dic227, C4×Dic227⋊C4, #28408915, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7264, 112);