Finite Group DatabasebetaFinite Group Databasebeta| order | 14528 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×C227⋊C32 |
| unambiguous semidirect product | (C2×C227)⋊C32 |
| derived, Sylow | C227 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | D227 |
| commutator, hypocenter | C227 | C2×C32 |
| Frattini | C16 | C2×D227 |
| Fitting | C2×C16×C227 | C2 |
| socle, prime radical | C22×C227 | C16 |
| cosocle | C16×C227 | C22 |
| LCS | G ▷ C227 | |
| UCS | C1 ◁ C2×C16 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14528 |
3680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×Dic227, C4×C227⋊C32, #44397867, … |
| maximal normal subgroup of | C32×Dic227, C4×C227⋊C32, #44397867, … |
| maximal quotient of | C4×C227⋊C32, #44397872, #44397930, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14528, 381);