Finite Group DatabasebetaFinite Group Databasebeta| order | 14528 |
| isoclinism | isoclinic class of D227 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C32×D227 |
| Fitting | C32×C227 ⋊ C2 |
| derived, Sylow | C227 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D227 |
| commutator, hypocenter | C227 | C2×C32 |
| Frattini | C16 | C2×D227 |
| Fitting | C32×C227 | C2 |
| socle | C2×C227 | C2×C16 |
| prime radical | C2×D227 | C16 |
| cosocle | C16×C227 | C22 |
| LCS | G ▷ C227 | |
| UCS | C1 ◁ C32 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7264 |
3680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C64×D227, #44397944, C2×C32×D227, … |
| maximal normal subgroup of | C64×D227, #44397944, C2×C32×D227, … |
| maximal quotient of | C32×Dic227, #44397871, #44397929, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14528, 380);