Finite Group DatabasebetaFinite Group Databasebeta| order | 23264 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×Dic727 |
| derived, Sylow | C727 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D727 |
| commutator, hypocenter | C727 | C4×C8 |
| Frattini | C2×C4 | C2×D727 |
| Fitting | C2×C8×C727 | C2 |
| socle, prime radical | C22×C727 | C2×C4 |
| cosocle | C2×C4×C727 | C22 |
| LCS | G ▷ C727 | |
| UCS | C1 ◁ C2×C8 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23264 |
5840 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23264, 54);