Finite Group DatabasebetaFinite Group Databasebeta| order | 23264 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×Dic727 |
| Sylow | C727 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D727 |
| commutator | C2×C727 | C22×C4 |
| Fitting, prime radical | C2×D4×C727 | C2 |
| socle, cosocle | C22×C727 | C23 |
| hypercenter | C2×D4 | D727 |
| hypocenter | C727 | C4×D4 |
| LCS | G ▷ C2×C727 ▷ C727 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11632 |
3650 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23264, 109);