Finite Group DatabasebetaFinite Group Databasebeta| order | 23264 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C727⋊C32 |
| derived, Sylow | C727 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D727 |
| commutator, hypocenter | C727 | C32 |
| Fitting, cosocle | C16×C727 | C2 |
| socle, prime radical | C2×C727 | C16 |
| LCS | G ▷ C727 | |
| UCS | C1 ◁ C16 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23264 |
Polycyclic presentation:
2^5,727|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^7265840 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23264, 52);