Finite Group DatabasebetaFinite Group Databasebeta| order | 23264 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D4×C727 ⋊ C2 |
| Sylow | C727 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D727 |
| commutator, socle, cosocle | C2×C727 | C24 |
| Fitting | C2×D4×C727 | C2 |
| hypercenter | C2×D4 | D727 |
| hypocenter | C727 | H(5,𝔽2) |
| LCS | G ▷ C2×C727 ▷ C727 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
166 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5816 |
Polycyclic presentation:
2^5,727|b^a=be,d^a=de,c^b=ce,f^d=f^7263647 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23264, 191);