Finite Group DatabasebetaFinite Group Databasebeta| order | 23264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C42×C727 ⋊ C2 |
| Sylow | C727 ⋊ #127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D727 |
| commutator, socle, cosocle | C22×C727 | C23 |
| Fitting | C42×C727 | C2 |
| hypercenter | C42 | D727 |
| hypocenter | C727 | #127 |
| LCS | G ▷ C22×C727 ▷ C727 | |
| UCS | C1 ◁ C22 ◁ C42 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11632 |
Polycyclic presentation:
2^5,727|b^2=d,c^2=e,b^a=bd,c^a=ce,f^a=f^7265822 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23264, 143);