Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #95×C509 ⋊ C2 |
| Sylow | C509 ⋊ #392 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D509 |
| commutator, socle, cosocle | C23×C509 | C23 |
| Fitting | #95×C509 | C2 |
| hypercenter | #95 | D509 |
| hypocenter | C509 | #392 |
| LCS | G ▷ C23×C509 ▷ C509 | |
| UCS | C1 ◁ C23 ◁ #95 | |
322 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16288 |
Polycyclic presentation:
2^6,509|b^a=bd,c^a=ce,g^a=g^508,c^b=cf,g^b=g^508,g^c=g^5085102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 459);