Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C509 ⋊ C2 |
| Sylow | C509 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D509 |
| commutator, socle | C2×C509 | C22×C8 |
| Fitting | M32×C509 | C2 |
| prime radical | #22550861 | C4 |
| cosocle | C8×C509 | C23 |
| hypercenter | M32 | D509 |
| hypocenter | C509 | #504 |
| LCS | G ▷ C2×C509 ▷ C509 | |
| UCS | C1 ◁ C8 ◁ M32 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16288 |
Polycyclic presentation:
2^6,509|a^2=d,d^2=e,e^2=f,g^a=g^508,c^b=cf,g^c=g^5085120 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 967);