Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#30654211 |
| Fitting | C22×D4×C509 ⋊ C2 |
| Sylow | C509 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D509 |
| commutator, cosocle | C22×C509 | C24 |
| Frattini | C22 | C23×D509 |
| Fitting | C22×D4×C509 | C2 |
| socle | C23×C509 | C23 |
| hypercenter | C22×D4 | D509 |
| hypocenter | C509 | C2×#127 |
| LCS | G ▷ C22×C509 ▷ C509 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16288 |
5108 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 1088);