Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | #126×D509 |
| Fitting | #126×C509 ⋊ C2 |
| Sylow | C509 ⋊ C2×#126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D509 |
| commutator, socle, cosocle | C22×C509 | C24 |
| Fitting | #126×C509 | C2 |
| prime radical | C23×D509 | C22 |
| hypercenter | #126 | D509 |
| hypocenter | C509 | C2×#126 |
| LCS | G ▷ C22×C509 ▷ C509 | |
| UCS | C1 ◁ C22 ◁ #126 | |
246 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8144 |
3584 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 1072);