Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C16×#14523266 |
| Fitting | C16×C509 ⋊ C4 |
| derived, Sylow | C509 ⋊ C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C16 | #14523266 |
| commutator, hypocenter | C509 | C4×C16 |
| Frattini | C8 | C2×#14523266 |
| Fitting | C16×C509 | C4 |
| socle | C2×C509 | C4×C8 |
| prime radical | C2×D509 | C2×C8 |
| cosocle | C8×D509 | C22 |
| LCS | G ▷ C509 | |
| UCS | C1 ◁ C16 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8144 |
2096 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 1433);