Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C43 |
| direct product | C42×#14523266 |
| Fitting | C42×C509 ⋊ C4 |
| derived, Sylow | C509 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #14523266 |
| commutator, hypocenter | C509 | C43 |
| Frattini | C22 | C22×#14523266 |
| Fitting | C42×C509 | C4 |
| socle | C22×C509 | C22×C4 |
| prime radical, cosocle | C22×D509 | C23 |
| LCS | G ▷ C509 | |
| UCS | C1 ◁ C42 | |
258 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, 1483);