Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C509 · Schur multiplier (H2) = C22×C4 |
| direct product | #382×C509 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C509 | C23 |
| commutator | C22 | C22×C4×C509 |
| Frattini, cosocle | C23 | C23×C509 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C509 ◁ G | |
154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32576 |
14252 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 63);