Finite Group DatabasebetaFinite Group Databasebeta| order | 32576 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C509 · Schur multiplier (H2) = C25 |
| direct product | C2×#95×C509 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C509 | C22 |
| commutator | C2 | C2×C42×C509 |
| Frattini, cosocle | C23 | C23×C509 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C509 ◁ G | |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32576 |
20360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32576, 56);