Finite Group DatabasebetaFinite Group Databasebeta| order | 32512 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C127 · Schur multiplier (H2) = C24×C42 |
| direct product | C127×#13824 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C127 | C24 |
| commutator | C22 | C22×C42×C127 |
| Frattini, cosocle | C24 | C24×C127 |
| prime radical | C23×D4×C127 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C127 ◁ G | |
2390 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16256 |
12700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32512, 6812);