Finite Group DatabasebetaFinite Group Databasebeta| order | 32896 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C4×#22551498 |
| derived, Sylow | C257 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C16 | D257 |
| commutator, hypocenter | C257 | C4×C32 |
| Frattini | C2×C16 | C2×D257 |
| Fitting | C4×C16×C257 | C2 |
| socle, prime radical | C22×C257 | C2×C16 |
| cosocle | C2×C16×C257 | C22 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C4×C16 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32896 |
8320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32896, 2642);