Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C24×C251⋊C8 |
| derived, Sylow | C251 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | D251 |
| commutator, hypocenter | C251 | C24×C8 |
| Frattini | C4 | C24×D251 |
| Fitting | C24×C4×C251 | C2 |
| socle, prime radical | C25×C251 | C4 |
| cosocle | C4×C251 | C25 |
| LCS | G ▷ C251 | |
| UCS | C1 ◁ C24×C4 | |
1976 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32128 |
8128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 19209);