Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C22×C8 |
| direct product | C2×C8×C251⋊C8 |
| unambiguous semidirect product | (C2×C251)⋊C82 |
| derived, Sylow | C251 ⋊ C2×C82 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C8 | D251 |
| commutator, hypocenter | C251 | C2×C82 |
| Frattini | C42 | C22×D251 |
| Fitting | C2×C4×C8×C251 | C2 |
| socle, prime radical | C23×C251 | C42 |
| cosocle | C42×C251 | C23 |
| LCS | G ▷ C251 | |
| UCS | C1 ◁ C2×C4×C8 | |
280 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, 2783);