Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C4×C251⋊C8 |
| derived, Sylow | C251 ⋊ C22×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C42 | D251 |
| commutator, hypocenter | C251 | C22×C4×C8 |
| Frattini | C2×C4 | C23×D251 |
| Fitting | C22×C42×C251 | C2 |
| socle, prime radical | C24×C251 | C2×C4 |
| cosocle | C2×C4×C251 | C24 |
| LCS | G ▷ C251 | |
| UCS | C1 ◁ C22×C42 | |
760 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, 12911);