Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C8 |
| direct product | C16×C251⋊C8 |
| derived, Sylow | C251 ⋊ C8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C16 | D251 |
| commutator, hypocenter | C251 | C8×C16 |
| Frattini | C4×C8 | C2×D251 |
| Fitting | C4×C16×C251 | C2 |
| socle, prime radical | C22×C251 | C4×C8 |
| cosocle | C4×C8×C251 | C22 |
| LCS | G ▷ C251 | |
| UCS | C1 ◁ C4×C16 | |
104 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, 2424);