Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | #525×D251 |
| Fitting | #525×C251 ⋊ C2 |
| Sylow | C251 ⋊ C2×#525 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D251 |
| commutator, socle, cosocle | C22×C251 | C25 |
| Frattini | C22 | C24×D251 |
| Fitting | #525×C251 | C2 |
| hypercenter | #525 | D251 |
| hypocenter | C251 | C2×#525 |
| LCS | G ▷ C22×C251 ▷ C251 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
1880 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4016 |
3556 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 17746);