Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #556×D251 |
| Fitting | #556×C251 ⋊ C2 |
| Sylow | C251 ⋊ C2×#556 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D251 |
| commutator, socle, cosocle | C22×C251 | C25 |
| Fitting | #556×C251 | C2 |
| prime radical | C2×D4×D251 | C22 |
| hypercenter | #556 | D251 |
| hypocenter | C251 | C2×#556 |
| LCS | G ▷ C22×C251 ▷ C251 | |
| UCS | C1 ◁ C22 ◁ #556 | |
1112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8032 |
3175 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 18052);