Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C24×D1004 |
| Fitting | C24×C4×C251 ⋊ C2 |
| Sylow | C251 ⋊ C24×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D251 |
| commutator, cosocle | C2×C251 | C26 |
| Frattini | C2 | C25×D251 |
| Fitting | C24×C4×C251 | C2 |
| socle | C25×C251 | C22 |
| hypercenter | C24×C4 | D251 |
| hypocenter | C251 | C24×D4 |
| LCS | G ▷ C2×C251 ▷ C251 | |
| UCS | C1 ◁ C25 ◁ C24×C4 | |
10552 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16064 |
8080 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 19303);