Finite Group DatabasebetaFinite Group Databasebeta| order | 32288 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×C22⋊D1009 |
| Fitting | C24×C1009 ⋊ C2 |
| Sylow | C1009 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D1009 |
| commutator, cosocle | C2×C1009 | C24 |
| Frattini | C2 | C23×D1009 |
| Fitting | C24×C1009 | C2 |
| socle | C23×C1009 | C22 |
| hypercenter | C24 | D1009 |
| hypocenter | C1009 | C22×D4 |
| LCS | G ▷ C2×C1009 ▷ C1009 | |
| UCS | C1 ◁ C23 ◁ C24 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16144 |
8084 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32288, 183);