Finite Group DatabasebetaFinite Group Databasebeta| order | 33286 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊(D89⋊C11) |
| unambiguous semidirect product | (C89⋊C11)⋊D17 |
| unambiguous semidirect product | D1513⋊C11 |
| Fitting, socle, derived, Hall | C17×C89 ⋊ C2×C11 |
| Hall | C17×C89⋊C11 ⋊ C2 |
| Hall | D1513 ⋊ C11 |
| Hall | C89⋊C11 ⋊ D17 |
| Sylow | C89 ⋊ C11×D17 |
| Sylow | C17 ⋊ D89⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C17×C89 | C2×C11 |
| LCS | G ▷ C17×C89 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1513 |
Polycyclic presentation:
2,11,17,89|c^a=c^16,d^a=d^88,d^b=d^64178 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33286, 12);