Finite Group DatabasebetaFinite Group Databasebeta| order | 32946 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | C3⋊(C17⋊D323) |
| unambiguous semidirect product | C17⋊D969 |
| unambiguous semidirect product | C19⋊(C3⋊(C17⋊D17)) |
| Fitting, socle, derived, Hall | C3×C172×C19 ⋊ C2 |
| Hall | C172×C19 ⋊ D3 |
| Hall | C3×C172 ⋊ D19 |
| Sylow | C172 ⋊ D57 |
| Hall | C3×C19 ⋊ C17⋊D17 |
| Sylow | C19 ⋊ C3⋊(C17⋊D17) |
| Sylow | C3 ⋊ C17⋊D323 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C172×C19 | C2 |
| LCS | G ▷ C3×C172×C19 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16473 |
Polycyclic presentation:
2,3,17^2,19|b^a=b^2,c^a=c^16,d^a=d^16,e^a=e^188238 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32946, 40);