Finite Group DatabasebetaFinite Group Databasebeta| order | 32946 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C17 |
| unambiguous semidirect product | D19⋊(C172⋊C3) |
| Fitting, socle, derived, Hall | C172×C19 ⋊ C2×C3 |
| Hall | C19⋊(C172⋊C3) ⋊ C2 |
| Hall | C172×D19 ⋊ C3 |
| Sylow | C172 ⋊ D19⋊C3 |
| Hall | D19 ⋊ C172⋊C3 |
| Sylow | C19 ⋊ C2×C172⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C172×C19 | C2×C3 |
| LCS | G ▷ C172×C19 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 969 |
Polycyclic presentation:
2,3,17^2,19|e^a=e^18,c^b=c^12d^6,d^b=c^5d^4,e^b=e^71065 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32946, 14);