Finite Group DatabasebetaFinite Group Databasebeta| order | 32946 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C172 · Schur multiplier (H2) = C17 |
| direct product | C172×D19⋊C3 |
| unambiguous semidirect product | D19⋊(C3×C172) |
| unambiguous semidirect product | (C19⋊C3)⋊(C2×C172) |
| unambiguous semidirect product | (C17×D19)⋊(C3×C17) |
| Fitting, socle, Hall | C172×C19 ⋊ C2×C3 |
| derived, Sylow | C19 ⋊ C2×C3×C172 |
| Hall | C172×C19⋊C3 ⋊ C2 |
| Hall | C172×D19 ⋊ C3 |
| Hall | C19⋊C3 ⋊ C2×C172 |
| Hall | D19 ⋊ C3×C172 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C172 | D19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C2×C3×C172 |
| Frattini | C1 | G |
| Fitting, socle | C172×C19 | C2×C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C172 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5491 |
2601 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32946, 22);