Finite Group DatabasebetaFinite Group Databasebeta| order | 32946 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C17 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C172×C19 ⋊ C2×C3 |
| derived | C17×C19 ⋊ C2×C3×C17 |
| Hall | C172×C19⋊C3 ⋊ C2 |
| Hall | C17×D323 ⋊ C3 |
| Sylow | C172 ⋊ D19⋊C3 |
| Hall | C19⋊C3 ⋊ C17×D17 |
| Sylow | C19 ⋊ C3×C17×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C17⋊(D19⋊C3) |
| commutator, cosocle, hypocenter | C17×C19 | C2×C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C172×C19 | C2×C3 |
| LCS | G ▷ C17×C19 | |
| UCS | C1 ◁ C17 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 646 |
1377 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32946, 23);