Finite Group DatabasebetaFinite Group Databasebeta| order | 32034 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×D281 |
| unambiguous semidirect product | C281⋊(C2×C19⋊C3) |
| unambiguous semidirect product | (C19×D281)⋊C3 |
| Fitting, socle, derived, Hall | C19×C281 ⋊ C2×C3 |
| Hall | C19⋊C3×C281 ⋊ C2 |
| Hall | C19×D281 ⋊ C3 |
| Sylow | C281 ⋊ C2×C19⋊C3 |
| Sylow | C19 ⋊ C3×D281 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C281 | C2×C3 |
| LCS | G ▷ C19×C281 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5339 |
1278 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32034, 10);