Finite Group DatabasebetaFinite Group Databasebeta| order | 34485 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×#10597244 |
| unambiguous semidirect product | C19⋊(C3×#10597244) |
| unambiguous semidirect product | (C19×#10597244)⋊C3 |
| Fitting, socle, derived, Hall | C112×C19 ⋊ C3×C5 |
| Hall | C19×#10597244 ⋊ C3 |
| Hall | C112×C19⋊C3 ⋊ C5 |
| Sylow | C112 ⋊ C5×C19⋊C3 |
| Sylow | C19 ⋊ C3×#10597244 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C19 | C3×C5 |
| LCS | G ▷ C112×C19 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1045 |
261 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34485, 10);