Finite Group DatabasebetaFinite Group Databasebeta| order | 34485 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×(C112⋊C3)⋊C5 |
| unambiguous semidirect product | (C112⋊C3)⋊(C5×C19) |
| unambiguous semidirect product | #10597243⋊(C3×C19) |
| unambiguous semidirect product | (C19×C112⋊C3)⋊C5 |
| Fitting, socle, Hall | C112×C19 ⋊ C3×C5 |
| derived, Sylow | C112 ⋊ C3×C5×C19 |
| Hall | C19×#10597243 ⋊ C3 |
| Hall | C19×C112⋊C3 ⋊ C5 |
| Hall | #10597243 ⋊ C3×C19 |
| Hall | C112⋊C3 ⋊ C5×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | (C112⋊C3)⋊C5 |
| commutator, cosocle, hypocenter | C112 | C3×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C112×C19 | C3×C5 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C19 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 627 |
437 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34485, 6);