Finite Group DatabasebetaFinite Group Databasebeta| order | 34485 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊((C112⋊C3)⋊C5) |
| unambiguous semidirect product | #10597243⋊(C19⋊C3) |
| unambiguous semidirect product | (C19⋊(C112⋊C3))⋊C5 |
| Fitting, socle, derived, Hall | C112×C19 ⋊ C3×C5 |
| Hall | C19×#10597243 ⋊ C3 |
| Hall | C19⋊(C112⋊C3) ⋊ C5 |
| Hall | #10597243 ⋊ C19⋊C3 |
| Sylow | C112 ⋊ C5×C19⋊C3 |
| Sylow | C19 ⋊ (C112⋊C3)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C19 | C3×C5 |
| LCS | G ▷ C112×C19 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 627 |
Polycyclic presentation:
3,5,11^2,19|c^a=c^7d^2,d^a=c^10d^3,e^a=e^7,c^b=c^3,d^b=d^3197 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34485, 7);