Finite Group DatabasebetaFinite Group Databasebeta| order | 19350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | (C5⋊D5)⋊(C43⋊C9) |
| derived, Hall | C52×C43 ⋊ C2×C9 |
| Hall | C52⋊(C43⋊C9) ⋊ C2 |
| Hall | C43×C5⋊D5 ⋊ C9 |
| Hall | C5⋊D5 ⋊ C43⋊C9 |
| Sylow | C43 ⋊ (C5⋊D5)⋊C9 |
| Sylow | C52 ⋊ C2×C43⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C5⋊D5)⋊(C43⋊C3) |
| commutator, hypocenter | C52×C43 | C2×C9 |
| Fitting, socle, cosocle | C3×C52×C43 | C2×C3 |
| prime radical | C3×C43×C5⋊D5 | C3 |
| LCS | G ▷ C52×C43 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1935 |
Polycyclic presentation:
2,3,5^2,43,3|b^3=f,c^a=c^4,d^a=d^4,c^b=cd^3,d^b=c^4d^3,e^b=e^36618 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19350, 43);