Finite Group DatabasebetaFinite Group Databasebeta| order | 18810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C11⋊(#4294⋊C2)) |
| unambiguous semidirect product | C11⋊(C5⋊(#4294⋊C2)) |
| unambiguous semidirect product | #4294⋊D55 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊(C11⋊(D19⋊C3)) |
| commutator, hypocenter | C5×C11×C19 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C11×C19 | C2×C3 |
| prime radical | C3×D1045 | C3 |
| LCS | G ▷ C5×C11×C19 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9405 |
Polycyclic presentation:
2,3,5,11,19,3|b^3=f,c^a=c^4,d^a=d^10,e^a=e^18,e^b=e^7756 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18810, 33);