Finite Group DatabasebetaFinite Group Databasebeta| order | 18810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D3135 |
| unambiguous semidirect product | C5⋊(C3⋊D627) |
| unambiguous semidirect product | C11⋊(C3⋊D285) |
| unambiguous semidirect product | C19⋊(C3⋊D165) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C11×C19 | C2 |
| LCS | G ▷ C32×C5×C11×C19 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9405 |
Polycyclic presentation:
2,3^2,5,11,19|b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^10,f^a=f^184704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D3135, D57×D165, D33×D285, … |
| maximal normal subgroup of | D3×D3135, D57×D165, D33×D285, … |
| maximal quotient of | C3⋊Dic3135, C2×C3⋊D3135 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18810, 86);