Finite Group DatabasebetaFinite Group Databasebeta| order | 18810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D9405 |
| unambiguous semidirect product | C5⋊D1881 |
| unambiguous semidirect product | C9⋊D1045 |
| unambiguous semidirect product | C11⋊D855 |
| unambiguous semidirect product | C19⋊D495 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C9×C11×C19 | C2 |
| Frattini | C3 | D3135 |
| socle | C3×C5×C11×C19 | D3 |
| LCS | G ▷ C5×C9×C11×C19 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 9405 |
A minimal faithful permutation representation — 2 generators on 44 points:
(1,2,3,4,5,6,7,8,9)(10,11,12,13,14)(15,16,17,18,19,20,21,22,23,24,25)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44);(2,9)(3,8)(4,7)(5,6)(11,14)(12,13)(16,25)(17,24)(18,23)(19,22)(20,21)(27,44)(28,43)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)Polycyclic presentation:
2,3,5,11,19,3|b^3=f^2,b^a=b^2f,c^a=c^4,d^a=d^10,e^a=e^18,f^a=f^24704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D495, D11×D855, D45×D209, … |
| maximal normal subgroup of | D19×D495, D11×D855, D45×D209, … |
| maximal quotient of | Dic9405, C2×D9405, D28215 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18810, 19);