Finite Group DatabasebetaFinite Group Databasebeta| order | 18180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(Dic101⋊C5) |
| unambiguous semidirect product | Dic909⋊C5 |
| derived, Hall | C9×C101 ⋊ C4×C5 |
| Hall | C9×C101⋊C5 ⋊ C4 |
| Hall | Dic909 ⋊ C5 |
| Hall | C101⋊C5 ⋊ Dic9 |
| Sylow | C101 ⋊ C5×Dic9 |
| Sylow | C9 ⋊ Dic101⋊C5 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3636 |
Polycyclic presentation:
2,3,5,101,2,3|a^2=e,b^3=f^2,b^a=b^2f,d^a=d^100,f^a=f^2,d^c=d^95240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18180, 12);