Finite Group DatabasebetaFinite Group Databasebeta| order | 18180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C9⋊#87938 |
| unambiguous semidirect product | C9⋊(C5×#87938) |
| Fitting, Hall | C5×C9×C101 ⋊ C4 |
| derived, Hall | C9×C101 ⋊ C4×C5 |
| Hall | C5×C101 ⋊ Dic9 |
| Sylow | C101 ⋊ C5×Dic9 |
| Hall | C5×C9 ⋊ #87938 |
| Sylow | C9 ⋊ C5×#87938 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4545 |
1185 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18180, 29);