Finite Group DatabasebetaFinite Group Databasebeta| order | 18270 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×C9×D29 |
| Fitting, Hall | C5×C7×C9×C29 ⋊ C2 |
| derived, Sylow | C29 ⋊ C2×C5×C7×C9 |
| Hall | C7×C9×C29 ⋊ C2×C5 |
| Hall | C5×C9×C29 ⋊ C2×C7 |
| Hall | C5×C7×C29 ⋊ C2×C9 |
| Hall | C9×C29 ⋊ C2×C5×C7 |
| Hall | C7×C29 ⋊ C2×C5×C9 |
| Hall | C5×C29 ⋊ C2×C7×C9 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9135 |
5040 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×C9×#1181, C5×C9×C7⋊#1181, C5×C9×D7×D29, … |
| maximal normal subgroup of | C5×C7×C9×#1181, C5×C9×C7⋊#1181, C5×C9×D7×D29, … |
| maximal quotient of | C5×C7×C9×Dic29, C2×C5×C7×C9×D29 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18270, 4);