Finite Group DatabasebetaFinite Group Databasebeta| order | 27090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9×C43 · Schur multiplier (H2) = C1 |
| direct product | C5×C9×D7×C43 |
| Fitting, Hall | C5×C7×C9×C43 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C5×C9×C43 |
| Hall | C7×C9×C43 ⋊ C2×C5 |
| Hall | C5×C7×C43 ⋊ C2×C9 |
| Hall | C5×C7×C9 ⋊ C2×C43 |
| Hall | C7×C43 ⋊ C2×C5×C9 |
| Hall | C7×C9 ⋊ C2×C5×C43 |
| Hall | C5×C7 ⋊ C2×C9×C43 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13545 |
9675 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27090, 9);