Finite Group DatabasebetaFinite Group Databasebeta| order | 27846 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9×C17 · Schur multiplier (H2) = C1 |
| direct product | C2×C7×C17×C13⋊C9 |
| unambiguous semidirect product | (C2×C13)⋊(C7×C9×C17) |
| unambiguous semidirect product | (C2×C13×C17)⋊(C7×C9) |
| derived, Sylow | C13 ⋊ C2×C7×C9×C17 |
| Hall | C2×C7×C13×C17 ⋊ C9 |
| Hall | C7×C13×C17 ⋊ C2×C9 |
| Hall | C2×C13×C17 ⋊ C7×C9 |
| Hall | C13×C17 ⋊ C2×C7×C9 |
| Hall | C2×C7×C13 ⋊ C9×C17 |
| Hall | C7×C13 ⋊ C2×C9×C17 |
| Hall | C2×C13 ⋊ C7×C9×C17 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27846 |
4998 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27846, 2);