Finite Group DatabasebetaFinite Group Databasebeta| order | 36162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×C7⋊C9×D41 |
| unambiguous semidirect product | C41⋊(C2×C7×C7⋊C9) |
| unambiguous semidirect product | (C7×D41)⋊(C7×C9) |
| derived | C7×C41 ⋊ C2×C7×C9 |
| Hall | C7×C41×C7⋊C9 ⋊ C2 |
| Hall | C72×D41 ⋊ C9 |
| Hall | C72×C41 ⋊ C2×C9 |
| Sylow | C72 ⋊ C9×D41 |
| Sylow | C41 ⋊ C2×C7×C7⋊C9 |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2583 |
2310 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36162, 36);