Finite Group DatabasebetaFinite Group Databasebeta| order | 36162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C41⋊(D49⋊C9) |
| unambiguous semidirect product | (C49⋊C9)⋊D41 |
| unambiguous semidirect product | D2009⋊C9 |
| derived, Hall | C41×C49 ⋊ C2×C9 |
| Hall | C41×C49⋊C9 ⋊ C2 |
| Hall | D2009 ⋊ C9 |
| Hall | C49⋊C9 ⋊ D41 |
| Sylow | C49 ⋊ C9×D41 |
| Sylow | C41 ⋊ D49⋊C9 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18081 |
Polycyclic presentation:
2,3,7,41,3,7|b^3=e,c^7=f^6,c^a=c^6f,d^a=d^40,f^a=f^6,c^b=c^4f^5,f^b=f^41182 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36162, 4);