Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C37×C49 ⋊ C2×C9 |
| Hall | #30654553 ⋊ C2 |
| Hall | C37×D49 ⋊ C9 |
| Hall | D49 ⋊ #66524 |
| Sylow | C49 ⋊ C2×#66524 |
| Sylow | C37 ⋊ D49⋊C9 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16317 |
Polycyclic presentation:
2,3,7,37,3,7|b^3=e,c^7=f^6,c^a=c^6f,f^a=f^6,c^b=c^2f^3,d^b=d^10,f^b=f^2978 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 11);