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 | #30654554 ⋊ C2 |
| Hall | C49×D37 ⋊ C9 |
| Hall | D37 ⋊ C49⋊C9 |
| Sylow | C49 ⋊ #66524⋊C2 |
| Sylow | C37 ⋊ C2×C49⋊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^4,d^a=d^36,c^b=c^4f,d^b=d^10,f^b=f^4996 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 6);