Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C49⋊C9)⋊D37 |
| derived, Hall | C37×C49 ⋊ C2×C9 |
| Hall | C37×C49⋊C9 ⋊ C2 |
| Hall | D1813 ⋊ C9 |
| Hall | C49⋊C9 ⋊ D37 |
| Sylow | C49 ⋊ C9×D37 |
| 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,d^a=d^36,f^a=f^6,c^b=c^4f^5,f^b=f^41068 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 9);