Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C37×C49 ⋊ C2×C9 |
| Hall | #30654558 ⋊ C2 |
| Hall | C49×D37 ⋊ C9 |
| Hall | D37 ⋊ C49⋊C9 |
| Sylow | C49 ⋊ #66526⋊C2 |
| Sylow | C37 ⋊ C2×C49⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C37×C49 | C2×C9 |
| Frattini | C7 | #17987959 |
| socle | C7×C37 | C2×C7⋊C9 |
| prime radical | C7×D37⋊C3 | ΓL(1,𝔽8) |
| cosocle | C49×C37⋊C3 | C2×C3 |
| LCS | G ▷ C37×C49 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1813 |
Polycyclic presentation:
2,3^2,7,37,7|b^3=c,d^7=f^2,e^a=e^36,d^b=d^2f,e^b=e^34,f^b=f^2,e^c=e^10212 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 34);