Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| Fitting, derived, Hall | C37×C49 ⋊ C2×C32 |
| Hall | C37⋊C3×C49⋊C3 ⋊ C2 |
| Hall | D1813 ⋊ C32 |
| Sylow | C49 ⋊ C3×D37⋊C3 |
| Sylow | C37 ⋊ C3×D49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C37×C49 | C2×C32 |
| Frattini | C7 | ΓL(1,𝔽8)⋊(D37⋊C3) |
| socle | C7×C37 | C3×AGL(1,𝔽7) |
| LCS | G ▷ C37×C49 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1813 |
Polycyclic presentation:
2,3^2,7,37,7|d^7=f^6,d^a=d^6f,e^a=e^36,f^a=f^6,e^b=e^26,d^c=d^2f^3,f^c=f^2156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 31);