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 | D1813 ⋊ C9 |
| Sylow | C49 ⋊ #66524⋊C2 |
| Sylow | C37 ⋊ D49⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #24925921 |
| commutator, hypocenter | C37×C49 | C2×C9 |
| Frattini | C3×C7 | #13095538 |
| Fitting, cosocle | C3×C37×C49 | C2×C3 |
| socle | C3×C7×C37 | AGL(1,𝔽7) |
| prime radical | C3×D1813 | C3 |
| LCS | G ▷ C37×C49 | |
| UCS | C1 ◁ C3 | |
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^2f^3,d^b=d^10,f^b=f^2924 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 13);