Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C72×C37 ⋊ C2×C9 |
| Hall | #30654570 ⋊ C2 |
| Hall | C72×D37 ⋊ C9 |
| Hall | D37 ⋊ #89204 |
| Sylow | C72 ⋊ #66524⋊C2 |
| Sylow | C37 ⋊ C2×#89204 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #24925974 |
| commutator, hypocenter | C72×C37 | C2×C9 |
| Fitting, socle, cosocle | C3×C72×C37 | C2×C3 |
| prime radical | C3×C72×D37 | C3 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 ◁ C3 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16317 |
Polycyclic presentation:
2,3,7^2,37,3|b^3=f,e^a=e^36,c^b=c^2,d^b=d^2,e^b=e^26996 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 126);