Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | #66526⋊(C7⋊D7) |
| Fitting, socle, derived, Hall | C72×C37 ⋊ C2×C9 |
| Hall | C72×#66526 ⋊ C2 |
| Hall | C7⋊D259 ⋊ C9 |
| Hall | #66526 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ #66526⋊C2 |
| Sylow | C37 ⋊ C9×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C37 | C2×C9 |
| prime radical | (C37⋊C3)⋊(C7⋊D7) | C3 |
| cosocle | C72×C37⋊C3 | C2×C3 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1813 |
Polycyclic presentation:
2,3^2,7^2,37|b^3=c,d^a=d^6,e^a=e^6,f^a=f^36,f^b=f^16,f^c=f^26332 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 257);