Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(ΓL(1,𝔽8)⋊D37) |
| Fitting, socle, derived, Hall | C72×C37 ⋊ C2×C32 |
| Hall | ΓL(1,𝔽8)2×C37 ⋊ C2 |
| Hall | C7⋊D259 ⋊ C32 |
| Hall | ΓL(1,𝔽8)2 ⋊ D37 |
| Sylow | C72 ⋊ C32×D37 |
| Sylow | C37 ⋊ ΓL(1,𝔽8)⋊AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C37 | C2×C32 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 777 |
Polycyclic presentation:
2,3^2,7^2,37|d^a=d^6,e^a=e^6,f^a=f^36,e^b=e^2,d^c=d^2476 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 221);