Finite Group DatabasebetaFinite Group Databasebeta| order | 32634 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Hall | C72×C37 ⋊ C3×D3 |
| derived | C37×#3862 ⋊ C2×C3 |
| Hall | ΓL(1,𝔽8)2×C37 ⋊ C2 |
| Hall | ΓL(1,𝔽8)2 ⋊ D37 |
| Sylow | C72 ⋊ C3×D111 |
| Sylow | C37 ⋊ #64418⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C37×#3862 | C2×C3 |
| Fitting, socle | C72×C37 | C3×D3 |
| LCS | G ▷ C37×#3862 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 518 |
Polycyclic presentation:
2,3^2,37,7^2|c^a=c^2,d^a=d^36,e^a=e^2f^3,f^a=e^6f^5,e^b=e^4,f^b=f^4,e^c=e^4f^4,f^c=f^2470 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32634, 169);