Finite Group DatabasebetaFinite Group Databasebeta| order | 34524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C7⋊C9)⋊#10587739 |
| unambiguous semidirect product | (C7⋊#10587739)⋊C9 |
| derived, Hall | C7×C137 ⋊ C4×C9 |
| Hall | C7⋊C9×C137 ⋊ C4 |
| Hall | C7⋊#10587739 ⋊ C9 |
| Sylow | C137 ⋊ Dic7⋊C9 |
| Hall | C7⋊C9 ⋊ #10587739 |
| Sylow | C7 ⋊ C9×#10587739 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)⋊#10587739 |
| commutator, hypocenter | C7×C137 | C4×C9 |
| Fitting, socle | C3×C7×C137 | C3×C4 |
| prime radical, cosocle | C3×C7×D137 | C2×C3 |
| LCS | G ▷ C7×C137 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8631 |
Polycyclic presentation:
2,3,2,7,137,3|a^2=c,b^3=f,d^a=d^6,e^a=e^100,d^b=d^2,e^c=e^136552 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34524, 14);