Finite Group DatabasebetaFinite Group Databasebeta| order | 34524 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C7⋊#19096903 |
| Fitting, socle, derived, Hall | C32×C7×C137 ⋊ C4 |
| Hall | C32×C137 ⋊ Dic7 |
| Hall | C7×C137 ⋊ #157 |
| Sylow | C137 ⋊ C7⋊#157 |
| Hall | C32×C7 ⋊ #10587739 |
| Sylow | C32 ⋊ C7⋊#10587739 |
| Sylow | C7 ⋊ #19096903 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C7×C137 | C4 |
| prime radical, cosocle | C7×C3⋊D411 | C2 |
| LCS | G ▷ C32×C7×C137 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5754 |
Polycyclic presentation:
2^2,3^2,7,137|a^2=b,c^a=cd,d^a=cd^2,e^a=e^6,f^a=f^100,c^b=c^2,d^b=d^2,f^b=f^1362166 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34524, 85);