Finite Group DatabasebetaFinite Group Databasebeta| order | 34524 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D63⋊D137 |
| unambiguous semidirect product | D959⋊D9 |
| unambiguous semidirect product | D1233⋊D7 |
| Fitting, derived, Hall | C7×C9×C137 ⋊ C22 |
| Hall | C9×C137 ⋊ C2×D7 |
| Hall | C7×C137 ⋊ C2×D9 |
| Sylow | C137 ⋊ D7×D9 |
| Hall | C7×C9 ⋊ C2×D137 |
| Sylow | C9 ⋊ D7×D137 |
| Sylow | C7 ⋊ D9×D137 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C7×C9×C137 | C22 |
| Frattini | C3 | D21⋊D137 |
| socle | C3×C7×C137 | C2×D3 |
| LCS | G ▷ C7×C9×C137 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8631 |
Polycyclic presentation:
2^2,3,7,137,3|c^3=f^2,d^a=d^6,e^a=e^136,c^b=c^2f,d^b=d^6,f^b=f^22274 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34524, 30);