Finite Group DatabasebetaFinite Group Databasebeta| order | 34914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊#15691772 |
| Fitting, socle, Hall | C11×C232 ⋊ D3 |
| derived, Hall | C11×C232⋊C3 ⋊ C2 |
| Hall | C232⋊C3 ⋊ D11 |
| Sylow | C232 ⋊ D33 |
| Sylow | C11 ⋊ #15691772 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C11×C232⋊C3 | C2 |
| Fitting, socle | C11×C232 | D3 |
| LCS | G ▷ C11×C232⋊C3 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 759 |
Polycyclic presentation:
2,3,11,23^2|b^a=b^2,c^a=c^10,d^a=de^2,e^a=e^22,d^b=d^7e^3,e^b=d^4e^151019 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34914, 74);