Finite Group DatabasebetaFinite Group Databasebeta| order | 34914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C3⋊(C11⋊(C23⋊D23)) |
| unambiguous semidirect product | C11⋊(C3⋊(C23⋊D23)) |
| unambiguous semidirect product | C23⋊D759 |
| Fitting, socle, derived, Hall | C3×C11×C232 ⋊ C2 |
| Hall | C11×C232 ⋊ D3 |
| Hall | C3×C232 ⋊ D11 |
| Sylow | C232 ⋊ D33 |
| Hall | C3×C11 ⋊ C23⋊D23 |
| Sylow | C11 ⋊ C3⋊(C23⋊D23) |
| Sylow | C3 ⋊ C11⋊(C23⋊D23) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C232 | C2 |
| LCS | G ▷ C3×C11×C232 | |
| UCS | C1 | |
208 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17457 |
Polycyclic presentation:
2,3,11,23^2|b^a=b^2,c^a=c^10,d^a=d^22,e^a=e^228730 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34914, 87);