Finite Group DatabasebetaFinite Group Databasebeta| order | 10734 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D1789⋊C3 |
| unambiguous semidirect product | (C1789⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C1789 ⋊ C2×C3 |
| Hall | C1789⋊C3 ⋊ C2 |
| Hall | D1789 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C1789 | C2×C3 |
| LCS | G ▷ C1789 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,1789|c^a=c^1788,c^b=c^152304 conjugacy classes — view the full character table.
| maximal subgroup of | #20297576⋊C3, C2×D1789⋊C3, C3×D1789⋊C3, … |
| maximal normal subgroup of | #20297576⋊C3, C2×D1789⋊C3, C3×D1789⋊C3 |
| maximal quotient of | Dic1789⋊C3, C2×D1789⋊C3, D1789⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10734, 1);