Finite Group DatabasebetaFinite Group Databasebeta| order | 6738 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D1123⋊C3 |
| unambiguous semidirect product | (C1123⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C1123 ⋊ C2×C3 |
| Hall | C1123⋊C3 ⋊ C2 |
| Hall | D1123 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1123 | C2×C3 |
| LCS | G ▷ C1123 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,1123|c^a=c^1122,c^b=c^33193 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D1123⋊C3, C3×D1123⋊C3, C3⋊(D1123⋊C3), … |
| maximal normal subgroup of | C2×D1123⋊C3, C3×D1123⋊C3, C5×D1123⋊C3 |
| maximal quotient of | (C1123⋊C3)⋊C4, C2×D1123⋊C3, D1123⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6738, 1);