Finite Group DatabasebetaFinite Group Databasebeta| order | 18162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D1009⋊C3) |
| unambiguous semidirect product | (C1009⋊C3)⋊D3 |
| unambiguous semidirect product | D3027⋊C3 |
| Fitting, socle, derived | C3×C1009 ⋊ C2×C3 |
| Hall | C3×C1009⋊C3 ⋊ C2 |
| Sylow | C1009 ⋊ C3×D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C1009 | C2×C3 |
| LCS | G ▷ C3×C1009 | |
| UCS | C1 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3027 |
Polycyclic presentation:
2,3^2,1009|c^a=c^2,d^a=d^1008,d^b=d^374513 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D1009⋊C3, C2×C3⋊(D1009⋊C3) |
| maximal normal subgroup of | D3×D1009⋊C3, C2×C3⋊(D1009⋊C3) |
| maximal quotient of | C3⋊(Dic1009⋊C3), C2×C3⋊(D1009⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18162, 11);