Finite Group DatabasebetaFinite Group Databasebeta| order | 18342 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D3057 |
| unambiguous semidirect product | C1019⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C1019 ⋊ C2 |
| Sylow | C1019 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ D1019 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C1019 | C2 |
| LCS | G ▷ C32×C1019 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9171 |
Polycyclic presentation:
2,3^2,1019|b^a=b^2,c^a=c^2,d^a=d^10184587 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D3057, C3⋊D3×D1019, C2×C3⋊D3057 |
| maximal normal subgroup of | D3×D3057, C3⋊D3×D1019, C2×C3⋊D3057 |
| maximal quotient of | C3⋊Dic3057, C2×C3⋊D3057 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18342, 6);