Finite Group DatabasebetaFinite Group Databasebeta| order | 18558 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D3093 |
| unambiguous semidirect product | C1031⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C1031 ⋊ C2 |
| Sylow | C1031 ⋊ C3⋊D3 |
| Sylow | C32 ⋊ D1031 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C1031 | C2 |
| LCS | G ▷ C32×C1031 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9279 |
Polycyclic presentation:
2,3^2,1031|b^a=b^2,c^a=c^2,d^a=d^10304641 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D3093, C3⋊D3×D1031, C2×C3⋊D3093 |
| maximal normal subgroup of | D3×D3093, C3⋊D3×D1031, C2×C3⋊D3093 |
| maximal quotient of | C3⋊Dic3093, C2×C3⋊D3093 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18558, 6);