Finite Group DatabasebetaFinite Group Databasebeta| order | 18162 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C1009 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D3×C1009 |
| unambiguous semidirect product | C3⋊(D3×C1009) |
| Fitting, socle, Hall | C32×C1009 ⋊ C2 |
| derived, Sylow | C32 ⋊ C2×C1009 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1009 | C3⋊D3 |
| commutator, cosocle, hypocenter | C32 | C2×C1009 |
| Frattini | C1 | G |
| Fitting, socle | C32×C1009 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C1009 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9081 |
6054 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #157×C1009, #49138060, D32×C1009, … |
| maximal normal subgroup of | #157×C1009, #49138060, D32×C1009, … |
| maximal quotient of | C3⋊Dic3×C1009, C2×C3⋊D3×C1009 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18162, 15);