Finite Group DatabasebetaFinite Group Databasebeta| order | 18246 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D3041 |
| unambiguous semidirect product | C3041⋊(C2×C3) |
| Fitting, socle, Hall | C3×C3041 ⋊ C2 |
| derived, Sylow | C3041 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3041 |
| commutator, cosocle, hypocenter | C3041 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C3041 | C2 |
| LCS | G ▷ C3041 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9123 |
4566 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#27131563, C3⋊#27131563, D3×D3041, … |
| maximal normal subgroup of | C3×#27131563, C3⋊#27131563, D3×D3041, … |
| maximal quotient of | C3×Dic3041, C2×C3×D3041 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18246, 2);