Finite Group DatabasebetaFinite Group Databasebeta| order | 18654 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D3109 |
| Fitting, socle, Hall | C3×C3109 ⋊ C2 |
| derived, Sylow | C3109 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3109 |
| commutator, cosocle, hypocenter | C3109 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C3109 | C2 |
| LCS | G ▷ C3109 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9327 |
4668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#27159138, C3⋊#27159138, D3×D3109, … |
| maximal normal subgroup of | C3×#27159138, C3⋊#27159138, D3×D3109, … |
| maximal quotient of | C3×Dic3109, C2×C3×D3109 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18654, 4);