Finite Group DatabasebetaFinite Group Databasebeta| order | 18642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C239 · Schur multiplier (H2) = C1 |
| direct product | D3×C13×C239 |
| unambiguous semidirect product | C3⋊(C2×C13×C239) |
| Fitting, socle, Hall | C3×C13×C239 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C13×C239 |
| Hall | C3×C239 ⋊ C2×C13 |
| Hall | C3×C13 ⋊ C2×C239 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C239 | D3 |
| commutator, cosocle, hypocenter | C3 | C2×C13×C239 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C239 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C13×C239 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9321 |
9321 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C13×D239, D3×D13×C239, D3×D3107, … |
| maximal normal subgroup of | D3×C13×D239, D3×D13×C239, D3×D3107, … |
| maximal quotient of | Dic3×C13×C239, C2×D3×C13×C239 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18642, 6);