Finite Group DatabasebetaFinite Group Databasebeta| order | 18642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×D239 |
| unambiguous semidirect product | C239⋊(C2×C3×C13) |
| Fitting, socle, Hall | C3×C13×C239 ⋊ C2 |
| derived, Sylow | C239 ⋊ C2×C3×C13 |
| Hall | C13×C239 ⋊ C2×C3 |
| Hall | C3×C239 ⋊ C2×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | D239 |
| commutator, cosocle, hypocenter | C239 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C239 | C2 |
| LCS | G ▷ C239 | |
| UCS | C1 ◁ C3×C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9321 |
4719 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D13×D239, D3×C13×D239, D39×D239, … |
| maximal normal subgroup of | C3×D13×D239, D3×C13×D239, D39×D239, … |
| maximal quotient of | C3×C13×Dic239, C2×C3×C13×D239 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18642, 3);