Finite Group DatabasebetaFinite Group Databasebeta| order | 18642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C239 · Schur multiplier (H2) = C1 |
| direct product | D13⋊C3×C239 |
| unambiguous semidirect product | D13⋊(C3×C239) |
| unambiguous semidirect product | (C13⋊C3)⋊(C2×C239) |
| unambiguous semidirect product | (D13×C239)⋊C3 |
| Fitting, socle, Hall | C13×C239 ⋊ C2×C3 |
| derived, Sylow | C13 ⋊ C2×C3×C239 |
| Hall | C13⋊C3×C239 ⋊ C2 |
| Hall | D13×C239 ⋊ C3 |
| Hall | C13⋊C3 ⋊ C2×C239 |
| Hall | D13 ⋊ C3×C239 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C239 | D13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C2×C3×C239 |
| Frattini | C1 | G |
| Fitting, socle | C13×C239 | C2×C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C239 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3107 |
1912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,𝔽13)×C239, C239⋊AGL(1,𝔽13), D13⋊C3×D239, … |
| maximal normal subgroup of | AGL(1,𝔽13)×C239, C239⋊AGL(1,𝔽13), D13⋊C3×D239, … |
| maximal quotient of | Dic13⋊C3×C239, C2×D13⋊C3×C239 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18642, 11);