Finite Group DatabasebetaFinite Group Databasebeta| order | 18759 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13×C37 · Schur multiplier (H2) = C1 |
| direct product | C13×C37×C13⋊C3 |
| unambiguous semidirect product | C13⋊(C3×C13×C37) |
| Fitting, socle, Hall | C132×C37 ⋊ C3 |
| derived | C13 ⋊ C3×C13×C37 |
| Sylow | C132 ⋊ C3×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C37 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C3×C13×C37 |
| Frattini | C1 | G |
| Fitting, socle | C132×C37 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C13×C37 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1443 |
3367 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×C13⋊C3×D37, C13×C37×D13⋊C3, C13×(C13⋊C3)⋊D37, … |
| maximal normal subgroup of | C13×C13⋊C3×D37, C13×C37×D13⋊C3, C13×(C13⋊C3)⋊D37, … |
| maximal quotient of | C2×C13×C37×C13⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18759, 11);