Finite Group DatabasebetaFinite Group Databasebeta| order | 18759 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×C169⋊C3 |
| unambiguous semidirect product | C169⋊(C3×C37) |
| Fitting, Hall | C37×C169 ⋊ C3 |
| derived, Sylow | C169 ⋊ C3×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C169⋊C3 |
| commutator, cosocle, hypocenter | C169 | C3×C37 |
| Frattini | C13 | C37×C13⋊C3 |
| Fitting | C37×C169 | C3 |
| socle | C13×C37 | C13⋊C3 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C37 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6253 |
2183 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C37×C169⋊C3, D37×C169⋊C3, C37×D169⋊C3, … |
| maximal normal subgroup of | C2×C37×C169⋊C3, D37×C169⋊C3, C37×D169⋊C3, … |
| maximal quotient of | C2×C37×C169⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18759, 2);