Finite Group DatabasebetaFinite Group Databasebeta| order | 18390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1839 |
| unambiguous semidirect product | C3⋊(C5×D613) |
| unambiguous semidirect product | C613⋊(C5×D3) |
| Fitting, socle, Hall | C3×C5×C613 ⋊ C2 |
| derived, Hall | C3×C613 ⋊ C2×C5 |
| Hall | C5×C613 ⋊ D3 |
| Sylow | C613 ⋊ C5×D3 |
| Hall | C3×C5 ⋊ D613 |
| Sylow | C3 ⋊ C5×D613 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1839 |
| commutator, cosocle, hypocenter | C3×C613 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C613 | C2 |
| LCS | G ▷ C3×C613 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9195 |
4605 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×D613, D5×D1839, D15⋊D613, … |
| maximal normal subgroup of | C5×D3×D613, D5×D1839, D15⋊D613, … |
| maximal quotient of | C5×Dic1839, C2×C5×D1839 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18390, 7);