Finite Group DatabasebetaFinite Group Databasebeta| order | 18590 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11×C13 · Schur multiplier (H2) = C1 |
| direct product | C5×C11×C13×D13 |
| unambiguous semidirect product | C13⋊(C2×C5×C11×C13) |
| Fitting, socle, Hall | C5×C11×C132 ⋊ C2 |
| derived | C13 ⋊ C2×C5×C11×C13 |
| Hall | C11×C132 ⋊ C2×C5 |
| Hall | C5×C132 ⋊ C2×C11 |
| Sylow | C132 ⋊ C2×C5×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11×C13 | D13 |
| commutator, cosocle, hypocenter | C13 | C2×C5×C11×C13 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C132 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C5×C11×C13 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1430 |
5720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C11×C13×#261, C5×C11×#10621730, C5×C11×D132, … |
| maximal normal subgroup of | C5×C11×C13×#261, C5×C11×#10621730, C5×C11×D132, … |
| maximal quotient of | C5×C11×C13×Dic13, C2×C5×C11×C13×D13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18590, 30);