Finite Group DatabasebetaFinite Group Databasebeta| order | 18590 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C13 |
| direct product | C11×C5⋊(C13⋊D13) |
| unambiguous semidirect product | C5⋊(C11×C13⋊D13) |
| unambiguous semidirect product | C13⋊(C11×D65) |
| Fitting, socle, Hall | C5×C11×C132 ⋊ C2 |
| derived, Hall | C5×C132 ⋊ C2×C11 |
| Hall | C11×C132 ⋊ D5 |
| Sylow | C132 ⋊ D5×C11 |
| Hall | C5×C11 ⋊ C13⋊D13 |
| Sylow | C5 ⋊ C11×C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C5⋊(C13⋊D13) |
| commutator, cosocle, hypocenter | C5×C132 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C132 | C2 |
| LCS | G ▷ C5×C132 | |
| UCS | C1 ◁ C11 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9295 |
4664 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#16810004, C11×#16810002, C11×#16810003, … |
| maximal normal subgroup of | C11×#16810004, C11×#16810002, C11×#16810003, … |
| maximal quotient of | C11×#16809991, C2×C11×C5⋊(C13⋊D13) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18590, 23);