Finite Group DatabasebetaFinite Group Databasebeta| order | 18590 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C13 |
| unambiguous semidirect product | C5⋊(C11⋊(C13⋊D13)) |
| unambiguous semidirect product | C11⋊(C5⋊(C13⋊D13)) |
| unambiguous semidirect product | C13⋊D715 |
| Fitting, socle, derived, Hall | C5×C11×C132 ⋊ C2 |
| Hall | C11×C132 ⋊ D5 |
| Hall | C5×C132 ⋊ D11 |
| Sylow | C132 ⋊ D55 |
| Hall | C5×C11 ⋊ C13⋊D13 |
| Sylow | C11 ⋊ C5⋊(C13⋊D13) |
| Sylow | C5 ⋊ C11⋊(C13⋊D13) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C11×C132 | C2 |
| LCS | G ▷ C5×C11×C132 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9295 |
Polycyclic presentation:
2,5,11,13^2|b^a=b^4,c^a=c^10,d^a=d^12,e^a=e^124649 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D13×D715, D55×C13⋊D13, D65×D143, … |
| maximal normal subgroup of | D13×D715, D55×C13⋊D13, D65×D143, … |
| maximal quotient of | C11⋊#16809991, C2×C5⋊(C11⋊(C13⋊D13)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18590, 20);