Finite Group DatabasebetaFinite Group Databasebeta| order | 19890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C17⋊(D13⋊C9)) |
| unambiguous semidirect product | C17⋊(C5⋊(D13⋊C9)) |
| unambiguous semidirect product | (C13⋊C9)⋊D85 |
| unambiguous semidirect product | D1105⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊(C17⋊(D13⋊C3)) |
| commutator, hypocenter | C5×C13×C17 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C13×C17 | C2×C3 |
| prime radical | C3×D1105 | C3 |
| LCS | G ▷ C5×C13×C17 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9945 |
Polycyclic presentation:
2,3,5,13,17,3|b^3=f,c^a=c^4,d^a=d^12,e^a=e^16,d^b=d^3906 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19890, 24);