Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(#15692425⋊C2) |
| unambiguous semidirect product | #15692425⋊D5 |
| Fitting, derived, Hall | C5×C361 ⋊ C2×C9 |
| Hall | C5×#15692425 ⋊ C2 |
| Hall | D1805 ⋊ C9 |
| Hall | #15692425 ⋊ D5 |
| Sylow | C361 ⋊ C9×D5 |
| Sylow | C5 ⋊ #15692425⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C361 | C2×C9 |
| Frattini | C19 | C5⋊AGL(1,𝔽19) |
| socle | C5×C19 | AGL(1,𝔽19) |
| prime radical | C5⋊(D361⋊C3) | C3 |
| cosocle | C5×C361⋊C3 | C2×C3 |
| LCS | G ▷ C5×C361 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1805 |
Polycyclic presentation:
2,3^2,5,19^2|b^3=c,e^19=f^18,d^a=d^4,e^a=e^18f,f^a=f^18,e^b=e^4f^14,f^b=f^4,e^c=e^7f^4,f^c=f^7136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 16);