Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C5⋊(D361⋊C3)) |
| unambiguous semidirect product | C5⋊(C3⋊(D361⋊C3)) |
| unambiguous semidirect product | (C361⋊C3)⋊D15 |
| unambiguous semidirect product | D5415⋊C3 |
| Fitting, derived | C3×C5×C361 ⋊ C2×C3 |
| Hall | C3×C5×C361⋊C3 ⋊ C2 |
| Hall | C3×C361⋊C3 ⋊ D5 |
| Hall | C5×C361 ⋊ C3×D3 |
| Sylow | C361 ⋊ C3×D15 |
| Sylow | C5 ⋊ C3⋊(D361⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C5×C361 | C2×C3 |
| Frattini | C19 | C3⋊(C5⋊(D19⋊C3)) |
| socle | C3×C5×C19 | D19⋊C3 |
| LCS | G ▷ C3×C5×C361 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5415 |
Polycyclic presentation:
2,3^2,5,19^2|e^19=f^18,c^a=c^2,d^a=d^4,e^a=e^18f,f^a=f^18,e^b=e^11f^16,f^b=f^11927 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 24);