Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D5415 |
| unambiguous semidirect product | C5⋊(C3⋊D1083) |
| unambiguous semidirect product | C361⋊(C3⋊D15) |
| Fitting, derived, Hall | C32×C5×C361 ⋊ C2 |
| Hall | C32×C361 ⋊ D5 |
| Hall | C5×C361 ⋊ C3⋊D3 |
| Sylow | C361 ⋊ C3⋊D15 |
| Hall | C32×C5 ⋊ D361 |
| Sylow | C32 ⋊ D1805 |
| Sylow | C5 ⋊ C3⋊D1083 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C5×C361 | C2 |
| Frattini | C19 | C3⋊D285 |
| socle | C32×C5×C19 | D19 |
| LCS | G ▷ C32×C5×C361 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16245 |
Polycyclic presentation:
2,3^2,5,19^2|e^19=f^18,b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^18f,f^a=f^188124 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 36);