Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊#16813380) |
| Fitting, socle, Hall | C32×C192 ⋊ D5 |
| derived, Hall | C32×C192⋊C5 ⋊ C2 |
| Hall | C192⋊C5 ⋊ C3⋊D3 |
| Sylow | C192 ⋊ C3⋊D15 |
| Sylow | C32 ⋊ #16813380 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×C192⋊C5 | C2 |
| Fitting, socle | C32×C192 | D5 |
| LCS | G ▷ C32×C192⋊C5 | |
| UCS | C1 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 855 |
Polycyclic presentation:
2,3^2,5,19^2|b^a=b^2,c^a=c^2,d^a=d^4,e^a=ef^12,f^a=f^18,e^d=e^16f^4,f^d=e^4f^7375 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 150);