Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(#15692423⋊C2) |
| unambiguous semidirect product | #15692423⋊D5 |
| derived, Hall | C5×C361 ⋊ C2×C9 |
| Hall | C5×#15692423 ⋊ C2 |
| Hall | D1805 ⋊ C9 |
| Hall | #15692423 ⋊ D5 |
| Sylow | C361 ⋊ C9×D5 |
| Sylow | C5 ⋊ #15692423⋊C2 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16245 |
Polycyclic presentation:
2,3,5,19,3,19|b^3=e,d^19=f^18,c^a=c^4,d^a=d^18f,f^a=f^18,d^b=d^7f^4,f^b=f^7936 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 4);