Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#20266615 |
| Fitting, socle, derived, Hall | C5×C192 ⋊ C2×C9 |
| Hall | C5×#15692438 ⋊ C2 |
| Hall | C19×D95 ⋊ C9 |
| Hall | #15692438 ⋊ D5 |
| Sylow | C192 ⋊ C9×D5 |
| Sylow | C5 ⋊ #20266615 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C192 | C2×C9 |
| prime radical | C19⋊C3×D95 | C3 |
| cosocle | C5×C19×C19⋊C3 | C2×C3 |
| LCS | G ▷ C5×C192 | |
| UCS | C1 | |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1710 |
Polycyclic presentation:
2,3^2,5,19^2|b^3=c,d^a=d^4,e^a=e^18,e^b=e^7,f^b=f^16,f^c=f^11179 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 128);