Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#20266620 |
| Fitting, socle, Hall | C5×C192 ⋊ D9 |
| derived, Hall | C5×#15692436 ⋊ C2 |
| Hall | #15692436 ⋊ D5 |
| Sylow | C192 ⋊ D45 |
| Sylow | C5 ⋊ #20266620 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×#15692436 | C2 |
| Fitting, socle | C5×C192 | D9 |
| LCS | G ▷ C5×#15692436 | |
| UCS | C1 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 190 |
Polycyclic presentation:
2,3,5,3,19^2|b^3=d,b^a=b^2d^2,c^a=c^4,d^a=d^2,e^a=e^5f^3,f^a=e^11f^14,e^b=e^4f^16,f^b=f^5,e^d=e^7f^7,f^d=f^11151 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 112);