Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C5⋊#14524212) |
| unambiguous semidirect product | C5⋊(C3⋊#14524212) |
| Fitting, socle | C3×C5×C192 ⋊ D3 |
| derived, Hall | C3×C5×#11762246 ⋊ C2 |
| Hall | C3×#11762246 ⋊ D5 |
| Hall | C5×C192 ⋊ C3⋊D3 |
| Sylow | C192 ⋊ C3⋊D15 |
| Sylow | C5 ⋊ C3⋊#14524212 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C5×#11762246 | C2 |
| Fitting, socle | C3×C5×C192 | D3 |
| LCS | G ▷ C3×C5×#11762246 | |
| UCS | C1 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 570 |
Polycyclic presentation:
2,3^2,5,19^2|b^a=b^2,c^a=c^2,d^a=d^4,e^a=f,f^a=e,e^b=e^7,f^b=f^11951 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 190);