Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(#14524212⋊C3) |
| unambiguous semidirect product | (C5⋊#14524212)⋊C3 |
| Fitting, socle, Hall | C5×C192 ⋊ C3×D3 |
| derived | C5×#11762246 ⋊ C2×C3 |
| Hall | C5×C19⋊C32 ⋊ C2 |
| Hall | C19⋊C32 ⋊ D5 |
| Sylow | C192 ⋊ C3×D15 |
| Sylow | C5 ⋊ #14524212⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C5×#11762246 | C2×C3 |
| Fitting, socle | C5×C192 | C3×D3 |
| LCS | G ▷ C5×#11762246 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 190 |
Polycyclic presentation:
2,3^2,5,19^2|c^a=c^2,d^a=d^4,e^a=f,f^a=e,e^b=e^11,f^b=f^11,e^c=e^7,f^c=f^11216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 113);