Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #20266582⋊C5 |
| derived, Sylow | C192 ⋊ C2×C5×C9 |
| Hall | #15692429⋊C5 ⋊ C2 |
| Hall | #20266582 ⋊ C5 |
| Hall | (C19⋊D19)⋊C5 ⋊ C9 |
| Hall | #15692429 ⋊ C2×C5 |
| Hall | C192⋊C5 ⋊ C2×C9 |
| Hall | C19⋊D19 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #14524206⋊C5 |
| commutator, hypocenter | C192 | C2×C5×C9 |
| Fitting, socle, cosocle | C3×C192 | C2×C3×C5 |
| prime radical | C3×(C19⋊D19)⋊C5 | C3 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 855 |
Polycyclic presentation:
2,3,5,19^2,3|b^3=f,d^a=d^18,e^a=e^18,d^b=d^11,e^b=e^11,d^c=d^12e^8,e^c=d^14e^11126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 39);