Finite Group DatabasebetaFinite Group Databasebeta| order | 32490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C5⋊(C9⋊(C19⋊D19)) |
| unambiguous semidirect product | C9⋊(C5⋊(C19⋊D19)) |
| unambiguous semidirect product | C19⋊D855 |
| Fitting, derived, Hall | C5×C9×C192 ⋊ C2 |
| Hall | C9×C192 ⋊ D5 |
| Hall | C5×C192 ⋊ D9 |
| Sylow | C192 ⋊ D45 |
| Hall | C5×C9 ⋊ C19⋊D19 |
| Sylow | C9 ⋊ C5⋊(C19⋊D19) |
| Sylow | C5 ⋊ C9⋊(C19⋊D19) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C9×C192 | C2 |
| Frattini | C3 | C3⋊(C5⋊(C19⋊D19)) |
| socle | C3×C5×C192 | D3 |
| LCS | G ▷ C5×C9×C192 | |
| UCS | C1 | |
264 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16245 |
Polycyclic presentation:
2,3,5,19^2,3|b^3=f^2,b^a=b^2f,c^a=c^4,d^a=d^18,e^a=e^18,f^a=f^28124 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32490, 69);