Finite Group DatabasebetaFinite Group Databasebeta| order | 19422 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D3237 |
| unambiguous semidirect product | C13⋊(C3⋊D249) |
| unambiguous semidirect product | C83⋊(C3⋊D39) |
| Fitting, socle, derived, Hall | C32×C13×C83 ⋊ C2 |
| Hall | C13×C83 ⋊ C3⋊D3 |
| Hall | C32×C83 ⋊ D13 |
| Hall | C32×C13 ⋊ D83 |
| Sylow | C83 ⋊ C3⋊D39 |
| Sylow | C13 ⋊ C3⋊D249 |
| Sylow | C32 ⋊ D1079 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C13×C83 | C2 |
| LCS | G ▷ C32×C13×C83 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9711 |
Polycyclic presentation:
2,3^2,13,83|b^a=b^2,c^a=c^2,d^a=d^12,e^a=e^824857 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19422, 22);