Finite Group DatabasebetaFinite Group Databasebeta| order | 1980 |
| isoclinism | isoclinic class of C9⋊AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(Dic11⋊C5) |
| unambiguous semidirect product | (C11⋊C5)⋊Dic9 |
| unambiguous semidirect product | Dic99⋊C5 |
| derived, Hall | C9×C11 ⋊ C4×C5 |
| Hall | C9×C11⋊C5 ⋊ C4 |
| Hall | Dic99 ⋊ C5 |
| Hall | C11⋊C5 ⋊ Dic9 |
| Sylow | C11 ⋊ C5×Dic9 |
| Sylow | C9 ⋊ Dic11⋊C5 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 396 |
Polycyclic presentation:
2,5,2,3,11,3|a^2=c,d^3=f,d^a=d^2f^2,e^a=e^10,f^a=f^2,e^b=e^378 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1980, 3);