Finite Group DatabasebetaFinite Group Databasebeta| order | 1980 |
| isoclinism | isoclinic class of AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×Dic11⋊C5 |
| unambiguous semidirect product | Dic11⋊(C5×C9) |
| unambiguous semidirect product | (C11⋊C5)⋊(C4×C9) |
| unambiguous semidirect product | (C9×Dic11)⋊C5 |
| derived, Sylow | C11 ⋊ C4×C5×C9 |
| Hall | C9×C11⋊C5 ⋊ C4 |
| Hall | C9×Dic11 ⋊ C5 |
| Hall | C9×C11 ⋊ C4×C5 |
| Hall | C11⋊C5 ⋊ C4×C9 |
| Hall | Dic11 ⋊ C5×C9 |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 396 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5,6,7,8,9)(11,14,15,19,18,12,13,16,17,20)(21,22,23,24);(10,11,14,17,15,18,20,16,19,13,12)198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1980, 1);