Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #120⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5×C8 · Schur multiplier (H2) = C22 |
| direct product | C5×#1779⋊C3 |
| unambiguous semidirect product | #1779⋊(C3×C5) |
| unambiguous semidirect product | (C5×#1779)⋊C3 |
| Fitting, Hall | C5×#1779 ⋊ C3 |
| derived | C24 ⋊ C3×C5×C8 |
| Sylow | #1779 ⋊ C3×C5 |
344 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,4,5)(6,7,8,10,9,11,12,13)(14,15)(16,19,18,21,17,20);(15,21)(19,20)200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236381);