Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#85430 |
| Fitting | C5×Q82 ⋊ D3 |
542 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 320 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3,4,5)(6,8,9,12)(7,10,11,13)(14,20,21)(15,19,17);(6,7,9,11)(8,13,12,10);(8,12)(10,13)(15,18)(16,20)(19,21)200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236866);