Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#85293 |
726 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 240 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3,4,5)(7,9)(10,11,13)(14,16,17,21)(15,18,19,20);(6,7)(8,9);(11,12)(14,15,17,19)(16,20,21,18)190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236729);