Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#72989 |
354 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 28 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)(6,8,9,13)(7,10,11,12)(14,18,16,19,17,15)(20,21);(6,7,9,11)(8,12,13,10)(16,21)(18,19)110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236411);