Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#85302 |
638 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 108 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) = 480 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3,4,5)(6,8,9,7)(10,11,13)(16,20)(18,21);(14,16,17,20)(15,18,19,21);(6,7,9,8)(11,12)(14,15,17,19)(16,18,20,21)250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236738);