Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#85424 |
| Fitting | C5×#557 ⋊ D3 |
418 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 29 points:
(1,2,3,4,5)(6,8,9,13)(7,10,11,12)(14,26,23,19,24,29,18,20,25,15,16,28)(17,21,22,27);(6,7,9,11)(8,12,13,10);(15,19)(16,22)(17,24)(20,21)(23,25)(26,27)170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236860);