Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#73048 |
| Fitting | C22×C42×C5 ⋊ D3 |
334 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 30 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)(7,9)(10,11,18)(12,15,14)(13,16,20)(17,21,19);(6,7)(8,9)(11,14)(15,20)(16,19)(18,21)140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236470);