Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C5×#85307 |
| Fitting | C22×C5×C4⋊C4 ⋊ D3 |
690 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 104 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)(6,7,8,9)(10,11,13)(15,19)(16,20);(14,16,17,20)(15,18,19,21);(11,12)(14,15)(16,18)(17,19)(20,21)250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236743);