Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C22 |
| direct product | C5×SL(2,ℤ/4)⋊C8 |
| unambiguous semidirect product | SL(2,ℤ/4)⋊(C5×C8) |
326 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 68 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 — 2 generators on 21 points:
(1,2,3,4,5)(7,9)(10,11,13)(14,15,16,18,17,19,20,21);(6,7,8,9)(11,12)280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236529);