Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#85325 |
| Fitting | C2×C4×C5×Q8 ⋊ D3 |
556 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 320 |
A minimal faithful permutation representation — 3 generators on 21 points:
(1,2,3,4,5)(7,11)(10,13)(14,20,21)(15,19,17);(6,8,9,12)(7,10,11,13);(6,7)(8,10)(9,11)(12,13)(15,18)(16,20)(19,21)230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236761);