Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×C4⋊#859 |
| unambiguous semidirect product | C4⋊(C5×#859) |
350 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 640 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,4,5)(10,11,12,13)(14,20,21)(15,19,17);(6,7,8,9)(11,13)(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, 236482);