Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#85301 |
| Fitting | C22×C5×C22⋊C4 ⋊ D3 |
768 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 88 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)(16,21);(14,16)(15,18)(17,21)(19,20);(7,9)(11,12)(14,15)(16,20)(17,19)(18,21)190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236737);