Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#85346 |
| Fitting | C4×C5×#41 ⋊ D3 |
658 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 658 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) = 25 |
| transitive degree | μt(G) = 320 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,3,4,5)(10,22,19,15,20,25,14,16,21,11,12,24)(13,17,18,23);(6,7,8,9);(7,9)(11,15)(12,18)(13,20)(16,17)(19,21)(22,23)200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236782);