Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#85305 |
510 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 510 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) = 25 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,3,4,5)(6,7,9)(11,15)(12,16)(18,20,21,25)(19,22,23,24);(10,12,13,16)(11,14,15,17);(7,8)(10,11)(12,14)(13,15)(16,17)(18,19,21,23)(20,24,25,22)190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236741);