Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#85344 |
| Fitting | C4×C5×#41 ⋊ D3 |
556 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 80 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)(10,24,19,17,20,25,14,15,21,11,12,23)(13,16,18,22);(6,7,8,9);(7,9)(12,18)(13,20)(15,22)(16,24)(19,21)(23,25)230 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236780);