Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#85380 |
| Fitting | C5×#548 ⋊ D3 |
610 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 160 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,3,4,5)(7,9)(10,24,19,17,20,25,14,15,21,11,12,23)(13,16,18,22);(6,7)(8,9);(12,18)(13,20)(15,22)(16,24)(19,21)(23,25)200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236816);