Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#85391 |
| Fitting | C5×D4×Q8 ⋊ D3 |
550 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 550 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) = 320 |
A minimal faithful permutation representation — 3 generators on 25 points:
(1,2,3,4,5)(7,9)(10,20,22)(11,16,25,15,21,24)(12,19,14)(17,18);(6,7)(8,9);(10,11,14,15)(12,18,20,17)(13,21,23,16)(19,25,22,24)170 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236827);