Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#87524 |
| Fitting | C26×C5 ⋊ D3 |
1652 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 1652 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 60 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,3,4,5)(6,12,14)(7,11,16,10,15,13)(8,9,17);(6,10,8,7)(9,16)(11,17,15,14)(12,13)140 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#87524, C5×#11713200, #72243415, … |
| maximal normal subgroup of | D5×#87524, C5×#11713200, #72243415 |
| maximal quotient of | C5×AGL(2,ℤ/4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237156);