Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#73117 |
| Fitting | C22×C5×M16 ⋊ D3 |
378 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 52 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) = 120 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,3,4,5)(6,7,9)(10,12,13,11,14,15,17,16);(7,8)(10,11)(12,17)(13,15)(14,16)190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236539);