Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#10603925 |
| Fitting | C3×C5×#100 ⋊ C4 |
| Hall | C3×C5 ⋊ #1856 |
| Sylow | C5 ⋊ C3×#1856 |
648 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 136 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
129 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽5)×#453, D3×#10603925, #72230884 |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×#453, D3×#10603925, #72230884 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 25279);