Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C26 |
| direct product | C3×#10605017 |
| Fitting | C3×C5×H(5,𝔽2) ⋊ C4 |
| Hall | C3×C5 ⋊ #1790 |
| Sylow | C5 ⋊ C3×#1790 |
1340 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 1340 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
147 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽5)×B(4,𝔽2), D3×#10605017, #72230802, … |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×B(4,𝔽2), D3×#10605017, #72230802 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 22835);