Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q32×ΓL(1,𝔽16) |
| Fitting | C3×C5×Q32 ⋊ C4 |
| Hall | C3×C5 ⋊ C4×Q32 |
| Sylow | C5 ⋊ Dic3×Q32 |
| Sylow | C3 ⋊ AGL(1,𝔽5)×Q32 |
300 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
99 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 41128);