Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | AGL(1,𝔽5)×#826 |
| Fitting | C3×C5×D8 ⋊ C2×C4 |
| Hall | C3×C5 ⋊ C4×D16 |
| Sylow | C5 ⋊ C4×#826 |
| Sylow | C3 ⋊ AGL(1,𝔽5)×D16 |
348 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 41038);