Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | D3×ΓL(1,𝔽81) |
| Fitting | C3×C5×C16 ⋊ C2×C4 |
| Hall | C3×C5 ⋊ C2×#365 |
| Sylow | C5 ⋊ D3×#365 |
| Sylow | C3 ⋊ C2×ΓL(1,𝔽81) |
304 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 40191);