Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | #127×ΓL(1,𝔽16) |
| Fitting | C3×C5×#127 ⋊ C4 |
| Hall | C3×C5 ⋊ C4×#127 |
| Sylow | C5 ⋊ Dic3×#127 |
| Sylow | C3 ⋊ AGL(1,𝔽5)×#127 |
1848 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 1848 conjugacy classes of subgroups — too many to draw. Only its 341 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
126 conjugacy classes — view the full character table.
| maximal subgroup of | D3×AGL(1,𝔽5)×#127, ΓL(1,𝔽16)×#453, #72230866, … |
| maximal normal subgroup of | D3×AGL(1,𝔽5)×#127, ΓL(1,𝔽16)×#453, #72230866 |
| maximal quotient of | #127×C3⋊#1043, #127×C3⋊ΓL(1,𝔽16) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 47956);