Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of ΓL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C42×C3⋊#170 |
| derived, Hall | C3×C5 ⋊ C42×C8 |
| Sylow | C5 ⋊ C42×C3⋊C8 |
| Sylow | C3 ⋊ C42×#170 |
816 conjugacy classes of subgroups; only the 441 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 441 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1920 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 19889);