Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C3×C42×#170 |
| derived, Sylow | C5 ⋊ C3×C42×C8 |
| Hall | C3×C5 ⋊ C42×C8 |
816 conjugacy classes of subgroups; only the 516 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 516 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1920 |
480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 19888);