Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #4133⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | C4×#4133⋊C3 |
| unambiguous semidirect product | (C4×#4133)⋊C3 |
| Hall | C4×#4133 ⋊ C3 |
| Sylow | C5 ⋊ C4×#131⋊C3 |
314 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238216);