Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #548⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C2×C5×#557⋊C3 |
| unambiguous semidirect product | (C2×#557)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C5×#557)⋊C3 |
| Fitting, Hall | C2×C5×#557 ⋊ C3 |
| Sylow | C2×#557 ⋊ C3×C5 |
566 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
350 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237034);