Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D5×#120⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | Dic5×#120⋊C3 |
| unambiguous semidirect product | (Dic5×#120)⋊C3 |
| derived | C24×C5 ⋊ C2×C3×C4 |
| Hall | Dic5×#120 ⋊ C3 |
| Sylow | C5 ⋊ C4×#120⋊C3 |
508 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237939);