Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of (#126⋊C3)⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (#126⋊C3)⋊Dic5 |
| unambiguous semidirect product | #10614807⋊C3 |
| derived | C42×C5 ⋊ C2×C3×C4 |
| Hall | #10614807 ⋊ C3 |
| Sylow | C5 ⋊ (#126⋊C3)⋊C4 |
232 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^2,3,2^3,5,2^2|a^2=d,e^2=h,f^2=hi,e^a=eh,f^a=fhi,g^a=g^4,e^b=ehi,f^b=fi,e^c=ef,f^c=ehi,h^c=i,i^c=hi74 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237945);