Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #10617729⋊C3 |
| Hall | #10617729 ⋊ C3 |
| Sylow | C5 ⋊ #3503⋊C3 |
530 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^3,3,2^3,5,2|a^2=e,b^2=e,c^2=i,f^2=i,g^2=i,b^a=be,c^a=ci,h^a=h^4,f^d=fg,g^d=f,g^f=gi164 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239725);