Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #65800⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #10605025⋊C3 |
| derived | C24×C5 ⋊ C3×C8 |
| Hall | #10605025 ⋊ C3 |
| Sylow | C5 ⋊ #1779⋊C3 |
344 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2,3,2^6,5|a^2=c,c^2=d,e^a=eg,f^a=fgh,i^a=i^2,e^b=ef,f^b=e,g^b=h,h^b=gh,i^c=i^456 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237305);