Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #65690⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10604188⋊C3 |
| derived | C42×C5 ⋊ C3×C8 |
| Hall | #10604188 ⋊ C3 |
| Sylow | C5 ⋊ #1839⋊C3 |
120 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 120 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:
2,3,2^4,5,2^2|a^2=c,c^2=d,e^2=h,f^2=i,e^a=ehi,f^a=fh,g^a=g^2,e^b=ef,f^b=ei,h^b=hi,i^b=h,g^c=g^456 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237297);