Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #857⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #857⋊Dic5 |
| derived | C5×C42⋊C3 ⋊ C2×C4 |
| Sylow | C5 ⋊ #857⋊C4 |
294 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 27 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:
2^3,3,5,2^4|a^2=c,f^2=h,g^2=i,e^a=e^4,f^a=fh,g^a=gi,d^b=d^2,f^b=fgi,g^b=gi,h^b=hi,f^d=gh,g^d=fg,h^d=i,i^d=hi68 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237325);