Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D5⋊#4625 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D5⋊#4625 |
| unambiguous semidirect product | #11751559⋊C2 |
| Fitting | C5×#120 ⋊ Dic3 |
| derived | C5×C22⋊A4 ⋊ C2×C4 |
| Sylow | C5 ⋊ C2×#4625 |
282 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 282 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) = 80 |
Polycyclic presentation:
2^3,3,5,2^4|a^2=c,d^a=d^2,e^a=e^2,f^a=fgh,g^a=ghi,h^a=hi,f^b=fh,g^b=gi,e^c=e^4,f^c=fh,g^c=gi,f^d=g,g^d=fg,h^d=i,i^d=hi32 conjugacy classes — view the full character table.
| maximal subgroup of | #72221428, AGL(1,𝔽5)×#4625, #72253380, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#4625, #72253380, #72253396 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 238152);