Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| isoclinism | isoclinic class of #66297 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | ((C24⋊C5)⋊C2)⋊C8 |
| derived | C24⋊C5 ⋊ C2×C8 |
265 conjugacy classes of subgroups; only the 17 normal subgroups are shown.
This group has 265 conjugacy classes of subgroups — too many to draw. Only its 17 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^2,5,2^6|a^2=b,b^2=i,h^2=i,c^a=c^2,d^a=de,e^a=fg,f^a=e,c^b=c^4,d^b=defg,e^b=eg,f^b=fg,d^c=g,e^c=dg,f^c=deg,g^c=defg44 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1116367);