Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×H(3,ℤ/4) ⋊ C4 |
| Sylow | C5 ⋊ #11335 |
790 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 790 conjugacy classes of subgroups — too many to draw. Only its 154 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:
2^8,5|a^2=g,b^2=d,c^2=e,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^2,c^b=cf,e^b=eh,d^c=dh,i^g=i^474 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2010, #72221404, #72221417, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#2010, #72221404, #72221417, … |
| maximal quotient of | #72226407 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1093142);