Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C8 |
No aliases for this group.
| Fitting | C5×C82 ⋊ C4 |
| Sylow | C5 ⋊ #8813 |
486 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=d,c^2=e,d^2=g,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^2,i^f=i^4140 conjugacy classes — view the full character table.
| maximal subgroup of | #72221169, #72221433, #72221445, … |
| maximal normal subgroup of | #72221433, #72221445, AGL(1,𝔽5)×#1705, … |
| maximal quotient of | #72221169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1089072);