Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C5×#443 ⋊ C4 |
| Sylow | C5 ⋊ #20512 |
1014 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=g,c^2=g,d^2=f,e^2=h,f^2=h,b^a=be,e^a=eh,i^a=i^3,e^b=eh,i^b=i^3,d^c=dh,i^c=i^3,i^d=i^2,i^f=i^4,i^g=i^4116 conjugacy classes — view the full character table.
| maximal subgroup of | #72221472, #72221480, AGL(1,𝔽5)×#2956, … |
| maximal normal subgroup of | #72221472, #72221480, AGL(1,𝔽5)×#2956, … |
| maximal quotient of | #72223043, #72223444 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1104087);