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×#444 ⋊ 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,e^b=eh,i^b=i^3,d^c=dh,i^c=i^2,i^g=i^4110 conjugacy classes — view the full character table.
| maximal subgroup of | #72221465, AGL(1,𝔽5)×#2956, #72223077, … |
| maximal normal subgroup of | #72221465, AGL(1,𝔽5)×#2956, #72258413 |
| maximal quotient of | #72223077, #72223438 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1104083);