Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#518 ⋊ C4 |
| Sylow | C5 ⋊ #10785 |
1394 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=g,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,g^a=gh,i^a=i^2,d^b=dh,f^b=fh,e^c=eh,f^c=fh,i^f=i^492 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1904, #72221404, #72221450, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#1904, #72221404, #72221450 |
| maximal quotient of | #72226469 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1092135);