Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#476 ⋊ C4 |
| Sylow | C5 ⋊ #8973 |
664 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=df,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=ce,i^a=i^3,d^b=dg,e^b=eh,f^b=fg,i^b=i^2,d^c=dh,e^c=eh,f^c=fh,i^f=i^471 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1629 |
| maximal normal subgroup of | AGL(1,𝔽5)×#1629 |
| maximal quotient of | #72221529, #72221542 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1089504);