Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C5×AGL(1,ℤ/8) ⋊ C4 |
| Sylow | C5 ⋊ #60168 |
2882 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,c^2=g,f^2=h,b^a=bf,e^a=eh,f^a=fh,i^a=i^3,f^b=fh,d^c=dh,i^c=i^2,i^g=i^4104 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3585, #72221394, #72221402, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3585, #72221394, #72221402, … |
| maximal quotient of | #72223001, #72223011, #72223026, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1115015);