Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C2×C5×AGL(1,ℤ/8) ⋊ C4 |
| Sylow | C5 ⋊ #21249 |
1562 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=eg,c^2=f,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^3,e^b=eh,g^b=gh,i^b=i^2,d^c=dh,i^g=i^480 conjugacy classes — view the full character table.
| maximal subgroup of | #72221478, AGL(1,𝔽5)×#3068, #72221552, … |
| maximal normal subgroup of | #72221478, AGL(1,𝔽5)×#3068, #72221552 |
| maximal quotient of | #72223544, #72226392, #72226581 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1105871);