Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#413 ⋊ C4 |
| Sylow | C5 ⋊ #10746 |
1246 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^3,e^b=eh,f^b=fh,i^b=i^2,d^c=dh,i^f=i^4,i^g=i^486 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1891, #72221454, #72221457, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#1891, #72221454, #72221457 |
| maximal quotient of | #72221703, #72226447 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1092014);