Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4 |
No aliases for this group.
| Fitting | C5×#386 ⋊ C4 |
| Sylow | C5 ⋊ #14064 |
2330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=h,b^2=eh,d^2=g,b^a=be,c^a=cf,d^a=de,i^a=i^3,c^b=cg,i^b=i^2,i^h=i^4104 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2404, #72269422, #72269428 |
| maximal normal subgroup of | AGL(1,𝔽5)×#2404, #72269422, #72269428 |
| maximal quotient of | #72269840, #72269854 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1098559);