Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C5×#551 ⋊ C4 |
| Sylow | C5 ⋊ #34457 |
2500 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=h,b^2=f,d^2=h,b^a=bf,c^a=cg,d^a=dg,e^a=ef,i^a=i^3,c^b=cg,d^b=df,i^d=i^2,i^h=i^4101 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3532, #72242932, #72242943 |
| maximal normal subgroup of | AGL(1,𝔽5)×#3532, #72242932, #72242943 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114568);