Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C5×#535 ⋊ C4 |
| Sylow | C5 ⋊ #34265 |
3586 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=h,b^2=h,c^2=h,d^2=f,b^a=bf,c^a=cg,e^a=ef,i^a=i^3,d^b=df,i^b=i^3,i^c=i^2,i^h=i^4110 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3484, #72221409, #72221417, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3484, #72221409, #72221417, … |
| maximal quotient of | #72223244, #72269428 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1114376);