Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C5×#469 ⋊ C4 |
| Sylow | C5 ⋊ #21536 |
1066 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=eh,d^2=g,e^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^3,c^b=ch,d^c=dh,i^d=i^2,i^g=i^480 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3058, AGL(1,𝔽5)×#3060, #72242608, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3058, AGL(1,𝔽5)×#3060 |
| maximal quotient of | #72242608, #72242643, #72253315, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1106618);