Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| unambiguous semidirect product | D5⋊#1913 |
| Fitting | C5×#534 ⋊ C4 |
| Sylow | C5 ⋊ C2×#1913 |
2078 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=eg,b^a=be,c^a=cf,e^a=eh,f^a=fh,i^a=i^3,e^b=eh,f^b=fh,g^b=gh,i^b=i^2,e^c=eh,g^c=gh,i^d=i^4,i^g=i^480 conjugacy classes — view the full character table.
| maximal subgroup of | #72221422, #72221752, #72242832, … |
| maximal normal subgroup of | #72221422, #72242832, AGL(1,𝔽5)×#1913, … |
| maximal quotient of | #72221752 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1105351);