Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C5×#120 ⋊ C4 |
| Sylow | C5 ⋊ #10991 |
3122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,b^a=bd,c^a=ce,d^a=dh,f^a=fh,i^a=i^2,c^b=cf,e^b=eh,g^b=gh,i^g=i^480 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2021, #72242740, #72242743, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#2021, #72242740, #72242743, … |
| maximal quotient of | #72242770, #72242787 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1092708);