Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#535 ⋊ C4 |
| Sylow | C5 ⋊ #10997 |
1630 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,d^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^2,c^b=cf,d^b=dh,e^b=eh,d^c=dh,i^g=i^474 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2002, #72221412, #72221468, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#2002, #72221412, #72221468 |
| maximal quotient of | #72226455 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1092715);