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 ⋊ #11004 |
1462 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,d^2=h,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fh,i^a=i^2,c^b=cf,d^b=dh,d^c=dh,e^c=eh,g^c=gh,i^g=i^468 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2008, #72221409, #72221418, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#2008, #72221409, #72221418, … |
| maximal quotient of | #72226458 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1092724);