Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C5×AGL(1,ℤ/8) ⋊ C4 |
| Sylow | C5 ⋊ #11030 |
1422 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,i^a=i^2,c^b=cf,d^b=dh,f^b=fh,f^c=fh,g^c=gh,i^g=i^468 conjugacy classes — view the full character table.
| maximal subgroup of | #72221394, #72221402, AGL(1,𝔽5)×#2008, … |
| maximal normal subgroup of | #72221394, #72221402, AGL(1,𝔽5)×#2008, … |
| maximal quotient of | #72223425 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1092764);