Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#568 ⋊ C4 |
| Sylow | C5 ⋊ #20679 |
1330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=e,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^2,d^b=dh,f^c=fh,g^c=gh,i^g=i^492 conjugacy classes — view the full character table.
| maximal subgroup of | #72221478, #72221485, AGL(1,𝔽5)×#3068, … |
| maximal normal subgroup of | #72221478, #72221485, AGL(1,𝔽5)×#3068 |
| maximal quotient of | #72223506, #72226382, #72226575 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1104605);