Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#472 ⋊ C4 |
| Sylow | C5 ⋊ #23046 |
896 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=egh,d^2=eh,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^3,d^b=de,e^b=eh,g^b=gh,i^b=i^2,f^c=fh,i^g=i^474 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3292, #72221465, #72221514, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3292, #72221465, #72221514 |
| maximal quotient of | #72223127, #72223465, #72223522 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1111828);