Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C5×#577 ⋊ C4 |
| Sylow | C5 ⋊ #60174 |
2734 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=g,c^2=g,f^2=h,b^a=bf,c^a=ch,f^a=fh,i^a=i^3,f^b=fh,i^c=i^2,e^d=eh,i^g=i^4104 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3585, #72221465, #72221480, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3585, #72221465, #72221480 |
| maximal quotient of | #72222999, #72223003, #72223398, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1115021);