Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C22×C8 |
No aliases for this group.
| Fitting | C5×C82 ⋊ C4 |
| Sylow | C5 ⋊ #7846 |
582 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=d,b^2=e,c^2=f,d^2=g,e^2=h,c^a=cg,c^b=ch,i^c=i^2,i^f=i^4176 conjugacy classes — view the full character table.
| maximal subgroup of | #72221097, #72221433, #72221441, … |
| maximal normal subgroup of | #72221433, #72221441, AGL(1,𝔽5)×#1455, … |
| maximal quotient of | #72221097 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1085534);