Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4 |
No aliases for this group.
| Fitting | C5×#381 ⋊ C4 |
| Sylow | C5 ⋊ #13776 |
2318 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=h,c^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,i^b=i^2,i^h=i^4116 conjugacy classes — view the full character table.
| maximal subgroup of | #72269428, AGL(1,𝔽5)×#2308 |
| maximal normal subgroup of | #72269428, AGL(1,𝔽5)×#2308 |
| maximal quotient of | #72269862 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1098213);