Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#364 ⋊ C4 |
| Sylow | C5 ⋊ #7179 |
274 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=d,b^2=e,c^2=fh,d^2=g,e^2=fg,f^2=h,g^2=h,b^a=bc,c^a=cf,e^a=efh,f^a=fh,i^b=i^2,i^e=i^4116 conjugacy classes — view the full character table.
| maximal subgroup of | #72221496, AGL(1,𝔽5)×#1335, #72221529, … |
| maximal normal subgroup of | #72221496, AGL(1,𝔽5)×#1335, #72221529, … |
| maximal quotient of | #72223150 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1083865);