Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×B(4,𝔽2) ⋊ C4 |
| Sylow | C5 ⋊ #13041 |
964 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 964 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=df,b^a=bd,c^a=ce,e^a=eg,g^a=gh,i^a=i^3,e^b=egh,i^b=i^2,d^c=dg,f^c=fg,e^d=eh,f^e=fh,i^f=i^456 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2196, #72242862, #72242878, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#2196, #72242862, #72242878, … |
| maximal quotient of | #72242770 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1097168);