Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×C5×C22⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ #12795 |
600 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=d,b^a=bd,c^a=ce,e^a=eg,g^a=gh,i^a=i^2,c^b=ch,f^c=fg,i^c=i^4,f^e=fh,i^f=i^474 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1096647);