Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C5×C4⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ #11877 |
644 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 80 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=e,c^2=gh,d^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fh,i^a=i^2,c^b=cfh,d^b=dg,e^b=efg,i^b=i^4,d^c=dh,i^c=i^4,e^d=eh,i^e=i^477 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1094953);