Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C52 ⋊ #421 |
308 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 45 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:
2^6,5^2|b^2=def,d^2=f,e^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^4,h^a=g^2h,c^b=cf,g^b=g^3h^3,h^b=h^2,g^d=g^4,h^d=h^482 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6574);