Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22×C5 |
| unambiguous semidirect product | C22⋊#87765 |
| Sylow | C52 ⋊ C22⋊C16 |
208 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 60 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:
2^6,5^2|a^2=c,c^2=e,e^2=f,b^a=bd,g^a=g^3,h^a=h^2,g^c=g^4,h^c=h^4136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 2737);