Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D4⋊#6016 |
| Sylow | C25 ⋊ D4⋊C8 |
123 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 123 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^6,5^2|a^2=c,c^2=f,d^2=e,g^5=h,b^a=bd,d^a=de,g^a=g^2h,h^a=h^2,d^b=de,g^c=g^4h^4,h^c=h^488 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 259);