Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D5⋊(C4⋊#168) |
| Sylow | C52 ⋊ C2×C4⋊C8 |
291 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 291 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=f,c^2=e,d^2=f,c^a=ce,g^a=g^2,h^a=h^4,g^d=g^4184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6916);