Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D25⋊(C4⋊C8) |
| Sylow | C25 ⋊ C2×C4⋊C8 |
207 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 207 conjugacy classes of subgroups — too many to draw. Only its 83 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=d,b^2=f,c^2=e,d^2=f,g^5=h,c^a=ce,g^a=g^2h,h^a=h^2,g^d=g^4h^4,h^d=h^4136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 1019);