Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#87707 |
| Sylow | C25 ⋊ C4⋊C16 |
75 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1600 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=c,d^2=e,e^2=f,g^5=h,b^a=bc,g^a=g^4h^4,h^a=h^4424 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 18);