Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C52 ⋊ C22⋊C16 |
180 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^6,5^2|a^2=c,b^2=f,c^2=e,e^2=f,b^a=bd,g^a=h,h^a=g^2,g^c=g^2,h^c=h^2,g^e=g^4,h^e=h^464 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5761);