Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4×C5 |
No aliases for this group.
| Fitting | C52×C8 ⋊ Q8 |
| Sylow | C52 ⋊ #498 |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=d,c^2=e,e^2=f,b^a=bd,g^a=gh,h^a=g^3h^4,c^b=ce,e^b=ef,g^b=g^3h^3,h^b=h^2,g^d=g^4,h^d=h^446 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6750);