Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C25×C32 ⋊ C2 |
| Sylow | C25 ⋊ SD64 |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^6,5^2|b^2=cdf,c^2=de,d^2=ef,e^2=f,g^5=h,b^a=bc,c^a=cd,d^a=de,e^a=ef,g^a=g^4h^4,h^a=h^4403 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6);