Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#92536 |
| Fitting | C4×C5×C25 ⋊ C4 |
| Sylow | C5×C25 ⋊ C4⋊C4 |
182 conjugacy classes of subgroups.
| transitive degree | μt(G) = 500 |
Polycyclic presentation:
2^4,5^3|a^2=c,b^2=d,f^5=g,b^a=bd,e^a=e^2,f^a=f^2g,g^a=g^2,e^c=e^4,f^c=f^4g^4,g^c=g^4134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 326);