Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of D5⋊#1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D25⋊#170 |
| derived, Sylow | C5×C25 ⋊ C2×C8 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^4,5^3|a^2=c,b^2=d,c^2=d,f^5=g,e^a=e^2,f^a=f^2g,g^a=g^2,e^b=e^4,e^c=e^4,f^c=f^4g^4,g^c=g^468 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 256);