Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C5⋊D25)⋊Q8 |
| Sylow | C5×C25 ⋊ C2×Q8 |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^4,5^3|a^2=d,b^2=d,c^2=d,e^5=g,c^a=cd,e^a=e^4g^4,g^a=g^4,c^b=cd,f^b=f^4176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 354);