Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #87722⋊C5 |
| Fitting | D4×5−1+2 ⋊ C2 |
| Sylow | 5−1+2 ⋊ D8 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^2,5,2^2,5^2|d^2=e,f^5=g,b^a=bd,d^a=de,f^a=f^4g^4,g^a=g^4,d^b=de,f^c=fg^495 conjugacy classes — view the full character table.
| maximal subgroup of | D8×D25⋊C5, #72275751, #72275753, … |
| maximal normal subgroup of | D8×D25⋊C5, #72275751, #72275753, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 165);