Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊(Dic25⋊C5) |
| unambiguous semidirect product | (C22⋊Dic25)⋊C5 |
| Sylow | 5−1+2 ⋊ C22⋊C4 |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^2,5,2^2,5^2|a^2=e,f^5=g,b^a=bd,f^a=f^4g^4,g^a=g^4,f^c=fg^4146 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊C4×D25⋊C5, #72275633, #72275637, … |
| maximal normal subgroup of | C22⋊C4×D25⋊C5, #72275633, #72275637, … |
| maximal quotient of | #72275769, #72275770, #72275800 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 177);