Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #87720⋊C5 |
| Fitting | C2×C4×5−1+2 ⋊ C2 |
| Sylow | 5−1+2 ⋊ C22⋊C4 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^2,5,2^2,5^2|b^2=d,f^5=g,b^a=be,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, #72275639 |
| maximal normal subgroup of | C22⋊C4×D25⋊C5, #72275633, #72275639 |
| maximal quotient of | #72275768, #72275771, #72275803, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 157);