Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊(#1043⋊C5) |
| unambiguous semidirect product | (C22⋊#1043)⋊C5 |
| Fitting | C22×H(3,𝔽5) ⋊ C4 |
| Sylow | H(3,𝔽5) ⋊ C22⋊C4 |
129 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
Polycyclic presentation:
2^2,5,2^2,5^2|a^2=d,b^a=be,f^a=f^2,g^a=g^2,f^c=fg,f^d=f^4,g^d=g^474 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 298);