Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#92539 |
| Fitting | C4×H(3,𝔽5) ⋊ C4 |
| Sylow | H(3,𝔽5) ⋊ C4⋊C4 |
123 conjugacy classes of subgroups.
| transitive degree | μt(G) = 100 |
Polycyclic presentation:
2^4,5^3|a^2=c,b^2=d,b^a=bd,e^a=e^3,f^a=f^2,e^c=e^4,f^c=f^4,f^e=fg74 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 344);