Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊D25 |
| Sylow | C5×C25 ⋊ C22⋊C4 |
112 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^4,5^3|b^2=c,f^5=g,b^a=bd,f^a=f^4g^4,g^a=g^4,e^b=e^2,e^c=e^4134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 241);