Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22×C5 |
| unambiguous semidirect product | #87808⋊C5 |
| Fitting | C2×C4×H(3,𝔽5) ⋊ C2 |
| Sylow | H(3,𝔽5) ⋊ C22⋊C4 |
151 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 151 conjugacy classes of subgroups — too many to draw. Only its 40 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:
2^2,5,2^2,5^2|b^2=d,b^a=be,f^a=f^4,g^a=g^4,f^c=fg146 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 151);