Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C5 |
| unambiguous semidirect product | C22⋊#92560 |
| Fitting | C22×C53 ⋊ C4 |
| Sylow | C53 ⋊ C22⋊C4 |
260 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^4,5^3|a^2=c,b^a=bd,e^a=e^3,f^a=f^2,g^a=g^4,e^c=e^4,f^c=f^4146 conjugacy classes — view the full character table.
| maximal subgroup of | D5×C22⋊#1044, #72259195, #72259205 |
| maximal normal subgroup of | D5×C22⋊#1044, #72259195, #72259205 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 799);