Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| unambiguous semidirect product | D5⋊(C22⋊AGL(1,𝔽5)) |
| Fitting | C22×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ C2×C22⋊C4 |
298 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 57 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:
2^5,5^2|a^2=d,c^a=ce,f^a=f^3,g^a=g^3,f^b=f^4,f^d=f^4,g^d=g^444 conjugacy classes — view the full character table.
| maximal subgroup of | #13103284, D5⋊#3999, D5⋊#4011, … |
| maximal normal subgroup of | #13103284, D5⋊#3999, D5⋊#4011, … |
| maximal quotient of | #13103981, #13103988, D5⋊#3999, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1035);