Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ C4×D4 |
196 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^5,5^2|a^2=d,c^a=ce,g^a=g^2,c^b=ce,f^b=f^4,g^d=g^453 conjugacy classes — view the full character table.
| maximal subgroup of | #13107617, #13107620, D4×D5×AGL(1,𝔽5), … |
| maximal normal subgroup of | #13107617, #13107620, D4×D5×AGL(1,𝔽5), … |
| maximal quotient of | #13103605, #13103609, #13103612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1011);