Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4×C5 |
No aliases for this group.
| Fitting | C52×C22⋊C4 ⋊ C2 |
| Sylow | C52 ⋊ #124 |
304 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|b^2=d,b^a=be,c^a=cde,f^a=f^4,g^a=g^4,c^b=ce134 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4031, #13105127, #13105129, … |
| maximal normal subgroup of | D5×#4031, #13105127, #13105129, … |
| maximal quotient of | #13102511, #13102514, #13102520, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 864);