Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C5 |
No aliases for this group.
| Fitting | C52×C22⋊C4 ⋊ C2 |
| Sylow | C52 ⋊ C4×D4 |
376 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 109 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|c^2=d,b^a=be,f^a=f^4,g^a=g^4,c^b=ce140 conjugacy classes — view the full character table.
| maximal subgroup of | #13104704, #13104705, #13104706, … |
| maximal normal subgroup of | #13104704, #13104705, #13104706, … |
| maximal quotient of | #13102509, #13102513, #13102515, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 860);