Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C52 ⋊ C4×D4 |
218 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^5,5^2|b^2=d,c^2=e,c^a=ce,g^a=g^4,c^b=ce,f^b=f^492 conjugacy classes — view the full character table.
| maximal subgroup of | #13099878, #13099879, #13100614, … |
| maximal normal subgroup of | #13099878, #13099879, #13100614, … |
| maximal quotient of | #13100508, #13100509, #13100519, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 676);