Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C52 ⋊ C2×M16 |
144 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 48 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,b^2=e,c^2=e,d^2=e,c^a=ce,g^a=g^2,f^b=f^4,g^d=g^456 conjugacy classes — view the full character table.
| maximal subgroup of | #13103259, #13103262, #13103454, … |
| maximal normal subgroup of | #13103259, #13103262, #13103454, … |
| maximal quotient of | #13103477, #13103480, #13103485, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 990);