Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C52 ⋊ #117 |
160 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 50 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^a=ce,g^a=g^2,f^b=f^4,g^d=g^456 conjugacy classes — view the full character table.
| maximal subgroup of | #13103288, #13103289, #13103637, … |
| maximal normal subgroup of | #13103288, #13103289, #13103637, … |
| maximal quotient of | #13103473, #13103480, #13103487, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 998);