Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22×C5 |
| unambiguous semidirect product | C22⋊#6029 |
| Sylow | C52 ⋊ C22⋊C8 |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|a^2=c,c^2=e,b^a=bd,f^a=f^4,g^a=g^4212 conjugacy classes — view the full character table.
| maximal subgroup of | #13099315, #13099317, #13099319, … |
| maximal normal subgroup of | #13099315, #13099317, #13099319, … |
| maximal quotient of | #13099558, #13099559, #13099562, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 356);