Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D25⋊M16 |
| Sylow | C25 ⋊ C2×M16 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^5,5^2|a^2=d,b^2=e,d^2=e,f^5=g,c^a=ce,f^a=f^2g,g^a=g^2,f^d=f^4g^4,g^d=g^468 conjugacy classes — view the full character table.
| maximal subgroup of | #13097848, #13097849, #13097879, … |
| maximal normal subgroup of | #13097848, #13097849, #13097879, … |
| maximal quotient of | #13098665, C4×#87735, D25⋊(C4⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 205);