Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22×C4×C25 ⋊ C2 |
| Sylow | C25 ⋊ #123 |
117 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|c^2=e,f^5=g,b^a=be,c^a=cd,f^a=f^4g^4,g^a=g^4206 conjugacy classes — view the full character table.
| maximal subgroup of | #13097899, #13098328, #13098802, … |
| maximal normal subgroup of | #13097899, #13098328, #13098802, … |
| maximal quotient of | #13098207, #13098215, #13098225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 150);