Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C25 ⋊ #108 |
45 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|a^2=d,b^2=c,c^2=e,d^2=e,f^5=g,b^a=bd,f^a=f^4g^4,g^a=g^4,d^b=de134 conjugacy classes — view the full character table.
| maximal subgroup of | #13098023, #13098024, #13098029, … |
| maximal normal subgroup of | #13098023, #13098024, #13098029, … |
| maximal quotient of | #13097685, #13097686, #13097760, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 29);