Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C25 ⋊ #126 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|a^2=e,b^2=d,f^5=g,c^a=cde,f^a=f^4g^4,g^a=g^4,c^b=ce134 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11716441, #13098817, #13098818, … |
| maximal normal subgroup of | C2×#11716441, #13098817, #13098818, … |
| maximal quotient of | #13097928, #13097929, #13097934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 100);