Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C25 ⋊ SD32 |
39 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|a^2=e,c^2=de,d^2=e,f^5=g,b^a=bc,c^a=cd,d^a=de,f^a=f^4g^4,g^a=g^4,c^b=cd,d^b=de95 conjugacy classes — view the full character table.
| maximal subgroup of | #13098186, #13098187, SD32×D25, … |
| maximal normal subgroup of | #13098186, #13098187, SD32×D25, … |
| maximal quotient of | #13097696, #13097698, #13097768, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 34);