Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C52 ⋊ #117 |
186 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^5,5^2|a^2=d,b^2=e,c^a=ce,f^a=f^3,g^a=g^3,f^b=f^4,f^d=f^4,g^d=g^444 conjugacy classes — view the full character table.
| maximal subgroup of | #13103290, #13104007, #13104123, … |
| maximal normal subgroup of | #13103290, #13104007, #13104123, … |
| maximal quotient of | #13103881, #13103891, #13103897, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1026);