Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C5 |
No aliases for this group.
| Sylow | C52 ⋊ #97 |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^2=d,d^2=e,b^a=be,f^a=f^4,g^a=g^4212 conjugacy classes — view the full character table.
| maximal subgroup of | #13099276, #13099546, #13100267, … |
| maximal normal subgroup of | #13099276, #13099546, #13100267, … |
| maximal quotient of | #13099488, #13099489, #13099546, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 341);