Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#11719910 |
| Sylow | C53 ⋊ Q8⋊C16 |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=e,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^30,c^b=ce,h^d=h^52316 conjugacy classes — view the full character table.
| maximal subgroup of | C2×Q8⋊#11719910, D53⋊(Q8⋊C16), #28308526, … |
| maximal normal subgroup of | C2×Q8⋊#11719910, D53⋊(Q8⋊C16), #28308526, … |
| maximal quotient of | #28298217, #28298237, #28298351, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19476);