Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#11719908 |
| 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^52,c^b=ce1096 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×Q8⋊C16, C2×Q8⋊#11719908, #27293893, … |
| maximal normal subgroup of | D53×Q8⋊C16, C2×Q8⋊#11719908, #27293893, … |
| maximal quotient of | #27270874, #27270904, #27270996, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2489);