Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C53×#367 ⋊ C2 |
| Sylow | C53 ⋊ #2158 |
152 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,b^2=df,c^2=g,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,h^b=h^52,h^c=h^52616 conjugacy classes — view the full character table.
| maximal subgroup of | #27304553, #27304611, D53×#2158, … |
| maximal normal subgroup of | #27304553, #27304611, D53×#2158, … |
| maximal quotient of | #27295676, #27295740, #27295781, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6293);