Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#368 ⋊ C2 |
| Sylow | C53 ⋊ #2179 |
144 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=e,c^2=e,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,d^b=df,f^b=fg,h^b=h^52,h^c=h^52604 conjugacy classes — view the full character table.
| maximal subgroup of | #27304709, #27304713, #27304716, … |
| maximal normal subgroup of | #27304709, #27304713, #27304716, … |
| maximal quotient of | #27295830, #27295837, #27295842, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6395);