Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#508 ⋊ C2 |
| Sylow | C53 ⋊ #2263 |
112 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|d^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=de,e^a=ef,f^a=fg,d^b=de,e^b=ef,f^b=fg,h^b=h^52598 conjugacy classes — view the full character table.
| maximal subgroup of | #27304714, #27304717, #27304765, … |
| maximal normal subgroup of | #27304714, #27304717, #27304765, … |
| maximal quotient of | #27304531, #27304534, #27304600, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6822);