Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C53 ⋊ #1410 |
104 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,c^2=fg,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^52,c^b=cfg,d^b=def,e^b=eg,d^c=dfg,e^d=eg589 conjugacy classes — view the full character table.
| maximal subgroup of | #27271914, #27271915, #27271917, … |
| maximal normal subgroup of | #27271914, #27271915, #27271917, … |
| maximal quotient of | #27271475, #27271509, #27271605, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2677);