Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C53 ⋊ #1426 |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,53|a^2=d,b^2=cef,c^2=efg,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^52,d^b=dg1066 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1426, C2×#20272921, #27304611, … |
| maximal normal subgroup of | D53×#1426, C2×#20272921, #27304611, … |
| maximal quotient of | #27271775, #27271800, C2×#20272921 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2716);