Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#504 ⋊ C2 |
| Sylow | C53 ⋊ #3415 |
370 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,h^a=h^52,e^b=ef,f^b=fg,h^b=h^52,d^c=dg1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27304774, #27304778, #27304788, … |
| maximal normal subgroup of | #27304774, #27304778, #27304788, … |
| maximal quotient of | #27537005, #27537136, #27537436, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17651);