Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#508 ⋊ C2 |
| Sylow | C53 ⋊ #3415 |
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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,e^b=ef,f^b=fg,d^c=dg,h^c=h^52,h^d=h^52604 conjugacy classes — view the full character table.
| maximal subgroup of | #27304773, #27304777, #27304787, … |
| maximal normal subgroup of | #27304773, #27304777, #27304787, … |
| maximal quotient of | #27537000, #27537133, #27537429, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 17648);