Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C53×#448 ⋊ C2 |
| Sylow | C53 ⋊ #3211 |
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 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|b^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,h^b=h^52,f^c=fg,h^c=h^52526 conjugacy classes — view the full character table.
| maximal subgroup of | #27358111, #27358113, #27358122, … |
| maximal normal subgroup of | #27358111, #27358113, #27358122, … |
| maximal quotient of | #27393416, #27393778, #27394617, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 15474);