Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #3174 |
362 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 121 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=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^c=h^52604 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#3174, C2×#20285337, #28253941, … |
| maximal normal subgroup of | D53×#3174, C2×#20285337, #28253941, … |
| maximal quotient of | #27384649, #27388356, #27388470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 15132);