Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #2031 |
244 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|a^2=d,b^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^52,c^b=cf,d^c=dg,e^c=eg,f^c=fg754 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2031, C2×#20275887, #27411520, … |
| maximal normal subgroup of | D53×#2031, C2×#20275887, #27411520, … |
| maximal quotient of | #27287180, #27287185, #27287190, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5682);