Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #2249 |
184 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 53 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=df,c^2=eg,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^c=h^52610 conjugacy classes — view the full character table.
| maximal subgroup of | #27304890, #27304891, #27304897, … |
| maximal normal subgroup of | #27304890, #27304891, #27304897, … |
| maximal quotient of | #27298742, #27298751, #27298754, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6768);