Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#358 ⋊ C2 |
| Sylow | C53 ⋊ #2208 |
166 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 49 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=g,b^2=d,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^b=h^52,e^c=ef,f^c=fg,h^c=h^52601 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2208, C2×#20276759, #27538357, … |
| maximal normal subgroup of | D53×#2208, C2×#20276759, #27538357, … |
| maximal quotient of | #27298235, #27298239, #27298273, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6554);