Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #1584 |
152 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 67 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=e,b^2=f,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,d^b=df,h^b=h^52766 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1584, C2×#20273563, #27353618, … |
| maximal normal subgroup of | D53×#1584, C2×#20273563, #27353618, … |
| maximal quotient of | #27274893, #27274945, #27275381, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 3358);