Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#340 ⋊ C2 |
| Sylow | C53 ⋊ #1853 |
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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=f,b^2=fg,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^52,d^b=dg,h^c=h^52766 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1853, C2×#20274909, #27384816, … |
| maximal normal subgroup of | D53×#1853, C2×#20274909, #27384816, … |
| maximal quotient of | #27277926, #27277943, #27278074, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4704);