Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #117×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#339 |
488 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 138 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,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^b=h^30,h^c=h^52,h^f=h^52316 conjugacy classes — view the full character table.
| maximal subgroup of | #339×#6157, #28306378, #28306395, … |
| maximal normal subgroup of | #339×#6157, #28306378, #28306395, … |
| maximal quotient of | #28300138, #28300146, #28300154, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20186);