Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C53×#432 ⋊ C2 |
| Sylow | C53 ⋊ #1469 |
256 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 73 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,c^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^52,c^b=cg,e^b=ef,h^b=h^52760 conjugacy classes — view the full character table.
| maximal subgroup of | #27276342, #27276344, #27276352, … |
| maximal normal subgroup of | #27276342, #27276344, #27276352, … |
| maximal quotient of | #27272435, #27272449, #27272462, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2863);