Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×M16×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1812 |
260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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=d,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^30,h^b=h^52,f^c=fg,h^f=h^52292 conjugacy classes — view the full character table.
| maximal subgroup of | #28298562, #28298563, #28309441, … |
| maximal normal subgroup of | #28298562, #28298563, #28309441, … |
| maximal quotient of | #28303044, #28303045, #28303048, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20393);