Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×C8×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1846 |
248 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 94 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,c^2=eg,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^30,h^f=h^52460 conjugacy classes — view the full character table.
| maximal subgroup of | #28298695, #28298696, #28298705, … |
| maximal normal subgroup of | #28298695, #28298696, #28298705, … |
| maximal quotient of | #28303583, #28303584, #28303585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20447);