Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1345 |
168 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 30 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=d,c^2=f,d^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^30,c^b=cf,d^b=def,h^b=h^52,d^c=dg,h^d=h^52283 conjugacy classes — view the full character table.
| maximal subgroup of | D53⋊#1345, C2×#20289698, #28308833, … |
| maximal normal subgroup of | D53⋊#1345, C2×#20289698, #28308833, … |
| maximal quotient of | #28298145, #28298149, #28298161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19493);