Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1381 |
128 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 50 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,b^2=e,c^2=fg,d^2=g,e^2=f,f^2=g,b^a=bc,c^a=cf,e^a=efg,f^a=fg,h^b=h^30,h^e=h^52226 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20289774, #28310278, #28310678, … |
| maximal normal subgroup of | C2×#20289774, #28310278, #28310678, … |
| maximal quotient of | #28298309, #28298368, #28298370, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19569);