Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×C22⋊C16 ⋊ C2 |
| Sylow | C53 ⋊ #1315 |
116 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 37 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=g,d^2=f,f^2=g,b^a=bc,c^a=ce,c^b=cg,d^b=deg,h^b=h^521078 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1315, C2×#20272640, #27293162, … |
| maximal normal subgroup of | D53×#1315, C2×#20272640, #27293162, … |
| maximal quotient of | #27270718, #27270720, #27270722, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2435);