Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×#106×C53 ⋊ C2 |
| Sylow | C53 ⋊ #1972 |
376 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 105 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=dfg,c^2=e,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cg,h^b=h^52760 conjugacy classes — view the full character table.
| maximal subgroup of | #27301238, #27301241, #27301343, … |
| maximal normal subgroup of | #27301238, #27301241, #27301343, … |
| maximal quotient of | #27282963, #27282997, #27283261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5384);