Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#340 ⋊ C2 |
| Sylow | C53 ⋊ #1893 |
432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^b=h^52,h^c=h^52772 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1893, C2×#20275142, #27385763, … |
| maximal normal subgroup of | D53×#1893, C2×#20275142, #27385763, … |
| maximal quotient of | #27279427, #27279447, #27279656, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4937);