Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#362 ⋊ C2 |
| Sylow | C53 ⋊ #2180 |
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 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=e,c^2=ef,d^2=f,f^2=g,b^a=bd,c^a=cf,d^a=df,f^a=fg,h^a=h^52,d^b=dfg,e^b=eg,f^b=fg,h^b=h^52,d^c=dg,h^c=h^52439 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2180, C2×#20276609, #27537537, … |
| maximal normal subgroup of | D53×#2180, C2×#20276609, #27537537, … |
| maximal quotient of | #27295968, #27295969, #27296046, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6404);