Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×M16×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1391 |
166 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 40 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,e^2=g,b^a=bc,c^a=cf,f^a=fg,h^a=h^30,d^b=df,h^b=h^52,d^c=dg,h^d=h^52286 conjugacy classes — view the full character table.
| maximal subgroup of | #28299031, #28299032, #28299107, … |
| maximal normal subgroup of | #28299031, #28299032, #28299107, … |
| maximal quotient of | #28298422, #28298473, #28298515, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19599);