Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | AGL(1,ℤ/8)×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1907 |
332 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 68 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=df,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^23,d^b=dg,e^b=eg,f^b=fg,h^b=h^30,d^c=dg,e^c=eg,f^c=fg,h^f=h^52175 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20290754, #28319851, #28319852, … |
| maximal normal subgroup of | C2×#20290754, #28319851, #28319852, … |
| maximal quotient of | #28304324, #28304325, #28304326, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20549);