Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×D8×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1879 |
438 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 80 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,e^2=g,f^2=g,b^a=bd,c^a=ce,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^52220 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20290710, #28319709, #28319710, … |
| maximal normal subgroup of | C2×#20290710, #28319709, #28319710, … |
| maximal quotient of | #28303924, #28303925, #28303926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20505);