Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #124×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1910 |
344 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 66 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,e^a=eg,h^a=h^23,e^b=eg,h^b=h^30,d^c=dg,f^c=fg,h^c=h^52,h^f=h^52211 conjugacy classes — view the full character table.
| maximal subgroup of | #28311110, #28311111, #28311114, … |
| maximal normal subgroup of | #28311110, #28311111, #28311114, … |
| maximal quotient of | #28304349, #28304351, #28304352, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20554);