Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C53×#380 ⋊ C2 |
| Sylow | C53 ⋊ #1964 |
408 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 93 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,c^2=e,b^a=bd,c^a=ce,d^a=dg,d^b=dg,f^b=fg,h^b=h^52760 conjugacy classes — view the full character table.
| maximal subgroup of | #27276282, #27276284, #27276289, … |
| maximal normal subgroup of | #27276282, #27276284, #27276289, … |
| maximal quotient of | #27282915, #27282919, #27282923, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5345);