Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C53×#343 ⋊ C2 |
| Sylow | C53 ⋊ C4×#100 |
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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=e,b^2=f,c^2=e,f^2=g,b^a=bd,f^a=fg,d^b=dg,h^c=h^52616 conjugacy classes — view the full character table.
| maximal subgroup of | #27294453, #27294455, #27294463, … |
| maximal normal subgroup of | #27294453, #27294455, #27294463, … |
| maximal quotient of | #27274593, #27274601, #27274614, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4301);