Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C4×C8×C53 ⋊ C2 |
| Sylow | C53 ⋊ #1764 |
300 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 113 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,d^2=g,e^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^521720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27299192, #27299195, #27299199, … |
| maximal normal subgroup of | #27299192, #27299195, #27299199, … |
| maximal quotient of | #27274765, #27274776, #27274782, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4347);