Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C53 ⋊ #1790 |
670 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 125 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^a=bd,c^a=ce,d^a=dg,h^a=h^52,e^b=eg,f^b=fg,d^c=dg916 conjugacy classes — view the full character table.
| maximal subgroup of | #27301354, #27301355, #27301361, … |
| maximal normal subgroup of | #27301354, #27301355, #27301361, … |
| maximal quotient of | #27275485, #27275488, #27275603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4458);