Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C42×C53 ⋊ C4 |
| Sylow | C53 ⋊ #1740 |
420 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 130 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=g,b^a=bd,d^a=dg,h^a=h^30,e^b=eg,h^e=h^52460 conjugacy classes — view the full character table.
| maximal subgroup of | #28298631, #28298633, #28306420, … |
| maximal normal subgroup of | #28298631, #28298633, #28306420, … |
| maximal quotient of | #28300317, #28300323, #28300329, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 20209);