Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C53×#357 ⋊ C2 |
| Sylow | C53 ⋊ #2218 |
170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|b^2=df,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,c^b=cg,h^b=h^52,h^c=h^52598 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2218, C2×#20276817, #27538557, … |
| maximal normal subgroup of | D53×#2218, C2×#20276817, #27538557, … |
| maximal quotient of | #27298314, #27298365, #27298433, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6612);