Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×#349 ⋊ C2 |
| Sylow | C53 ⋊ #1321 |
112 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 33 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=d,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,e^a=eg,c^b=cg,d^b=deg,h^b=h^52,d^c=dg598 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1321, C2×#20272652, #27293218, … |
| maximal normal subgroup of | D53×#1321, C2×#20272652, #27293218, … |
| maximal quotient of | #27270714, #27270716, #27270718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2447);