Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1376 |
148 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 77 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,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=cg,e^a=eg,h^b=h^521096 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D53×#1376, C2×#20272796, #27298946, … |
| maximal normal subgroup of | D53×#1376, C2×#20272796, #27298946, … |
| maximal quotient of | #27270923, #27270935, #27270942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2591);