Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1841 |
162 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 73 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^2=de,c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^52,f^c=fg1072 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #27271153, #27271154, #27271156, … |
| maximal normal subgroup of | #27271153, #27271154, #27271156, … |
| maximal quotient of | #27277812, #27277816, #27277820, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4659);