Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C53 ⋊ #1764 |
300 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 117 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=e,d^2=g,e^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^52,h^c=h^52784 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1764, C2×#20274553, #27381936, … |
| maximal normal subgroup of | D53×#1764, C2×#20274553, #27381936, … |
| maximal quotient of | #27274766, #27274777, #27274783, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 4348);