Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#532 ⋊ C2 |
| Sylow | C53 ⋊ #3169 |
456 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,53|c^2=fg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^c=h^52772 conjugacy classes — view the full character table.
| maximal subgroup of | #27279310, #27279311, #27279313, … |
| maximal normal subgroup of | #27279310, #27279311, #27279313, … |
| maximal quotient of | #27384627, #27388306, #27389272, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 15085);