Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#535 ⋊ C2 |
| Sylow | C53 ⋊ #3021 |
736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 736 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|d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,f^b=fg,h^b=h^52,e^c=eg601 conjugacy classes — view the full character table.
| maximal subgroup of | #27303092, #27303093, #27303099, … |
| maximal normal subgroup of | #27303092, #27303093, #27303099, … |
| maximal quotient of | #27356485, #27356532, #27356563, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 13881);