Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C53×#333 ⋊ C2 |
| Sylow | C53 ⋊ #1405 |
106 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 23 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,c^2=g,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^52,c^b=cg,d^b=de,e^b=eg,f^b=fg,h^b=h^52,d^c=dfg,e^c=eg,e^d=eg511 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1405, C2×#20272870, #27304357, … |
| maximal normal subgroup of | D53×#1405, C2×#20272870, #27304357, … |
| maximal quotient of | #27271455, #27271522, #27271621, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2665);