Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #1352 |
154 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 37 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,b^2=eg,c^2=fg,b^a=bc,c^a=ce,e^a=eg,h^a=h^52,c^b=cf,d^b=defg,d^c=dg595 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#1352, C2×#20272739, #27294371, … |
| maximal normal subgroup of | D53×#1352, C2×#20272739, #27294371, … |
| maximal quotient of | #27270889, #27270912, #27271211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 2534);