Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #1350 |
104 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 30 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=g,c^2=fg,d^2=g,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,h^a=h^30,c^b=cf,d^b=defg,e^b=eg,f^b=fg,h^b=h^52,h^d=h^52211 conjugacy classes — view the full character table.
| maximal subgroup of | D53⋊#1350, C2×#20289708, #28308872, … |
| maximal normal subgroup of | D53⋊#1350, C2×#20289708, #28308872, … |
| maximal quotient of | #28298147, #28298149, #28298155, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 19503);