Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #2074 |
222 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 79 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=eg,b^2=g,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^52,c^b=cf,f^b=fg,f^c=fg760 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2074, C2×#20276136, #27412847, … |
| maximal normal subgroup of | D53×#2074, C2×#20276136, #27412847, … |
| maximal quotient of | #27288839, #27288844, #27288856, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5931);