Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #2015 |
390 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 91 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=g,b^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^52,c^b=cf,d^b=dg,e^b=eg,d^c=dg,e^c=eg760 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#2015, C2×#20275809, #27411160, … |
| maximal normal subgroup of | D53×#2015, C2×#20275809, #27411160, … |
| maximal quotient of | #27284575, #27284582, #27284596, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 5604);