Finite Group DatabasebetaFinite Group Databasebeta| order | 6784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #2239 |
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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,c^2=df,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,e^b=eg,d^c=dg,e^c=efg,f^c=fg,h^c=h^52436 conjugacy classes — view the full character table.
| maximal subgroup of | #27297422, #27297423, #27297428, … |
| maximal normal subgroup of | #27297422, #27297423, #27297428, … |
| maximal quotient of | #27300417, #27300658, #27301133, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6784, 6727);