Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C47 ⋊ #1806 |
312 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|a^2=f,b^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^46,e^c=eg958 conjugacy classes — view the full character table.
| maximal subgroup of | #26108186, #26108188, #26108193, … |
| maximal normal subgroup of | #26108186, #26108188, #26108193, … |
| maximal quotient of | #26108961, #26108966, #26108971, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4530);