Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #1957 |
436 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 145 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=dfg,c^2=e,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^46,h^b=h^46688 conjugacy classes — view the full character table.
| maximal subgroup of | #26104055, #26108342, #26108345, … |
| maximal normal subgroup of | #26104055, #26108342, #26108345, … |
| maximal quotient of | #26115055, #26115081, #26115261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 5317);