Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C47 ⋊ #2943 |
492 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 221 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,c^2=f,d^2=g,e^2=g,b^a=be,c^a=cg,e^a=eg,h^a=h^46,e^b=eg,h^c=h^46688 conjugacy classes — view the full character table.
| maximal subgroup of | #26131565, #26131567, #26132924, … |
| maximal normal subgroup of | #26131565, #26131567, #26132924, … |
| maximal quotient of | #26185685, #26185853, #26186056, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 13311);