Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C47 ⋊ #1605 |
238 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 53 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=f,c^2=g,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^46,d^b=df,e^b=eg,h^b=h^46,d^c=dg529 conjugacy classes — view the full character table.
| maximal subgroup of | #26129098, #26129099, #26129110, … |
| maximal normal subgroup of | #26129098, #26129099, #26129110, … |
| maximal quotient of | #26105108, #26105129, #26105144, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 3486);