Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C47 ⋊ #1836 |
224 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 101 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=e,c^2=d,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^46,c^b=cg,h^b=h^46,h^c=h^46676 conjugacy classes — view the full character table.
| maximal subgroup of | #26103686, #26110636, #26110637, … |
| maximal normal subgroup of | #26103686, #26110636, #26110637, … |
| maximal quotient of | #26109946, #26109956, #26109977, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4645);