Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C47 ⋊ #1857 |
272 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 83 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=g,b^a=bd,c^a=ce,d^a=dg,d^b=dg,e^b=eg,d^c=dg,h^c=h^46538 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1857, C2×#20243601, #26217090, … |
| maximal normal subgroup of | D47×#1857, C2×#20243601, #26217090, … |
| maximal quotient of | #26110143, #26110153, #26110262, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4723);