Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊(C47⋊C16) |
| Sylow | C47 ⋊ Q8⋊C16 |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=d,b^2=e,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^46,c^b=ce976 conjugacy classes — view the full character table.
| maximal subgroup of | D47×Q8⋊C16, C2×Q8⋊(C47⋊C16), #26126079, … |
| maximal normal subgroup of | D47×Q8⋊C16, C2×Q8⋊(C47⋊C16), #26126079, … |
| maximal quotient of | #26103060, #26103090, #26103182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2489);