Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#15668452 |
| Sylow | C181 ⋊ C4⋊C16 |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|a^2=d,b^2=c,d^2=e,e^2=f,b^a=bc,g^a=g^162,g^d=g^180760 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#15668452, #37548672, #37548673, … |
| maximal normal subgroup of | D4⋊#15668452, #37548672, #37548673, … |
| maximal quotient of | #37548743, #37548750, #37548759, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1469);