Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D181⋊#100 |
| Sylow | C181 ⋊ C2×#100 |
186 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|a^2=e,e^2=f,b^a=bd,d^a=df,g^a=g^162,e^b=ef,g^c=g^180,g^e=g^180472 conjugacy classes — view the full character table.
| maximal subgroup of | #37548804, #100×#10624382, #37549567, … |
| maximal normal subgroup of | #37548804, #100×#10624382, #37549567, … |
| maximal quotient of | D181⋊#323, #37548961, #37548962, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1532);