Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D181⋊M32 |
| Sylow | C181 ⋊ C2×M32 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|a^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^162,g^c=g^180,g^d=g^180760 conjugacy classes — view the full character table.
| maximal subgroup of | #37548764, #37548767, #37548770, … |
| maximal normal subgroup of | #37548764, #37548767, #37548770, … |
| maximal quotient of | #37549922, #37549927, #37549928, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1605);