Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D181⋊#108 |
| Sylow | C181 ⋊ C2×#108 |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|a^2=e,b^2=d,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^162,g^c=g^180,g^e=g^180748 conjugacy classes — view the full character table.
| maximal subgroup of | #37548780, #37548783, #37548785, … |
| maximal normal subgroup of | #37548780, #37548783, #37548785, … |
| maximal quotient of | D181⋊#334, D181⋊#335, #37549268, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1562);