Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D181⋊(C4⋊C8) |
| Sylow | C181 ⋊ C2×C4⋊C8 |
138 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|a^2=e,b^2=d,e^2=f,b^a=bd,g^a=g^162,g^c=g^180,g^e=g^180760 conjugacy classes — view the full character table.
| maximal subgroup of | #37548550, #37548556, #37548585, … |
| maximal normal subgroup of | #37548550, #37548556, #37548585, … |
| maximal quotient of | D181⋊#334, D181⋊#335, #37549269, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1550);