Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#15668452 |
| Sylow | C181 ⋊ C22⋊C16 |
66 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|a^2=d,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 | #37548641, #37548642, #37548643, … |
| maximal normal subgroup of | #37548641, #37548642, #37548643, … |
| maximal quotient of | #37548641, #37548657, D4⋊#15668452, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1443);