Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#13089685 |
| Sylow | C181 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^162,c^b=ce,g^d=g^180478 conjugacy classes — view the full character table.
| maximal subgroup of | C2×Q8⋊#13089685, D181⋊(Q8⋊C8), #37549012, … |
| maximal normal subgroup of | C2×Q8⋊#13089685, D181⋊(Q8⋊C8), #37549012, … |
| maximal quotient of | #37548539, #37548541, #37548557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 1398);