Finite Group DatabasebetaFinite Group Databasebeta| order | 11584 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q32×C181 ⋊ C2 |
| Sylow | C181 ⋊ #508 |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,181|c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^180,d^b=de,e^b=ef,g^b=g^180,g^c=g^1801012 conjugacy classes — view the full character table.
| maximal subgroup of | #37536029, #37536031, #37536035, … |
| maximal normal subgroup of | #37536029, #37536031, #37536035, … |
| maximal quotient of | #37535427, #37535502, #37535567, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11584, 982);