Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D113⋊#100 |
| Sylow | C113 ⋊ C2×#100 |
186 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=e,e^2=f,b^a=bd,d^a=df,g^a=g^98,e^b=ef,g^c=g^112,g^e=g^112302 conjugacy classes — view the full character table.
| maximal subgroup of | #28405657, #100×#90673, #28406420, … |
| maximal normal subgroup of | #28405657, #100×#90673, #28406420, … |
| maximal quotient of | #28405800, #28405814, #28405815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1532);