Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#11744753 |
| Sylow | C113 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^98,c^b=ce,g^d=g^112308 conjugacy classes — view the full character table.
| maximal subgroup of | C2×Q8⋊#11744753, #28405863, #28405865, … |
| maximal normal subgroup of | C2×Q8⋊#11744753, #28405863, #28405865, … |
| maximal quotient of | #28405392, #28405394, #28405410, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1398);