Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C113 ⋊ #492 |
142 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^b=g^112806 conjugacy classes — view the full character table.
| maximal subgroup of | #28388738, #28389644, #28389645, … |
| maximal normal subgroup of | #28388738, #28389644, #28389645, … |
| maximal quotient of | #28390160, #28390163, #28390168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 921);