Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C113 ⋊ #487 |
98 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=f,b^2=e,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^b=g^112,g^c=g^112806 conjugacy classes — view the full character table.
| maximal subgroup of | #28389723, #28389724, #28389730, … |
| maximal normal subgroup of | #28389723, #28389724, #28389730, … |
| maximal quotient of | #28390701, #28391253, #28391377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 899);