Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ #461 |
120 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=f,b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^112,e^c=ef1139 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28389753, #28389755, #28389774, … |
| maximal normal subgroup of | #28389753, #28389755, #28389774, … |
| maximal quotient of | #28389949, #28389963, #28389973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 754);