Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C113 ⋊ #455 |
152 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^112,d^b=df,e^b=ef,d^c=df968 conjugacy classes — view the full character table.
| maximal subgroup of | #28392561, #28392562, #28392573, … |
| maximal normal subgroup of | #28392561, #28392562, #28392573, … |
| maximal quotient of | #28389526, #28389531, #28389554, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 727);