Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #125×C113 ⋊ C2 |
| Sylow | C113 ⋊ #490 |
110 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|b^2=ef,c^2=d,d^2=f,e^2=f,b^a=bd,c^a=ce,d^a=df,e^a=ef,g^a=g^112,c^b=cf,g^b=g^112,g^c=g^112800 conjugacy classes — view the full character table.
| maximal subgroup of | #28389867, #28389869, #28389872, … |
| maximal normal subgroup of | #28389867, #28389869, #28389872, … |
| maximal quotient of | #28390707, #28391270, #28391397, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 915);