Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #101×C113 ⋊ C2 |
| Sylow | C113 ⋊ #454 |
146 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^112,d^b=df,e^b=ef,g^b=g^112,d^c=df632 conjugacy classes — view the full character table.
| maximal subgroup of | #28392592, #28392596, #28392601, … |
| maximal normal subgroup of | #28392592, #28392596, #28392601, … |
| maximal quotient of | #28389505, #28389511, #28389516, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 724);