What is the SRID for EPSG 102743?

There is no EPSG SRID 102743. Note that EPSG is the authority, and 102743 is the SRID. If you look up SRID 102743 on spatialreference.org, the listing is for ESRI:102743, meaning that ESRI (the publishers of ArcGIS) is the authority, not EPSG (European Petroleum Survey Group, now absorbed by the International Association of Oil & Gas Producers). The PostGIS database does not by default populate spatial_ref_sys with non-EPSG reference systems, so if you are using an ESRI one you have two choices:

Add it manually

This is fairly easy. Each SRID page on spatialreference.org has a link for a PostGIS INSERT statement to add the code to spatial_ref_sys. The statement for this SRID is:

INSERT into spatial_ref_sys (srid, auth_name, auth_srid, proj4text, srtext) values ( 9102743, 'esri', 102743, '+proj=lcc +lat_1=39.01666666666667 +lat_2=40.65 +lat_0=38.33333333333334 +lon_0=-111.5 +x_0=500000.0000000002 +y_0=2000000 +ellps=GRS80 +datum=NAD83 +to_meter=0.3048006096012192 +no_defs ', 'PROJCS["NAD_1983_StatePlane_Utah_Central_FIPS_4302_Feet",GEOGCS["GCS_North_American_1983",DATUM["North_American_Datum_1983",SPHEROID["GRS_1980",6378137,298.257222101]],PRIMEM["Greenwich",0],UNIT["Degree",0.017453292519943295]],PROJECTION["Lambert_Conformal_Conic_2SP"],PARAMETER["False_Easting",1640416.666666667],PARAMETER["False_Northing",6561666.666666666],PARAMETER["Central_Meridian",-111.5],PARAMETER["Standard_Parallel_1",39.01666666666667],PARAMETER["Standard_Parallel_2",40.65],PARAMETER["Latitude_Of_Origin",38.33333333333334],UNIT["Foot_US",0.30480060960121924],AUTHORITY["EPSG","102743"]]');

Use a "close enough" SRID

The PostGIS database includes a number of suitable SRIDs. As you have found, EPSG:3566 is a close match. In fact, 3566 (NAD83), 3569 (NAD83(HARN)), and 3677 (NAD83(NSRS2007)) are all extremely close matches. The only difference between 3566 and 102743 is the false easting and false northing parameters.

• 3566
  • PARAMETER["false_easting",1640416.6667]
  • PARAMETER["false_northing",6561666.666700001]
• 102743
  • PARAMETER["False_Easting",1640416.666666667]
  • PARAMETER["False_Northing",6561666.666666666]

So using the "wrong" one might lead to a misalignment of 3/100,000th of a foot.

Using prj2epsg.org I discovered that the SRID for EPSG 102743 is 3566. The WKT definition is:

PROJCS["NAD_1983_StatePlane_Utah_Central_FIPS_4302_Feet",GEOGCS["GCS_North_American_1983",DATUM["D_North_American_1983",SPHEROID["GRS_1980",6378137,298.257222101]],PRIMEM["Greenwich",0],UNIT["Degree",0.017453292519943295]],PROJECTION["Lambert_Conformal_Conic"],PARAMETER["False_Easting",1640416.666666667],PARAMETER["False_Northing",6561666.666666666],PARAMETER["Central_Meridian",-111.5],PARAMETER["Standard_Parallel_1",39.01666666666667],PARAMETER["Standard_Parallel_2",40.65],PARAMETER["Latitude_Of_Origin",38.33333333333334],UNIT["Foot_US",0.30480060960121924]]