His name could also be "Sumett"; it is indexed as Sennet on FamilySearch.org. He is enumerated with the Wiley Gilder family in the 1850 census. Linked here as brothers for no better reason than that!
FURTHER RESEARCH is needed to determine the family of this person.
Slightly better reason: In 1880 "Sinett", age 60 born GA, is listed with Frances (Gilder) Williams and her family. His relationship is uncle, which is correct if he was her father's brother.
This person's first name was "Senate": "United States Civil War Soldiers Index, 1861-1865," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:XKJJ-9Z4 : 4 December 2014), S. G. Gilder, Private, Company K, 51st Regiment, Georgia Infantry, Confederate; citing NARA microfilm publication M226 (Washington D.C.: National Archives and Records Administration, n.d.), roll 23; FHL microfilm 821,722.
"United States Census, 1880," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M8GZ-L1S : 22 August 2017), Hes C Williams, Baileys, Laurens, Georgia, United States; citing enumeration district ED 62, sheet 486A, NARA microfilm publication T9 (Washington D.C.: National Archives and Records Administration, n.d.), roll 0154; FHL microfilm 1,254,154.
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