Cash and Due from Banks (Details)	Dec. 31, 2023 USD ($) account	Dec. 31, 2022 USD ($) account
Cash and Cash Equivalents [Abstract]
Reserve maintained at Federal Reserve Bank	$ 0	$ 0
Number of accounts that exceeded FDIC insurable limit \| account	3	3
Cash in excess of insurable limit	$ 1,200,000	$ 4,600,000

Represents the number of accounts at correspondent banks that exceeded the FDIC insurable limit.

No definition available.

Name:	fgbi_NumberOfAccountsThatExceededFDICInsurableLimit
Namespace Prefix:	fgbi_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant