You will need to configure your environment to use Kerberos on both the SharePoint and SQL servers. Once you have done that you will then use the passthrough option when configuring your External Content Type. Instead of a SharePoint group you will then need to use an AD group.
Understanding Passthrough Authentication
Passthrough authentication is in the Impersonation and Delegation authentication
model. Setting the value of the AuthenticationMode element to
Passthrough causes BCS to use the credentials of the current user to
access the external system. Passthrough is simple to set up by
selecting Connect with User’s Identity when configuring the external
system connection in SharePoint Designer, as was shown in the
walk-through earlier in this chapter. However, Passthrough
authentication is unlikely to be useful in many situations because of
limitations inherent in Windows authentication.
-Business Connectivity Services security overview (SharePoint Server 2010)
Configuring Kerberos is a pretty complex process so I can only offer you some links as well as point you in the direction of some tools to help assist you.
You may also find this SQL query helpful to determine which accounts are legged in via NTLM and which via Kerberos.
FROM sys.dm_exec_connections c
INNER JOIN sys.dm_exec_sessions s on s.session_id = c.session_id