Cómo agregar un número de secuencia para cada elemento en un grupo usando una consulta SQL sin tablas temporales

Tal vez algo como esto:

SELECT
    ROW_NUMBER() OVER(PARTITION BY [Group] ORDER BY Record) AS GroupSequence1,
    RANK() OVER(PARTITION BY [Group] ORDER BY Record) AS GroupSequence2,
    DENSE_RANK() OVER(PARTITION BY [Group] ORDER BY Record) AS GroupSequence3,
    Table1.Group,
    Table1.Record
FROM
    Table1

GroupSequence1 , GroupSequence2 y GroupSequence3 obtendrá el resultado que desea.