Sum of Avg of Groups in SQLite

Simple table "test":

Name Value
A    2
A    3
B    2
B    3
B    5
C    7

With a simple query I can get the following result:

select Name, count(*), sum(Value), avg(Value) from test group by Name

    Count Sum   Avg
A     2    5    2,50
B     3   10    3,33
C     1    7    7,00

The total count, sum and avg are easy, too:

select count(*), sum(Value), avg(Value) from test

      6   22    3,67 

But how to query the sum of avg?

12,83 = 2,5 + 3,33 + 7,00

Needed result:

    Count Sum   Avg   Avg / 12,83 * 100
A     2    5    2,50  19% = 2,50 / 12,83 * 100  
B     3   10    3,33  26%
C     1    7    7,00  55%