Try using xs
to be very precise:
In [5]: df.xs('a', level=0)
Out[5]:
value1 value2
group2
c 1.1 7.1
c 2.0 8.0
d 3.0 9.0
In [6]: df.xs('c', level="group2")
Out[6]:
value1 value2
group1
a 1.1 7.1
a 2.0 8.0