GeocodeDVD will append the following Geographic Identifiers:

Zip+4
Census 2000 Block FIPS code
County Subdivision/MCD FIPS code
Place FIPS code
Latitude
Longitude
Census 1970 Tract FIPS code
Census 1980 Tract FIPS code
Census 1980 Block Group FIPS code
Census 1990 Block Group FIPS code
Census 2000 Tract or Block Group
108th Congressional District

Using the Census 2000 Block FIPS code, the following can be derived:

State FIPS Code
County FIPS Code
Tract FIPS Code
Block Group FIPS code

A Census Block FIPS code has 15 digits and is structured as follows:

AABBBCCCCCCDEEE

A = State (2 digit FIPS code)
B = County (3 digit FIPS code)
C = Tract (6 digit FIPS code)
D = Block Group (1 digit FIPS code)
E = Block (3 digit FIPS code)

So if you want the Block Group Code it would be the first 12 digits (AABBBCCCCCCD)