It is also possible to decompress it using standard shell-script + gzip, if you don't have, or want to use openssl or other tools.
The trick is to prepend the gzip magic number and compress method to the actual data from zlib.compress:

printf "\x1f\x8b\x08\x00\x00\x00\x00\x00" |cat - /tmp/data |gzip -dc >/tmp/out

Edits:
@d0sboots commented: For RAW Deflate data, you need to add 2 more null bytes:
→ "\x1f\x8b\x08\x00\x00\x00\x00\x00\x00\x00"

This Q on SO gives more information about this approach. An answer there suggests that there is also an 8 byte footer.

Users @Vitali-Kushner and @mark-bessey reported success even with truncated files, so a gzip footer does not seem strictly required.

@tobias-kienzler suggested this function for the bashrc:
zlibd() (printf "\x1f\x8b\x08\x00\x00\x00\x00\x00" | cat - "$@" | gzip -dc)

I stumbled across pigz which allows for just this via pigz -z [input_file_name] to output a compressed file.

Looks like zlib compressed data, here's more info how to deflate it: https://unix.stackexchange.com/questions/22834/how-to-uncompress-zlib-data-in-unix

Something like the following will print the raw content, including the "$type $length\0" header:

perl -MCompress::Zlib -e 'undef $/; print uncompress(<>)' \
     < .git/objects/27/de0a1dd5a89a94990618632967a1c86a82d577

I don't find a Python 2.4 package for Ubuntu, so I assume you tried to compile it from source. If so, you would have had to explicitly configure and compile it with zlib support.

I found a blog article on how to do this here:

http://www.1stbyte.com/2005/06/26/configure-and-compile-python-with-zlib/

basically install zlib1g-dev, and then configure Python with

./configure --with-zlib=/usr/include

then you can do "make" to generate the Python 2.4 binaries.

use git cat-file -p SHA1 to view the file content of the blob.

The content of the file is this: blob XXX NULL Content

ex:

a.txt contain Hello World

The Content of the SHA-1 is:

blob 11\000Hello World and this strign is then GZipped

If you are on unix u can use this to deflate the content:
perl -MCompress::Zlib -e 'undef $/; print uncompress(<>)'

The documentation is scant, but from what I can tell, qCompress() writes a four-byte length followed by a zlib stream. There is no file format, extension, nor command line tool for that format. You would have to write your own.

It would be quite straightforward. Just discard the first four bytes, and feed the rest to zlib (a C library likely already installed on your machine).

If you are on a Unixish system, you can use dd to strip the first four bytes, and then feed the resulting zlib stream to pigz -dz.