	The groups of order 3^8

We give a complete list of the gorups of order 3^8.  The groups
are given by their SmallGroup codes, which are understood by both
GAP and Magma. If c is the code for one of the groups, then to
obtain the corresponding group in Magma enter:
	SmallGroupDecoding(c,3^8);

The codes are given in a set of files, each file of the same form.
For example the file "rank7class2" contains the codes for the ten
seven generator groups of class two and order 3^8. The codes are
given as a sequence "codes":

codes:=[
34359738432,
34359738496,
225468603171008,
225468603170945,
225468604219520,
1479299539764510912,
1479299539764510849,
1479299540301381760,
9705684280422972784832,
9705684280422972784769];

In Magma the command "load rank7class2;" will load these codes into
memory. For GAP you may (or perhaps not?) need to minimally edit the
files. There are 22 files in all, each of the form "rankmclassn",
where m is the rank of G/(G^3.[G,G]) and n is the p-class of G.
(The classification of finite p-groups uses the lower exponent p
central series
	G = G_1 > G_2 > G_3 > ... > G_n > G_{n+1} = {1},
where, for i > 1, G_i = G_{i-1}^3.[G_{i-1},G].)

Note that if you load in more than one of the files, the later
files will overwrite the codes from the earlier files.

The number of groups of rank m and class n is given below
as the n-th entry in the m-th row.

[
    [ 0, 0, 0, 0, 0, 0, 0, 1 ],
    [ 0, 0, 58, 486, 1343, 330, 9, 0 ],
    [ 0, 4, 216747, 40521, 2163, 24, 0, 0 ],
    [ 0, 23361, 494666, 22343, 51, 0, 0, 0 ],
    [ 0, 578478, 14796, 80, 0, 0, 0, 0 ],
    [ 0, 566, 39, 0, 0, 0, 0, 0 ],
    [ 0, 10, 0, 0, 0, 0, 0, 0 ],
    [ 1, 0, 0, 0, 0, 0, 0, 0 ]
]

The total number of groups of order 3^8 is 1396077.

