	The groups of order 3^8

We give a complete list of the groups 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) and
in GAP enter PcGroupCode(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];

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].)

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.

