Solvable Groups of High Derived Length

Tue Mar 29 10:37:19 CEST 2005

Here is a little GAP program that just counts the numbers of solvable 
groups of each order up to 510 (other than 256) according to their 
derived length:

for sz in [2..510] do
if (sz <> 256) then
t := [0,0,0,0,0,0];
for i in [1..NrSmallGroups(sz)] do
g := SmallGroup(sz,i);
if IsSolvable(g) then
l := Length(DerivedSeries(g))-1;
t[l] := t[l] + 1;
fi;
od;
Print(sz," ",t,"\n");
fi;
od;

The results are below (cut off at 432), where a line such as

24 [ 3, 10, 2, 0, 0, 0 ]

indicates that for order 24, there are 3 groups of derived length 1, 10 
of derived length 2 and 2 of derived length 3.

Cheers

Gordon

RESULTS
--------------

2 [ 1, 0, 0, 0, 0, 0 ]
3 [ 1, 0, 0, 0, 0, 0 ]
4 [ 2, 0, 0, 0, 0, 0 ]
5 [ 1, 0, 0, 0, 0, 0 ]
6 [ 1, 1, 0, 0, 0, 0 ]
7 [ 1, 0, 0, 0, 0, 0 ]
8 [ 3, 2, 0, 0, 0, 0 ]
9 [ 2, 0, 0, 0, 0, 0 ]
10 [ 1, 1, 0, 0, 0, 0 ]
11 [ 1, 0, 0, 0, 0, 0 ]
12 [ 2, 3, 0, 0, 0, 0 ]
13 [ 1, 0, 0, 0, 0, 0 ]
14 [ 1, 1, 0, 0, 0, 0 ]
15 [ 1, 0, 0, 0, 0, 0 ]
16 [ 5, 9, 0, 0, 0, 0 ]
17 [ 1, 0, 0, 0, 0, 0 ]
18 [ 2, 3, 0, 0, 0, 0 ]
19 [ 1, 0, 0, 0, 0, 0 ]
20 [ 2, 3, 0, 0, 0, 0 ]
21 [ 1, 1, 0, 0, 0, 0 ]
22 [ 1, 1, 0, 0, 0, 0 ]
23 [ 1, 0, 0, 0, 0, 0 ]
24 [ 3, 10, 2, 0, 0, 0 ]
25 [ 2, 0, 0, 0, 0, 0 ]
26 [ 1, 1, 0, 0, 0, 0 ]
27 [ 3, 2, 0, 0, 0, 0 ]
28 [ 2, 2, 0, 0, 0, 0 ]
29 [ 1, 0, 0, 0, 0, 0 ]
30 [ 1, 3, 0, 0, 0, 0 ]
31 [ 1, 0, 0, 0, 0, 0 ]
32 [ 7, 44, 0, 0, 0, 0 ]
33 [ 1, 0, 0, 0, 0, 0 ]
34 [ 1, 1, 0, 0, 0, 0 ]
35 [ 1, 0, 0, 0, 0, 0 ]
36 [ 4, 10, 0, 0, 0, 0 ]
37 [ 1, 0, 0, 0, 0, 0 ]
38 [ 1, 1, 0, 0, 0, 0 ]
39 [ 1, 1, 0, 0, 0, 0 ]
40 [ 3, 11, 0, 0, 0, 0 ]
41 [ 1, 0, 0, 0, 0, 0 ]
42 [ 1, 5, 0, 0, 0, 0 ]
43 [ 1, 0, 0, 0, 0, 0 ]
44 [ 2, 2, 0, 0, 0, 0 ]
45 [ 2, 0, 0, 0, 0, 0 ]
46 [ 1, 1, 0, 0, 0, 0 ]
47 [ 1, 0, 0, 0, 0, 0 ]
48 [ 5, 41, 4, 2, 0, 0 ]
49 [ 2, 0, 0, 0, 0, 0 ]
50 [ 2, 3, 0, 0, 0, 0 ]
51 [ 1, 0, 0, 0, 0, 0 ]
52 [ 2, 3, 0, 0, 0, 0 ]
53 [ 1, 0, 0, 0, 0, 0 ]
54 [ 3, 11, 1, 0, 0, 0 ]
55 [ 1, 1, 0, 0, 0, 0 ]
56 [ 3, 10, 0, 0, 0, 0 ]
57 [ 1, 1, 0, 0, 0, 0 ]
58 [ 1, 1, 0, 0, 0, 0 ]
59 [ 1, 0, 0, 0, 0, 0 ]
60 [ 2, 10, 0, 0, 0, 0 ]
61 [ 1, 0, 0, 0, 0, 0 ]
62 [ 1, 1, 0, 0, 0, 0 ]
63 [ 2, 2, 0, 0, 0, 0 ]
64 [ 11, 256, 0, 0, 0, 0 ]
65 [ 1, 0, 0, 0, 0, 0 ]
66 [ 1, 3, 0, 0, 0, 0 ]
67 [ 1, 0, 0, 0, 0, 0 ]
68 [ 2, 3, 0, 0, 0, 0 ]
69 [ 1, 0, 0, 0, 0, 0 ]
70 [ 1, 3, 0, 0, 0, 0 ]
71 [ 1, 0, 0, 0, 0, 0 ]
72 [ 6, 37, 7, 0, 0, 0 ]
73 [ 1, 0, 0, 0, 0, 0 ]
74 [ 1, 1, 0, 0, 0, 0 ]
75 [ 2, 1, 0, 0, 0, 0 ]
76 [ 2, 2, 0, 0, 0, 0 ]
77 [ 1, 0, 0, 0, 0, 0 ]
78 [ 1, 5, 0, 0, 0, 0 ]
79 [ 1, 0, 0, 0, 0, 0 ]
80 [ 5, 47, 0, 0, 0, 0 ]
81 [ 5, 10, 0, 0, 0, 0 ]
82 [ 1, 1, 0, 0, 0, 0 ]
83 [ 1, 0, 0, 0, 0, 0 ]
84 [ 2, 13, 0, 0, 0, 0 ]
85 [ 1, 0, 0, 0, 0, 0 ]
86 [ 1, 1, 0, 0, 0, 0 ]
87 [ 1, 0, 0, 0, 0, 0 ]
88 [ 3, 9, 0, 0, 0, 0 ]
89 [ 1, 0, 0, 0, 0, 0 ]
90 [ 2, 8, 0, 0, 0, 0 ]
91 [ 1, 0, 0, 0, 0, 0 ]
92 [ 2, 2, 0, 0, 0, 0 ]
93 [ 1, 1, 0, 0, 0, 0 ]
94 [ 1, 1, 0, 0, 0, 0 ]
95 [ 1, 0, 0, 0, 0, 0 ]
96 [ 7, 198, 18, 8, 0, 0 ]
97 [ 1, 0, 0, 0, 0, 0 ]
98 [ 2, 3, 0, 0, 0, 0 ]
99 [ 2, 0, 0, 0, 0, 0 ]
100 [ 4, 12, 0, 0, 0, 0 ]
101 [ 1, 0, 0, 0, 0, 0 ]
102 [ 1, 3, 0, 0, 0, 0 ]
103 [ 1, 0, 0, 0, 0, 0 ]
104 [ 3, 11, 0, 0, 0, 0 ]
105 [ 1, 1, 0, 0, 0, 0 ]
106 [ 1, 1, 0, 0, 0, 0 ]
107 [ 1, 0, 0, 0, 0, 0 ]
108 [ 6, 35, 4, 0, 0, 0 ]
109 [ 1, 0, 0, 0, 0, 0 ]
110 [ 1, 5, 0, 0, 0, 0 ]
111 [ 1, 1, 0, 0, 0, 0 ]
112 [ 5, 38, 0, 0, 0, 0 ]
113 [ 1, 0, 0, 0, 0, 0 ]
114 [ 1, 5, 0, 0, 0, 0 ]
115 [ 1, 0, 0, 0, 0, 0 ]
116 [ 2, 3, 0, 0, 0, 0 ]
117 [ 2, 2, 0, 0, 0, 0 ]
118 [ 1, 1, 0, 0, 0, 0 ]
119 [ 1, 0, 0, 0, 0, 0 ]
120 [ 3, 38, 3, 0, 0, 0 ]
121 [ 2, 0, 0, 0, 0, 0 ]
122 [ 1, 1, 0, 0, 0, 0 ]
123 [ 1, 0, 0, 0, 0, 0 ]
124 [ 2, 2, 0, 0, 0, 0 ]
125 [ 3, 2, 0, 0, 0, 0 ]
126 [ 2, 14, 0, 0, 0, 0 ]
127 [ 1, 0, 0, 0, 0, 0 ]
128 [ 15, 2299, 14, 0, 0, 0 ]
129 [ 1, 1, 0, 0, 0, 0 ]
130 [ 1, 3, 0, 0, 0, 0 ]
131 [ 1, 0, 0, 0, 0, 0 ]
132 [ 2, 8, 0, 0, 0, 0 ]
133 [ 1, 0, 0, 0, 0, 0 ]
134 [ 1, 1, 0, 0, 0, 0 ]
135 [ 3, 2, 0, 0, 0, 0 ]
136 [ 3, 12, 0, 0, 0, 0 ]
137 [ 1, 0, 0, 0, 0, 0 ]
138 [ 1, 3, 0, 0, 0, 0 ]
139 [ 1, 0, 0, 0, 0, 0 ]
140 [ 2, 9, 0, 0, 0, 0 ]
141 [ 1, 0, 0, 0, 0, 0 ]
142 [ 1, 1, 0, 0, 0, 0 ]
143 [ 1, 0, 0, 0, 0, 0 ]
144 [ 10, 159, 22, 6, 0, 0 ]
145 [ 1, 0, 0, 0, 0, 0 ]
146 [ 1, 1, 0, 0, 0, 0 ]
147 [ 2, 4, 0, 0, 0, 0 ]
148 [ 2, 3, 0, 0, 0, 0 ]
149 [ 1, 0, 0, 0, 0, 0 ]
150 [ 2, 10, 1, 0, 0, 0 ]
151 [ 1, 0, 0, 0, 0, 0 ]
152 [ 3, 9, 0, 0, 0, 0 ]
153 [ 2, 0, 0, 0, 0, 0 ]
154 [ 1, 3, 0, 0, 0, 0 ]
155 [ 1, 1, 0, 0, 0, 0 ]
156 [ 2, 16, 0, 0, 0, 0 ]
157 [ 1, 0, 0, 0, 0, 0 ]
158 [ 1, 1, 0, 0, 0, 0 ]
159 [ 1, 0, 0, 0, 0, 0 ]
160 [ 7, 229, 2, 0, 0, 0 ]
161 [ 1, 0, 0, 0, 0, 0 ]
162 [ 5, 39, 11, 0, 0, 0 ]
163 [ 1, 0, 0, 0, 0, 0 ]
164 [ 2, 3, 0, 0, 0, 0 ]
165 [ 1, 1, 0, 0, 0, 0 ]
166 [ 1, 1, 0, 0, 0, 0 ]
167 [ 1, 0, 0, 0, 0, 0 ]
168 [ 3, 48, 5, 0, 0, 0 ]
169 [ 2, 0, 0, 0, 0, 0 ]
170 [ 1, 3, 0, 0, 0, 0 ]
171 [ 2, 3, 0, 0, 0, 0 ]
172 [ 2, 2, 0, 0, 0, 0 ]
173 [ 1, 0, 0, 0, 0, 0 ]
174 [ 1, 3, 0, 0, 0, 0 ]
175 [ 2, 0, 0, 0, 0, 0 ]
176 [ 5, 37, 0, 0, 0, 0 ]
177 [ 1, 0, 0, 0, 0, 0 ]
178 [ 1, 1, 0, 0, 0, 0 ]
179 [ 1, 0, 0, 0, 0, 0 ]
180 [ 4, 32, 0, 0, 0, 0 ]
181 [ 1, 0, 0, 0, 0, 0 ]
182 [ 1, 3, 0, 0, 0, 0 ]
183 [ 1, 1, 0, 0, 0, 0 ]
184 [ 3, 9, 0, 0, 0, 0 ]
185 [ 1, 0, 0, 0, 0, 0 ]
186 [ 1, 5, 0, 0, 0, 0 ]
187 [ 1, 0, 0, 0, 0, 0 ]
188 [ 2, 2, 0, 0, 0, 0 ]
189 [ 3, 10, 0, 0, 0, 0 ]
190 [ 1, 3, 0, 0, 0, 0 ]
191 [ 1, 0, 0, 0, 0, 0 ]
192 [ 11, 1405, 77, 50, 0, 0 ]
193 [ 1, 0, 0, 0, 0, 0 ]
194 [ 1, 1, 0, 0, 0, 0 ]
195 [ 1, 1, 0, 0, 0, 0 ]
196 [ 4, 8, 0, 0, 0, 0 ]
197 [ 1, 0, 0, 0, 0, 0 ]
198 [ 2, 8, 0, 0, 0, 0 ]
199 [ 1, 0, 0, 0, 0, 0 ]
200 [ 6, 44, 2, 0, 0, 0 ]
201 [ 1, 1, 0, 0, 0, 0 ]
202 [ 1, 1, 0, 0, 0, 0 ]
203 [ 1, 1, 0, 0, 0, 0 ]
204 [ 2, 10, 0, 0, 0, 0 ]
205 [ 1, 1, 0, 0, 0, 0 ]
206 [ 1, 1, 0, 0, 0, 0 ]
207 [ 2, 0, 0, 0, 0, 0 ]
208 [ 5, 46, 0, 0, 0, 0 ]
209 [ 1, 0, 0, 0, 0, 0 ]
210 [ 1, 11, 0, 0, 0, 0 ]
211 [ 1, 0, 0, 0, 0, 0 ]
212 [ 2, 3, 0, 0, 0, 0 ]
213 [ 1, 0, 0, 0, 0, 0 ]
214 [ 1, 1, 0, 0, 0, 0 ]
215 [ 1, 0, 0, 0, 0, 0 ]
216 [ 9, 126, 39, 3, 0, 0 ]
217 [ 1, 0, 0, 0, 0, 0 ]
218 [ 1, 1, 0, 0, 0, 0 ]
219 [ 1, 1, 0, 0, 0, 0 ]
220 [ 2, 13, 0, 0, 0, 0 ]
221 [ 1, 0, 0, 0, 0, 0 ]
222 [ 1, 5, 0, 0, 0, 0 ]
223 [ 1, 0, 0, 0, 0, 0 ]
224 [ 7, 190, 0, 0, 0, 0 ]
225 [ 4, 2, 0, 0, 0, 0 ]
226 [ 1, 1, 0, 0, 0, 0 ]
227 [ 1, 0, 0, 0, 0, 0 ]
228 [ 2, 13, 0, 0, 0, 0 ]
229 [ 1, 0, 0, 0, 0, 0 ]
230 [ 1, 3, 0, 0, 0, 0 ]
231 [ 1, 1, 0, 0, 0, 0 ]
232 [ 3, 11, 0, 0, 0, 0 ]
233 [ 1, 0, 0, 0, 0, 0 ]
234 [ 2, 14, 0, 0, 0, 0 ]
235 [ 1, 0, 0, 0, 0, 0 ]
236 [ 2, 2, 0, 0, 0, 0 ]
237 [ 1, 1, 0, 0, 0, 0 ]
238 [ 1, 3, 0, 0, 0, 0 ]
239 [ 1, 0, 0, 0, 0, 0 ]
240 [ 5, 181, 10, 4, 0, 0 ]
241 [ 1, 0, 0, 0, 0, 0 ]
242 [ 2, 3, 0, 0, 0, 0 ]
243 [ 7, 60, 0, 0, 0, 0 ]
244 [ 2, 3, 0, 0, 0, 0 ]
245 [ 2, 0, 0, 0, 0, 0 ]
246 [ 1, 3, 0, 0, 0, 0 ]
247 [ 1, 0, 0, 0, 0, 0 ]
248 [ 3, 9, 0, 0, 0, 0 ]
249 [ 1, 0, 0, 0, 0, 0 ]
250 [ 3, 11, 1, 0, 0, 0 ]
251 [ 1, 0, 0, 0, 0, 0 ]
252 [ 4, 42, 0, 0, 0, 0 ]
253 [ 1, 1, 0, 0, 0, 0 ]
254 [ 1, 1, 0, 0, 0, 0 ]
255 [ 1, 0, 0, 0, 0, 0 ]
257 [ 1, 0, 0, 0, 0, 0 ]
258 [ 1, 5, 0, 0, 0, 0 ]
259 [ 1, 0, 0, 0, 0, 0 ]
260 [ 2, 13, 0, 0, 0, 0 ]
261 [ 2, 0, 0, 0, 0, 0 ]
262 [ 1, 1, 0, 0, 0, 0 ]
263 [ 1, 0, 0, 0, 0, 0 ]
264 [ 3, 33, 3, 0, 0, 0 ]
265 [ 1, 0, 0, 0, 0, 0 ]
266 [ 1, 3, 0, 0, 0, 0 ]
267 [ 1, 0, 0, 0, 0, 0 ]
268 [ 2, 2, 0, 0, 0, 0 ]
269 [ 1, 0, 0, 0, 0, 0 ]
270 [ 3, 25, 2, 0, 0, 0 ]
271 [ 1, 0, 0, 0, 0, 0 ]
272 [ 5, 49, 0, 0, 0, 0 ]
273 [ 1, 4, 0, 0, 0, 0 ]
274 [ 1, 1, 0, 0, 0, 0 ]
275 [ 2, 2, 0, 0, 0, 0 ]
276 [ 2, 8, 0, 0, 0, 0 ]
277 [ 1, 0, 0, 0, 0, 0 ]
278 [ 1, 1, 0, 0, 0, 0 ]
279 [ 2, 2, 0, 0, 0, 0 ]
280 [ 3, 37, 0, 0, 0, 0 ]
281 [ 1, 0, 0, 0, 0, 0 ]
282 [ 1, 3, 0, 0, 0, 0 ]
283 [ 1, 0, 0, 0, 0, 0 ]
284 [ 2, 2, 0, 0, 0, 0 ]
285 [ 1, 1, 0, 0, 0, 0 ]
286 [ 1, 3, 0, 0, 0, 0 ]
287 [ 1, 0, 0, 0, 0, 0 ]
288 [ 14, 876, 123, 32, 0, 0 ]
289 [ 2, 0, 0, 0, 0, 0 ]
290 [ 1, 3, 0, 0, 0, 0 ]
291 [ 1, 1, 0, 0, 0, 0 ]
292 [ 2, 3, 0, 0, 0, 0 ]
293 [ 1, 0, 0, 0, 0, 0 ]
294 [ 2, 20, 1, 0, 0, 0 ]
295 [ 1, 0, 0, 0, 0, 0 ]
296 [ 3, 11, 0, 0, 0, 0 ]
297 [ 3, 2, 0, 0, 0, 0 ]
298 [ 1, 1, 0, 0, 0, 0 ]
299 [ 1, 0, 0, 0, 0, 0 ]
300 [ 4, 40, 4, 0, 0, 0 ]
301 [ 1, 1, 0, 0, 0, 0 ]
302 [ 1, 1, 0, 0, 0, 0 ]
303 [ 1, 0, 0, 0, 0, 0 ]
304 [ 5, 37, 0, 0, 0, 0 ]
305 [ 1, 1, 0, 0, 0, 0 ]
306 [ 2, 8, 0, 0, 0, 0 ]
307 [ 1, 0, 0, 0, 0, 0 ]
308 [ 2, 7, 0, 0, 0, 0 ]
309 [ 1, 1, 0, 0, 0, 0 ]
310 [ 1, 5, 0, 0, 0, 0 ]
311 [ 1, 0, 0, 0, 0, 0 ]
312 [ 3, 54, 4, 0, 0, 0 ]
313 [ 1, 0, 0, 0, 0, 0 ]
314 [ 1, 1, 0, 0, 0, 0 ]
315 [ 2, 2, 0, 0, 0, 0 ]
316 [ 2, 2, 0, 0, 0, 0 ]
317 [ 1, 0, 0, 0, 0, 0 ]
318 [ 1, 3, 0, 0, 0, 0 ]
319 [ 1, 0, 0, 0, 0, 0 ]
320 [ 11, 1621, 6, 2, 0, 0 ]
321 [ 1, 0, 0, 0, 0, 0 ]
322 [ 1, 3, 0, 0, 0, 0 ]
323 [ 1, 0, 0, 0, 0, 0 ]
324 [ 10, 131, 35, 0, 0, 0 ]
325 [ 2, 0, 0, 0, 0, 0 ]
326 [ 1, 1, 0, 0, 0, 0 ]
327 [ 1, 1, 0, 0, 0, 0 ]
328 [ 3, 12, 0, 0, 0, 0 ]
329 [ 1, 0, 0, 0, 0, 0 ]
330 [ 1, 11, 0, 0, 0, 0 ]
331 [ 1, 0, 0, 0, 0, 0 ]
332 [ 2, 2, 0, 0, 0, 0 ]
333 [ 2, 3, 0, 0, 0, 0 ]
334 [ 1, 1, 0, 0, 0, 0 ]
335 [ 1, 0, 0, 0, 0, 0 ]
336 [ 5, 202, 14, 4, 0, 0 ]
337 [ 1, 0, 0, 0, 0, 0 ]
338 [ 2, 3, 0, 0, 0, 0 ]
339 [ 1, 0, 0, 0, 0, 0 ]
340 [ 2, 13, 0, 0, 0, 0 ]
341 [ 1, 0, 0, 0, 0, 0 ]
342 [ 2, 16, 0, 0, 0, 0 ]
343 [ 3, 2, 0, 0, 0, 0 ]
344 [ 3, 9, 0, 0, 0, 0 ]
345 [ 1, 0, 0, 0, 0, 0 ]
346 [ 1, 1, 0, 0, 0, 0 ]
347 [ 1, 0, 0, 0, 0, 0 ]
348 [ 2, 10, 0, 0, 0, 0 ]
349 [ 1, 0, 0, 0, 0, 0 ]
350 [ 2, 8, 0, 0, 0, 0 ]
351 [ 3, 11, 0, 0, 0, 0 ]
352 [ 7, 188, 0, 0, 0, 0 ]
353 [ 1, 0, 0, 0, 0, 0 ]
354 [ 1, 3, 0, 0, 0, 0 ]
355 [ 1, 1, 0, 0, 0, 0 ]
356 [ 2, 3, 0, 0, 0, 0 ]
357 [ 1, 1, 0, 0, 0, 0 ]
358 [ 1, 1, 0, 0, 0, 0 ]
359 [ 1, 0, 0, 0, 0, 0 ]
360 [ 6, 137, 13, 0, 0, 0 ]
361 [ 2, 0, 0, 0, 0, 0 ]
362 [ 1, 1, 0, 0, 0, 0 ]
363 [ 2, 1, 0, 0, 0, 0 ]
364 [ 2, 9, 0, 0, 0, 0 ]
365 [ 1, 0, 0, 0, 0, 0 ]
366 [ 1, 5, 0, 0, 0, 0 ]
367 [ 1, 0, 0, 0, 0, 0 ]
368 [ 5, 37, 0, 0, 0, 0 ]
369 [ 2, 0, 0, 0, 0, 0 ]
370 [ 1, 3, 0, 0, 0, 0 ]
371 [ 1, 0, 0, 0, 0, 0 ]
372 [ 2, 13, 0, 0, 0, 0 ]
373 [ 1, 0, 0, 0, 0, 0 ]
374 [ 1, 3, 0, 0, 0, 0 ]
375 [ 3, 3, 1, 0, 0, 0 ]
376 [ 3, 9, 0, 0, 0, 0 ]
377 [ 1, 0, 0, 0, 0, 0 ]
378 [ 3, 55, 2, 0, 0, 0 ]
379 [ 1, 0, 0, 0, 0, 0 ]
380 [ 2, 9, 0, 0, 0, 0 ]
381 [ 1, 1, 0, 0, 0, 0 ]
382 [ 1, 1, 0, 0, 0, 0 ]
383 [ 1, 0, 0, 0, 0, 0 ]
384 [ 15, 19338, 459, 357, 0, 0 ]
385 [ 1, 1, 0, 0, 0, 0 ]
386 [ 1, 1, 0, 0, 0, 0 ]
387 [ 2, 2, 0, 0, 0, 0 ]
388 [ 2, 3, 0, 0, 0, 0 ]
389 [ 1, 0, 0, 0, 0, 0 ]
390 [ 1, 11, 0, 0, 0, 0 ]
391 [ 1, 0, 0, 0, 0, 0 ]
392 [ 6, 36, 2, 0, 0, 0 ]
393 [ 1, 0, 0, 0, 0, 0 ]
394 [ 1, 1, 0, 0, 0, 0 ]
395 [ 1, 0, 0, 0, 0, 0 ]
396 [ 4, 26, 0, 0, 0, 0 ]
397 [ 1, 0, 0, 0, 0, 0 ]
398 [ 1, 1, 0, 0, 0, 0 ]
399 [ 1, 4, 0, 0, 0, 0 ]
400 [ 10, 201, 10, 0, 0, 0 ]
401 [ 1, 0, 0, 0, 0, 0 ]
402 [ 1, 5, 0, 0, 0, 0 ]
403 [ 1, 0, 0, 0, 0, 0 ]
404 [ 2, 3, 0, 0, 0, 0 ]
405 [ 5, 11, 0, 0, 0, 0 ]
406 [ 1, 5, 0, 0, 0, 0 ]
407 [ 1, 0, 0, 0, 0, 0 ]
408 [ 3, 40, 3, 0, 0, 0 ]
409 [ 1, 0, 0, 0, 0, 0 ]
410 [ 1, 5, 0, 0, 0, 0 ]
411 [ 1, 0, 0, 0, 0, 0 ]
412 [ 2, 2, 0, 0, 0, 0 ]
413 [ 1, 0, 0, 0, 0, 0 ]
414 [ 2, 8, 0, 0, 0, 0 ]
415 [ 1, 0, 0, 0, 0, 0 ]
416 [ 7, 228, 0, 0, 0, 0 ]
417 [ 1, 1, 0, 0, 0, 0 ]
418 [ 1, 3, 0, 0, 0, 0 ]
419 [ 1, 0, 0, 0, 0, 0 ]
420 [ 2, 38, 0, 0, 0, 0 ]
421 [ 1, 0, 0, 0, 0, 0 ]
422 [ 1, 1, 0, 0, 0, 0 ]
423 [ 2, 0, 0, 0, 0, 0 ]
424 [ 3, 11, 0, 0, 0, 0 ]
425 [ 2, 0, 0, 0, 0, 0 ]
426 [ 1, 3, 0, 0, 0, 0 ]
427 [ 1, 0, 0, 0, 0, 0 ]
428 [ 2, 2, 0, 0, 0, 0 ]
429 [ 1, 1, 0, 0, 0, 0 ]
430 [ 1, 3, 0, 0, 0, 0 ]
431 [ 1, 0, 0, 0, 0, 0 ]
432 [ 15, 566, 161, 32, 1, 0 ]

> iii. I am pretty sure that the general affine group 3^2:GL(2,3) has 
> derived length 5. In this case, the next term is bounded from above by 
> 432 and from below by 96. With further work, I have reduced the 
> possible candidates for this number to one of 144, 192, 288, 320, 336, 
> 360, 384, 400, or 432. In any
> of these cases, it is not a factorial or a double of a factorial. 
> Therefore this sequence is different from A099144!
>
> ---- David Harden