Quintic symmetric and semisymmetric G-graphs

We have introduce a new type of graphs from a group called G-graphs, these graphs give us a lot of information about the structure of groups. Moreover, these type of graphs can be used in any area of sciences where CAYLEY graphs occurs. G-graphs are very efficient to construct symmetric and semisymmetric graphs. Indeed we have built a power full algorithm to construct symmetric and semisymmetric graphs. The following table has been built in 32 minutes on a 2 gigahertz Athlon (32 bit processor).
In green are semisymmetric G-graphs, the others are symmetric.

O(Gamma)O(G)GNauty KeyAutomorphism groupSimple
25sg-5-1[ 44 9a902 248b4d]1 orbit; group size=2; No
1025sg-25-2[ 17ec 6f7beba 74b941b]1 orbit; group size=28800; Yes
2255sg-55-1[84ca24d e37024c b3ceb4c]1 orbit; group size=1320; Yes
2460sg-60-5[a682f88 fe69114 96269a9]1 orbit; group size=480; Yes
3280sg-80-49[e632901 3fdc154 caf3957]1 orbit; group size=3840; Yes
48120sg-120-5[cec8526 dc9b56e 618613b]1 orbit; group size=960; Yes
50125sg-125-3[8c13162 f781a4 fc6d418]1 orbit; group size=4000; Yes
62155sg-155-1[973e140 27e0787 1e325ea]1 orbit; group size=310; Yes
64160sg-160-199[9cf125c 55ae425 1b29490]1 orbit; group size=640; Yes
82205sg-205-1[239a563 d5ab3d2 e0c2c7]1 orbit; group size=410; Yes
110275sg-275-3[e02bd46 52ad388 eca7d67]1 orbit; group size=550; Yes
120300sg-300-22[105963d c545b09 6297140]2 orbits; group size=1200; Yes
122305sg-305-1[654d2a5 746b57e fef3dc]1 orbit; group size=610; Yes
128320sg-320-1012[5b012c9 6160bc8 f44a2cc]1 orbit; group size=2560; Yes
142355sg-355-1[db90525 6d0d695 84c9a72]1 orbit; group size=710; Yes
144360sg-360-118[a6c3285 b470740 d9b5ee0]1 orbit; group size=5760; Yes
160400sg-400-213[cdd3ce8 b85abb0 d822e2]1 orbit; group size=3200; Yes
162405sg-405-15[78bd51f beaf7bc 1dfc116]1 orbit; group size=19440; Yes
202505sg-505-1[b84d3e9 16def22 49d50c]1 orbit; group size=1010; Yes
240600sg-600-54[1cc14af 63c66b5 e3b98f]2 orbits; group size=2400; Yes
242605sg-605-1[b654e37 ec9390a 889ea2f]1 orbit; group size=1210; Yes
242605sg-605-5[86821dc 30e35ea 93922ba]1 orbit; group size=1210; Yes
242605sg-605-6[b25419e 844d2ef 7045aba]1 orbit; group size=2420; Yes
250625sg-625-7[faf53ab 2951997 5181f7b]2 orbits; group size=10000; Yes
262655sg-655-1[ f57274 da877ae bc0b31c]1 orbit; group size=1310; Yes
264660sg-660-13[7a4e488 95005d8 215b670]1 orbit; group size=5280; Yes
288720sg-720-409[ad4452e 7bb48c8 308676b]1 orbit; group size=2880; Yes
302755sg-755-1[ebc6451 657b8fa a1a7211]1 orbit; group size=1510; Yes
310775sg-775-3[dd864a2 4f240f1 375e5ac]1 orbit; group size=1550; Yes
320800sg-800-1065[7203dd4 7ac19ff d517839]1 orbit; group size=6400; Yes
352880sg-880-214[554549c b77c94b 86321b4]1 orbit; group size=1760; Yes
362905sg-905-1[5ffd5ea 44a5ca1 d96e357]1 orbit; group size=1810; Yes
382955sg-955-1[c7ca940 a476869 19c3807]1 orbit; group size=1910; Yes
384960sg-960-11357[b731617 7f11e73 de30654]1 orbit; group size=7680; Yes
384960sg-960-11358[a59b657 4d0c38 ba578e0]1 orbit; group size=46080; Yes
4101025sg-1025-3[ da0ba0 f0683f dab745b]1 orbit; group size=2050; Yes
4221055sg-1055-1[905c63a 728fdd4 392ac38]1 orbit; group size=2110; Yes
4321080sg-1080-260[8471367 65d4d11 8d34325]1 orbit; group size=4320; Yes
4821205sg-1205-1[ 9a5503 1462a9e 9ca8fa8]1 orbit; group size=2410; Yes
4861215sg-1215-68[87973f9 2107d3d 673a23d]1 orbit; group size=4860; Yes
5021255sg-1255-1[16ca8d6 cb8f523 37c1316]1 orbit; group size=2510; Yes
5281320sg-1320-13[29cac7d 2cd202a 579582d]1 orbit; group size=5280; Yes
5421355sg-1355-1[37ef318 36a5e41 28e017]1 orbit; group size=2710; Yes
5501375sg-1375-9[969847d f6a526f d21a28c]1 orbit; group size=2750; Yes
5621405sg-1405-1[57e48cd 745c663 5297ed2]1 orbit; group size=2810; Yes
6001500sg-1500-112[bf23345 abae174 c35723f]1 orbit; group size=12000; Yes
6101525sg-1525-3[916739a ddedb6e f2150bf]1 orbit; group size=3050; Yes
6221555sg-1555-1[5a282c9 f6f8170 f93d10e]1 orbit; group size=3110 Yes
6401600sg-1600-6786[e6a21de 94d5614 a11e55e]1 orbit; group size=12800; Yes
6621655sg-1655-1[55f5a6d d763c1b 356199e]1 orbit; group size=3310; Yes
6821705sg-1705-3[c234669 ef4d649 b19b2b2]1 orbit; group size=3410; Yes
6821705sg-1705-4[72cd144 b7cf15e 405ce60]1 orbit; group size=3410; Yes
6821705sg-1705-5[f1ce571 452cc29 31fbcc3]1 orbit; group size=3410; Yes
6821705sg-1705-6[66328f7 5a926a4 3e3edcd]1 orbit; group size=3410; Yes
7041760sg-1760-1139[5098afa 21391a0 aaea452]1 orbit; group size=3520; Yes
7101775sg-1775-3[abadb68 e2a501 ce90797]1 orbit; group size=3550; Yes
7201800sg-1800-555[a983e28 57fbbfe e198e0f]2 orbits; group size=14400; Yes
7221805sg-1805-2[60b3990 7757b91 aba498d]1 orbit; group size=7220; Yes
8002000sg-2000-488[2c52f03 48caf84 cd54c3b]1 orbit; group size=16000; Yes