Groups of order 960

Factorization and useful forms
The number 960 has prime factors 2, 3, and 5, and prime factorization:

$$\! 960 = 2^6 \cdot 3^1 \cdot 5^1 =64\cdot 3 \cdot 5$$

Other useful expressions for this number are:

$$\! 960 = 2(5^2 - 1)(5^2 - 5) = 2^3 \cdot 5!$$

GAP implementation
gap> SmallGroupsInformation(960);

There are 11394 groups of order 960. They are sorted by their Frattini factors. 1 has Frattini factor [ 30, 1 ]. 2 has Frattini factor [ 30, 2 ]. 3 has Frattini factor [ 30, 3 ]. 4 has Frattini factor [ 30, 4 ]. 5 has Frattini factor [ 60, 6 ]. 6 has Frattini factor [ 60, 7 ]. 7 - 215 have Frattini factor [ 60, 8 ]. 216 - 217 have Frattini factor [ 60, 9 ]. 218 - 339 have Frattini factor [ 60, 10 ]. 340 - 461 have Frattini factor [ 60, 11 ]. 462 - 583 have Frattini factor [ 60, 12 ]. 584 - 636 have Frattini factor [ 60, 13 ]. 637 - 639 have Frattini factor [ 120, 34 ]. 640 - 642 have Frattini factor [ 120, 35 ]. 643 - 779 have Frattini factor [ 120, 36 ]. 780 - 787 have Frattini factor [ 120, 37 ]. 788 - 795 have Frattini factor [ 120, 38 ]. 796 - 812 have Frattini factor [ 120, 39 ]. 813 - 906 have Frattini factor [ 120, 40 ]. 907 - 1000 have Frattini factor [ 120, 41 ]. 1001 - 3720 have Frattini factor [ 120, 42 ]. 3721 - 3737 have Frattini factor [ 120, 43 ]. 3738 - 4339 have Frattini factor [ 120, 44 ]. 4340 - 4941 have Frattini factor [ 120, 45 ]. 4942 - 5543 have Frattini factor [ 120, 46 ]. 5544 - 5680 have Frattini factor [ 120, 47 ]. 5681 - 5725 have Frattini factor [ 240, 189 ]. 5726 - 5747 have Frattini factor [ 240, 190 ]. 5748 has Frattini factor [ 240, 191 ]. 5749 - 5754 have Frattini factor [ 240, 192 ]. 5755 - 5761 have Frattini factor [ 240, 193 ]. 5762 - 5835 have Frattini factor [ 240, 194 ]. 5836 - 6250 have Frattini factor [ 240, 195 ]. 6251 - 6298 have Frattini factor [ 240, 196 ]. 6299 - 6346 have Frattini factor [ 240, 197 ]. 6347 - 6401 have Frattini factor [ 240, 198 ]. 6402 has Frattini factor [ 240, 199 ]. 6403 - 6528 have Frattini factor [ 240, 200 ]. 6529 - 6654 have Frattini factor [ 240, 201 ]. 6655 - 9638 have Frattini factor [ 240, 202 ]. 9639 - 9666 have Frattini factor [ 240, 203 ]. 9667 - 9672 have Frattini factor [ 240, 204 ]. 9673 - 10046 have Frattini factor [ 240, 205 ]. 10047 - 10420 have Frattini factor [ 240, 206 ]. 10421 - 10794 have Frattini factor [ 240, 207 ]. 10795 - 10862 have Frattini factor [ 240, 208 ]. 10863 - 10883 have Frattini factor [ 480, 1186 ]. 10884 - 10892 have Frattini factor [ 480, 1187 ]. 10893 has Frattini factor [ 480, 1188 ]. 10894 - 10908 have Frattini factor [ 480, 1189 ]. 10909 has Frattini factor [ 480, 1190 ]. 10910 - 10924 have Frattini factor [ 480, 1191 ]. 10925 - 10939 have Frattini factor [ 480, 1192 ]. 10940 - 10994 have Frattini factor [ 480, 1193 ]. 10995 - 10997 have Frattini factor [ 480, 1194 ]. 10998 - 11000 have Frattini factor [ 480, 1195 ]. 11001 - 11003 have Frattini factor [ 480, 1196 ]. 11004 - 11066 have Frattini factor [ 480, 1197 ]. 11067 - 11087 have Frattini factor [ 480, 1198 ]. 11088 - 11108 have Frattini factor [ 480, 1199 ]. 11109 - 11115 have Frattini factor [ 480, 1200 ]. 11116 - 11122 have Frattini factor [ 480, 1201 ]. 11123 - 11143 have Frattini factor [ 480, 1202 ]. 11144 - 11148 have Frattini factor [ 480, 1203 ]. 11149 - 11151 have Frattini factor [ 480, 1204 ]. 11152 - 11172 have Frattini factor [ 480, 1205 ]. 11173 - 11193 have Frattini factor [ 480, 1206 ]. 11194 - 11273 have Frattini factor [ 480, 1207 ]. 11274 - 11282 have Frattini factor [ 480, 1208 ]. 11283 - 11287 have Frattini factor [ 480, 1209 ]. 11288 - 11307 have Frattini factor [ 480, 1210 ]. 11308 - 11327 have Frattini factor [ 480, 1211 ]. 11328 - 11347 have Frattini factor [ 480, 1212 ]. 11348 - 11354 have Frattini factor [ 480, 1213 ]. 11355 - 11394 have trivial Frattini subgroup.

For the selection functions the values of the following attributes are precomputed and stored: IsAbelian, IsNilpotentGroup, IsSupersolvableGroup, IsSolvableGroup, LGLength, FrattinifactorSize and FrattinifactorId.

This size belongs to layer 2 of the SmallGroups library. IdSmallGroup is available for this size.