Groups of order 672

Statistics at a glace
The number 672 has prime factors 2, 3, and 7. The prime factorization is as follows:

$$\! 672 = 2^5 \cdot 3^1 \cdot 7^1 = 32 \cdot 3 \cdot 7$$

There are both solvable and non-solvable groups of this order. The only possible simple non-abelian composition factor is projective special linear group:PSL(3,2) of order 168, and thus every non-solvable group has composition factors: two copies of cyclic group:Z2 and one copy of $$PSL(3,2)$$.

GAP implementation
gap> SmallGroupsInformation(672);

There are 1280 groups of order 672. They are sorted by their Frattini factors. 1 has Frattini factor [ 42, 1 ]. 2 has Frattini factor [ 42, 2 ]. 3 has Frattini factor [ 42, 3 ]. 4 has Frattini factor [ 42, 4 ]. 5 has Frattini factor [ 42, 5 ]. 6 has Frattini factor [ 42, 6 ]. 7 - 47 have Frattini factor [ 84, 7 ]. 48 - 114 have Frattini factor [ 84, 8 ]. 115 - 133 have Frattini factor [ 84, 9 ]. 134 has Frattini factor [ 84, 10 ]. 135 has Frattini factor [ 84, 11 ]. 136 - 176 have Frattini factor [ 84, 12 ]. 177 - 217 have Frattini factor [ 84, 13 ]. 218 - 258 have Frattini factor [ 84, 14 ]. 259 - 277 have Frattini factor [ 84, 15 ]. 278 - 281 have Frattini factor [ 168, 45 ]. 282 - 285 have Frattini factor [ 168, 46 ]. 286 - 371 have Frattini factor [ 168, 47 ]. 372 - 378 have Frattini factor [ 168, 48 ]. 379 - 386 have Frattini factor [ 168, 49 ]. 387 - 721 have Frattini factor [ 168, 50 ]. 722 - 745 have Frattini factor [ 168, 51 ]. 746 - 752 have Frattini factor [ 168, 52 ]. 753 - 760 have Frattini factor [ 168, 53 ]. 761 - 846 have Frattini factor [ 168, 54 ]. 847 - 932 have Frattini factor [ 168, 55 ]. 933 - 1018 have Frattini factor [ 168, 56 ]. 1019 - 1042 have Frattini factor [ 168, 57 ]. 1043 - 1045 have Frattini factor [ 336, 208 ]. 1046 - 1048 have Frattini factor [ 336, 209 ]. 1049 has Frattini factor [ 336, 210 ]. 1050 has Frattini factor [ 336, 211 ]. 1051 - 1065 have Frattini factor [ 336, 212 ]. 1066 has Frattini factor [ 336, 213 ]. 1067 - 1077 have Frattini factor [ 336, 214 ]. 1078 - 1088 have Frattini factor [ 336, 215 ]. 1089 - 1103 have Frattini factor [ 336, 216 ]. 1104 - 1114 have Frattini factor [ 336, 217 ]. 1115 - 1125 have Frattini factor [ 336, 218 ]. 1126 - 1178 have Frattini factor [ 336, 219 ]. 1179 - 1184 have Frattini factor [ 336, 220 ]. 1185 - 1191 have Frattini factor [ 336, 221 ]. 1192 - 1198 have Frattini factor [ 336, 222 ]. 1199 - 1200 have Frattini factor [ 336, 223 ]. 1201 - 1202 have Frattini factor [ 336, 224 ]. 1203 - 1217 have Frattini factor [ 336, 225 ]. 1218 - 1232 have Frattini factor [ 336, 226 ]. 1233 - 1247 have Frattini factor [ 336, 227 ]. 1248 - 1253 have Frattini factor [ 336, 228 ]. 1254 - 1280 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.