Torsion Free Space Groups

Degree: 1 2 3 4 5 6 all

Has trivial center: Yes No all

Order of point group: 1 2 3 4 5 6 8 9 10 12 16 18 20 24 32 36 48 64 72 80 96 120 all

Isomorphism type of point group:

id C2 C22 C23 C24 C25 C3 C2 x C3 C22 x C3 C23 x C3 C24 x C3 C32 C2 x C32 C22 x C32 C4 C2 x C4 C22 x C4

C23 x C4 C3 x C4 C2 x C3 x C4 C22 x C3 x C4 C42 C5 C2 x C5 C22 x C5 C8 C2 x C8 D8 C2 x D8 C22 x D8 C3 x D8 C2 x C3 x D8 C4 x D8

D10 C2 x D10 D16 D24 C2 x D24 S3 C2 x S3 C22 x S3 C23 x S3 C3 x S3 C2 x C3 x S3 C4 x S3 C2 x C4 x S3 S32 S4 C2 x S4

C3 x S4 A4 C2 x A4 C22 x A4 C23 x A4 C3 x A4 C2 x C3 x A4 C4 x A4 C2 x C4 x A4 Q8 C3 x Q8 C3 ><| C4 C2 x (C3 ><| C4) C3 x (C3 ><| C4) C3 ><| C8 C32 ><| C2

C2 x (C32 ><| C2) [16,8] [16,9] C2 x [16,9] [16,10] [16,11] [16,13] [24,11] [32,31] [32,33] [32,36] [32,46] [32,47] [64,250] [80,52] C2 x [80,52] all