| 晶体点群 | 元素 | 含一个以上元素的共轭元素类 | 正规真子群 | |||||
| C1 | {e} | |||||||
| C2 | {e,C2^1} | |||||||
| C3 | {e,C3^1,C3^2} | |||||||
| C4 | {e,C4^1,C2^1,C4^3} | C2 | ||||||
| C6 | {e,C6^1,C3^1,C2^1,C3^2,C6^5} | C3,C2 | 说明： 1.C3^1、C4^3等表示旋转主轴；I3^5、I6^1等表示主轴为旋转反轴； 2.I表示反演； 3.σ表示垂直于旋转主轴的镜面； 4.(C2^1)0、(C2^1)60等表示与主轴垂直的二次轴,括号外的数字表示二次轴与(C2^1)0的夹角度数； 5.σ60、σ135等表示平行于主轴的镜面(即主轴在镜面上),数字表示镜面法线与σ0的夹角度数。 |
|||||
| Ci(S2) | {e,i} | |||||||
| Cs(C1h) | {e,σ} | |||||||
| C3i(S6) | {e,i,C3^1,C3^2,I3^1,I3^5} | C3,Ci | ||||||
| S4 | {e,I4^1,C2^1,I4^2} | C2 | ||||||
| C3h | {e,σ,C3^1,C3^2,I6^5,I6^1} | C3,Cs | ||||||
| C2h | {e,σ,C2^1,i} | C2,Cs,Ci | ||||||
| C4h | {e,σ,C2^1,i,C4^1,C4^3,σC4^1,σC4^3} | Ci,C4,C2h,S4 | ||||||
| C6h | {e,σ,C6^1,C3^1,C2^1,C3^2,C6^5,σC6^1,σC3^1,i,σC3^2， σC6^5} |
C3h,C3i,C2h,C6,C2,Ci,Cs | ||||||
| C2v | {e,C2^1,σ0,σ90} | C2,Cs | ||||||
| C3v | {e,C3^1,C3^2,σ0,σ60,σ120} | {σ0,σ60,σ120},{C3^1,C3^2} | C3 | |||||
| C4v | {e,C4^1,C2^1,C4^3,σ0,σ45,σ90,σ135} | {C4^1,C4^3},{σ0,σ90},{σ45,σ135} | C2v,C4,C2 | |||||
| C6v | {e,C6^1,C3^1,C2^1,C3^2,C6^5,σ0,σ30,σ60,σ90,σ120, σ150} |
{σ0,σ60,σ120},{σ30,σ90,σ150}, {C6^1,C6^5},{C3^1,C3^2} |
C3v,C6,C3,C2 | |||||
| D2 | {e,C2^1,(C2^1)0,(C2^1)90} | C2 | ||||||
| D3 | {e,C3^1,C3^2,(C2^1)0,(C2^1)60,(C2^1)120} | {C3^1,C3^2}, {(C2^1)0,(C2^1)60,(C2^1)120} |
C3 | |||||
| D4 | {e,C4^1,C2^1,C4^3,(C2^1)0,(C2^1)45, (C2^1)90,(C2^1)135} |
{C4^1,C4^3},{(C2^1)0,(C2^1)90}, {(C2^1)45,(C2^1)135} |
D2,C4,C2 | |||||
| D6 | {e,C6^1,C3^1,C2^1,C3^2,C6^5,(C2^1)0,(C2^1)30,(C2^1)60,(C2^1)90,(C2^1)120,(C2^1)150} | {C6^1,C6^5},{C3^1,C3^2}, {(C2^1)0,(C2^1)60,(C2^1)120}, {(C2^1)30,(C2^1)90,(C2^1)150} |
D3,C6,C3,C2 | |||||
| D3d | {e,I3^1,C3^2,i,C3^1,I3^5,(C2^1)0,(C2^1)60,(C2^1)120, σ0,σ60,σ120} |
{I3^1,I3^5},{C3^1,C3^2}, {(C2^1)0,(C2^1)30,(C2^1)60}, {σ0,σ60,σ120} |
D3,C3v,C3i,C3,Cs | |||||
| D2d | {e,σ45,I4^1,(C2^1)90,C2^1,σ135,I4^3,(C2^1)0} | {I4^1,I4^3}, {σ45,σ135},{(C2^1)0,(C2^1)90} |
D2,S4,C2v,C2 | |||||
| D3h | {e,σ,C3^1,C3^2,I6^5,I6^1,(C2^1)0,(C2^1)60,(C2^1)120,σ0,σ60,σ120} | {I6^1,I6^5},{C3^1,C3^2}, {(C2^1)0,(C2^1)30,(C2^1)60}, {σ0,σ60,σ120} |
D3,C3v,C3h,C3,Cs | |||||
| D2h | {e,C2^1,i,σ,(C2^1)0,(C2^1)90,σ0,σ90} | D2,C2h,C2v,Cs,Ci | ||||||
| D4h | {e,C4^1,C2^1,C4^3,σ90,σ45,σ0,σ135,σ, I4^1,i,I4^3,(C2^1)0,(C2^1)45,(C2^1)90,(C2^1)135} |
{C4^1,C4^3},{(C2^1)0,(C2^1)90}, {(C2^1)45,(C2^1)135}, {σ0,σ90},{σ45,σ135},{I4^1,I4^3} |
D2d,D2h,D4,D2,C4v,C4h,C2v, C2h,C4,C2,Ci,Cs |
|||||
| D6h | {e,C6^1,C3^1,C2^1,C3^2,C6^5,σ,I6^1,I6^5,σ0,σ30, σ60,σ90,σ120,σ150,(C2^1)0,(C2^1)30,(C2^1)60, (C2^1)90,(C2^1)120,(C2^1)150,i,σC6^1,σC6^5} |
{I6^1,I6^5},{σI6^1,σI6^5}, {C3^1,C3^2},{C6^1,C6^5}, {(C2^1)0,(C2^1)60,(C2^1)120}, {(C2^1)30,(C2^1)90,(C2^1)150}, {σ0,σ60,σ120},{σ30,σ90,σ150} |
D6,D3h,D3d,D3,C6h,C6v,C6, C3,C2,Ci,Cs |
|||||
| （立方晶系的轴较多,群元素按共轭元素类写） | ||||||||
| T | {e,3C2,4C3,4C3^2} | D2 | ||||||
| Td | {e,3C2,8C3,6I4,6σ} | T,D2 | ||||||
| Th | {e,3C2,4C3,4C3^2,i,3σ,4I6,4I6^5} | T,D2h,D2,Ci | ||||||
| O | {e,3C2,8C3,6C4,6C2} | T,D2 | ||||||
| Oh | {e,3C2,8C3,6C4,6C2,i,3σ,8I6,6I4,6σ} | O,Td,Th,D2,Ci | ||||||