Some Group Tables
The Klein 4-Group
| * | | e | a | b | c |
| | | | | |
| e | | e | a | b | c |
| a | | a | e | c | b |
| b | | b | c | e | a |
| c | | c | b | a | e |
The Klein 4-Group expressed as Z2 X Z2
| + | | (0,0) | (1,0) | (0,1) | (1,1) |
| | | | | |
| (0,0) | | (0,0) | (1,0) | (0,1) | (1,1) |
| (1,0) | | (1,0) | (0,0) | (1,1) | (0,1) |
| (0,1) | | (0,1) | (1,1) | (0,0) | (1,0) |
| (1,1) | | (1,1) | (0,1) | (1,0) | (0,0) |
The Klein 4-Group expressed as a subgroup of S4
| o | | e | (12) | (34) | (12)(34) |
| | | | | |
| e | | e | (12) | (34) | (12)(34) |
| (12) | | (12) | e | (12)(34) | (34) |
| (34) | | (34) | (12)(34) | e | (12) |
| (12)(34) | | (12)(34) | (34) | (12) | e |
C6
| + | | [0] | [1] | [2] | [3] | [4] | [5] |
| | | | | | | |
| [0] | | [0] | [1] | [2] | [3] | [4] | [5] |
| [1] | | [1] | [2] | [3] | [4] | [5] | [0] |
| [2] | | [2] | [3] | [4] | [5] | [0] | [1] |
| [3] | | [3] | [4] | [5] | [0] | [1] | [2] |
| [4] | | [4] | [5] | [0] | [1] | [2] | [3] |
| [5] | | [5] | [0] | [1] | [2] | [3] | [4] |
C6 as C2 X C3 (cyclic table)
| + | | (0,0) | (1,1) | (0,2) | (1,0) | (0,1) | (1,2) |
| | | | | | | |
| (0,0) | | (0,0) | (1,1) | (0,2) | (1,0) | (0,1) | (1,2) |
| (1,1) | | (1,1) | (0,2) | (1,0) | (0,1) | (1,2) | (0,0) |
| (0,2) | | (0,2) | (1,0) | (0,1) | (1,2) | (0,0) | (1,1) |
| (1,0) | | (1,0) | (0,1) | (1,2) | (0,0) | (1,1) | (0,2) |
| (0,1) | | (0,1) | (1,2) | (0,0) | (1,1) | (0,2) | (1,0) |
| (1,2) | | (1,2) | (0,0) | (1,1) | (0,2) | (1,0) | (0,1) |
C6 as C2 X C3 (product table)
| + | | (0,0) | (0,1) | (0,2) | | (1,0) | (1,1) | (1,2) |
| | | | | | | | |
| (0,0) | | (0,0) | (0,1) | (0,2) | | (1,0) | (1,1) | (1,2) |
| (0,1) | | (0,1) | (0,2) | (0,0) | | (1,1) | (1,2) | (1,0) |
| (0,2) | | (0,2) | (0,0) | (0,1) | | (1,2) | (1,0) | (1,2) |
| | | | | | | | |
| (1,0) | | (1,0) | (1,1) | (1,2) | | (0,0) | (0,1) | (0,2) |
| (1,1) | | (1,1) | (1,2) | (1,0) | | (0,1) | (0,2) | (0,0) |
| (1,2) | | (1,2) | (1,0) | (1,1) | | (0,2) | (0,0) | (0,1) |
D8
| * | | e | a | b | s | | c | t | d | r |
| | | | | | | | | |
| e | | e | a | b | s | | c | t | d | r |
| a | | a | e | s | b | | t | c | r | d |
| b | | b | s | e | a | | r | d | t | c |
| s | | s | b | a | e | | d | r | c | t |
| | | | | | | | | | |
| c | | c | r | t | d | | e | b | s | a |
| t | | t | d | c | r | | a | s | b | e |
| d | | d | t | r | c | | s | a | e | b |
| r | | r | c | d | t | | b | e | a | s |
Len M. Smiley
Last modified: Mon Oct 30 14:27:23 AKST 2000