Finite Group Z4
One of the two groups of Order 4. Like 
, it is Abelian,but unlike , it is a Cyclic. Examples include the Point Groups 
and
and the Modulo Multiplication Groups 
and 
. Elements 
of the group satisfy 
, where 1 is the Identity Element, and two of the elements satisfy 
.
The Cycle Graph is shown above. The Multiplication Table for this group may be written in three equivalentways--denoted here by 
, 
, and 
--by permuting the symbols used for the group elements.
| 1 |  |  |  |
| 1 | 1 | | | |
| | | | 1 |
| | | 1 | |
| | 1 | | |
The Multiplication Table for is obtained from by interchanging and .
 | 1 | | | |
| 1 | 1 | | | |
| | 1 | | |
| | | | 1 |
| | | 1 | |
The Multiplication Table for is obtained from by interchanging and .
| 1 | | | |
| 1 | 1 | | | |
| | | 1 | |
| | 1 | | |
| | | | 1 |
The Conjugacy Classes of 
are 
, 
,
 |  |  | (1) |
 | | | (2) |
 | |  | (3) |
, | |  | (4) |
 | | | (5) |
 | |  | (6) |
and
. The group may be given a reducible representation using Complex Numbers
 | | | (7) |
| |  | (8) |
| |  | (9) |
 | |  | (10) |
or Real Matrices
| |  | (11) |
| |  | (12) |
| |  | (13) |
| |  | (14) |
See also Finite Group Z2Z2
- Orthogonal Array
- Orthogonal Basis
- Orthogonal Circles
- Orthogonal Curves
- Orthogonal Functions
- Orthogonal Group
- Orthogonal Group Representations
- Orthogonality Condition
- Orthogonality Theorem
- Orthogonal Lines
- Orthogonal Matrix
- Orthogonal Polynomials
- Orthogonal Projection
- Orthogonal Rotation Group
- Orthogonal Tensors
- Orthogonal Transformation
- Orthogonal Vectors
- Orthographic Projection
- Orthologic
- Orthonormal Basis
- Orthonormal Functions
- Orthonormal Vectors
- Orthopole
- Orthoptic Curve
- Orthotomic