List and discuss the different
properties, which will classify the group as a dihedral group of...

Question

List and discuss the different
properties, which will classify the group as a dihedral group of order 8.

Robert · Accepted Answer

Solution
Solution 
 
Question: - List and discuss the different properties, which will classify the group as a dihedral 
group of order 8.
Solution: - The Dihedral group of order 8 is also D (4) and it is defined as the group of all symmetries 
of the regular 4- gon that is square.
There are two ways two describe this :- 
A) One is the list of all properties of Dihedral group of order 8 which are as follows:-
1) Group of prime power order 
2) Nilpotent group. 
3) Super solvable group. 
4) Solvable group. 
5) Monolithic group. 
6) Automorph-conjugate subgroup 
7) Algebra group. 
8) Ambivalent group 
9) Rational group. 
10) Rational representation group. 
11) Extra special group 
12) Special group 
13) Frattini-in-center group 
14) UL- equivalent group. 
15) Maximal class group 
16) Camina group 
17) Directly indecomposable group 
18) Centrally indecomposable group 
19) Stem group.

List and discuss the different properties, which will classify the group as a dihedral group of order 8.

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