# Tagged Questions

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### Subgroups of order $5$ in Icosahedral group

Let $G$ denote the orientation preserving isometries of Icosahedron. I want to show the following using group-theoretic notions: Let $N\leq G$ be a subgroup with order $5.$ Show that it is a ...
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### Degrees of parabolic subgroups

Suppose a finite reflection group $G$ has the degrees $d_1,\ldots,d_n$. Let $G^*$ be a parabolic subgroup of $G$. What are the degrees of $G^*$. Since $|G^*|$ divides $|G|$ it is clear that the ...
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### Building invariant $S_n$ structures from two invariant $Z_n$ structures

Take two mathematical structures with a $Z_n$ symmetry (cyclic symmetry). Which are the different ways, in "gluing" these structures, to obtain a mathematical structure with a $S_n$ symmetry ...
### Solid whose full symmetry group corresponds to $A_4\times\mathbb Z_2$
I'm looking for a geometrical interpretation of the action of automorphisms of cyclic groups. I'll take one particular example to make it clear : I'm taking the cyclic group $\mathbb{Z}_{12}$, which ...