Consider the cube C as shown below in the picture. Let G denote the group of rotational symmetries of C.

1, IF V denote the set of vertices of C, then what is |V| ?

2, Let G act on V by the usual action, and consider some A in V. What is |OA| ?

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Problem 4 (12 points) Consider the cube 0 as shown below in the picture. Let G denote the group of rotational symmetries of C'. (1) If V denote the set of vertices of C' then what is |V|? (2) Let G act on V by the usual action (as discussed in class or notes) and consider some A E V. What is |0A|? Give full details. (3) For the same action as in (2), what is |Stab(A)|? Give full details. (4) Find 'G'. Write the statement of the theorem explicitly which you are using (if any) to nd 'G