Lee has two main "math suites" in the SMC. One suite has offices for Professor Gladden and Professor Singletary. The other suite has offices for seven regular faculty. Proceeding in clockwise order around the suite, these professors are Professor Jones, Professor Stephens, Professor Maher-Boulis, Professor Moy, Professor Cornett, Professor Schmurr, and Professor Minutolo. (Ignore any rooms used for other purposes.) In an emergency, Dr. Carroll can issue Secret Command ALPHA and each professor will move to the office (in the same suite) that is directly clockwise from his or her current office. Dr. Carroll will remain in his current office. 1. Explain how Secret Command ALPHA generates a cyclic group of permutations of the set of Lee math professors. 2. Compute the order of this group. 3. How many subgroups does this group have?