AATA A Project

Exercises 15.5 A Project

The main objective of finite group theory is to classify all possible finite groups up to isomorphism. This problem is very difficult even if we try to classify the groups of order less than or equal to

60 .

However, we can break the problem down into several intermediate problems. This is a challenging project that requires a working knowledge of the group theory you have learned up to this point. Even if you do not complete it, it will teach you a great deal about finite groups. You can use Table 15.21 as a guide.

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Table 15.21. Numbers of distinct groups

G,

| G | \leq 60

Order	Number	Order	Number	Order	Number	Order	Number
$1$	?	$16$	$14$	$31$	$1$	$46$	$2$
$2$	?	$17$	$1$	$32$	$51$	$47$	$1$
$3$	?	$18$	?	$33$	$1$	$48$	$52$
$4$	?	$19$	?	$34$	?	$49$	?
$5$	?	$20$	$5$	$35$	$1$	$50$	$5$
$6$	?	$21$	?	$36$	$14$	$51$	?
$7$	?	$22$	$2$	$37$	$1$	$52$	?
$8$	?	$23$	$1$	$38$	?	$53$	?
$9$	?	$24$	?	$39$	$2$	$54$	$15$
$10$	?	$25$	$2$	$40$	$14$	$55$	$2$
$11$	?	$26$	$2$	$41$	$1$	$56$	?
$12$	$5$	$27$	$5$	$42$	?	$57$	$2$
$13$	?	$28$	?	$43$	$1$	$58$	?
$14$	?	$29$	$1$	$44$	$4$	$59$	$1$
$15$	$1$	$30$	$4$	$45$	?	$60$	$13$