Groups of order 168

From Groupprops
Revision as of 22:26, 23 May 2011 by Vipul (talk | contribs) (Created page with "{{groups of order|168}} ==Statistics at a glance== The prime factorization of 168 is: <math>\! 169 = 2^3 \cdot 3 \cdot 7 = 8 \cdot 3 \cdot 7</math> {| class="sortable" border=...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
This article gives information about, and links to more details on, groups of order 168
See pages on algebraic structures of order 168| See pages on groups of a particular order

Statistics at a glance

The prime factorization of 168 is:

\! 169 = 2^3 \cdot 3 \cdot 7 = 8 \cdot 3 \cdot 7

Quantity Value List/comment
Total number of groups 57
Total number of abelian groups 3 ((number of abelian groups of order 8) = 3) times (number of abelian groups of order 3) = 1) times (number of abelian groups of order 7) = 1). See classification of finite abelian groups and structure theorem for finitely generated abelian groups.
Total number of nilpotent groups 5 ((number of groups of order 8) = 5) times ((number of groups of order 3) = 1) times ((number of groups of order 5) = 1). See equivalence of definitions of finite nilpotent group
Total number of solvable groups 56 the only non-solvable group is the simple non-abelian group projective special linear group:PSL(3,2), which is also isomorphic to PSL(2,7).
Total number of simple groups 1 the simple non-abelian group projective special linear group:PSL(3,2), which is also isomorphic to PSL(2,7).