Groups of order 120: Difference between revisions
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! Quantity !! Value | ! Quantity !! Value !! List/comment | ||
|- | |- | ||
| Total number of groups || 47 | | Total number of groups || 47 || | ||
|- | |- | ||
| Number of abelian groups || 3 | | 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 5) = 1) | ||
|- | |- | ||
| Number of nilpotent groups || 5 | | 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) | ||
|- | |- | ||
| Number of solvable groups || 44 | | Number of solvable groups || 44 || The three ''non''-solvable groups are [[special linear group:SL(2,5)]], [[direct product of A5 and Z2]], and [[symmetric group:S5]] | ||
|- | |- | ||
| Number of simple groups || 0 | | Number of simple groups || 0 || | ||
|- | |- | ||
| Number of [[almost simple group]]s || 1 | | Number of [[almost simple group]]s || 1 || [[symmetric group:S5]] (isomorphic to <math>PGL(2,5)</math>) | ||
|- | |- | ||
| Number of [[quasisimple group]]s || 1 | | Number of [[quasisimple group]]s || 1 || [[special linear group:SL(2,5)]] (also the binary icosahedral group) | ||
|} | |} | ||
Revision as of 22:19, 23 May 2011
This article gives information about, and links to more details on, groups of order 120
See pages on algebraic structures of order 120 | See pages on groups of a particular order
Statistics at a glance
| Quantity | Value | List/comment |
|---|---|---|
| Total number of groups | 47 | |
| 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 5) = 1) |
| 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) |
| Number of solvable groups | 44 | The three non-solvable groups are special linear group:SL(2,5), direct product of A5 and Z2, and symmetric group:S5 |
| Number of simple groups | 0 | |
| Number of almost simple groups | 1 | symmetric group:S5 (isomorphic to ) |
| Number of quasisimple groups | 1 | special linear group:SL(2,5) (also the binary icosahedral group) |