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Abelian Non-isomorphic Classes Lister

List all non-isomorphic abelian classes for natural numbers from 2 to 239

Please enter a number between 2 and 239 [inclusive].
The isomorphism classes of your number will then be listed.
(You can also simply hit "Find Groups" to have a number chosen at random.)

72 = 23 * 32
Thus there are six nonisomorphic abelian groups of order 72,
(1) Z2 ⊕ Z6 ⊕ Z6
(2) Z6 ⊕ Z12
(3) Z2 ⊕ Z2 ⊕ Z18
(4) Z3 ⊕ Z24
(5) Z2 ⊕ Z36
(6) Z72


  1. Determines factorization of number
  2. Determines type of options to arrange factors
  3. Determine all combinations
  4. Check against numerical prediction of types for groups