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Abelian Non-isomorphic Classes Lister

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

August . 20 . 2015
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.)

144 = 24 * 32
Thus there are ten nonisomorphic abelian groups of order 144,
(1) Z2 ⊕ Z2 ⊕ Z6 ⊕ Z6
(2) Z2 ⊕ Z2 ⊕ Z2 ⊕ Z18
(3) Z2 ⊕ Z6 ⊕ Z12
(4) Z2 ⊕ Z2 ⊕ Z36
(5) Z12 ⊕ Z12
(6) Z6 ⊕ Z24
(7) Z4 ⊕ Z36
(8) Z3 ⊕ Z48
(9) Z2 ⊕ Z72
(10) Z144


  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