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There are 5 groups of order 8 up to isomorphism. 3 abelian ones (C8, C4xC2, C2xC2xC2) and 2 non-abelian ones (dihedral group D8 and quaternion group Q)

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Q: What is the number of groups of order 8 upto isomorphisms?
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What is the numbers of groups of order 8 upto isomorphisms?

There are five groups of order 8: three of them are Abelian and the other two are not. These are 1. C8, the group generated by a where a8 = 1 2. C4xC2, the group generated by a and b where a4 = b2 = 1 3. C2xC2xC2, the group generated by a, b and c where a2 = b2 = c2= 1 4. the dihedral group 5. the quaternion group


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