query: cardinal of conjugacy class of $(123)(456)$ in $A_7$
positive_passages.docid: 21958
positive_passages.text: Splitting of conjugacy class in alternating group
negative_passages.docid: 143069
negative_passages.text: What are the direct summands in $\mathbb{Z}^n$?
negative_passages.docid: 102429
negative_passages.text: There are 2 groups of order 6 (up to isomorphism)
negative_passages.docid: 74734
negative_passages.text: (Enderton set theory) Hartog's theorem and cardinal numbers
negative_passages.docid: 13761
negative_passages.text: Automorphisms in $\mathbb{Z}_n$
negative_passages.docid: 33152
negative_passages.text: Classifying groups of order 18
negative_passages.docid: 89167
negative_passages.text: Cardinality of equivalence relations in $\mathbb{N}$
negative_passages.docid: 122959
negative_passages.text: How is number of conjugacy class related to the order of a group?
negative_passages.docid: 108049
negative_passages.text: Determining the number of subgroups of $\Bbb Z_{14} \oplus \Bbb Z_{6}$
negative_passages.docid: 97258
negative_passages.text: Give $\ker(\phi)$ for $\phi: \mathbb{Z} \to \mathbb{Z_7}$ such that $\phi(1)=4$
negative_passages.docid: 17978
negative_passages.text: Isomorphism classes of $\mathbb{Z}[i]$ modules.
negative_passages.docid: 86807
negative_passages.text: The units of $\mathbb Z[\sqrt{2}]$
negative_passages.docid: 41878
negative_passages.text: Cardinal of quotient rings of gaussian integers.
negative_passages.docid: 10998
negative_passages.text: Embedding $S_n$ in $A_{2n}$
negative_passages.docid: 66708
negative_passages.text: Elementary isomorphism between $\operatorname{PSL}(2,5)$ and $A_5$
negative_passages.docid: 76943
negative_passages.text: Existence of subgroup of order six in $A_4$
negative_passages.docid: 58267
negative_passages.text: Godel's pairing function and proving c = c*c for aleph cardinals