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The query [[Fact about.Page::Characteristic subgroup]] [[Category:Subgroup property implications]] was answered by the SMWSQLStore3 in 0.0188 seconds.

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Characteristic and self-centralizing implies coprime automorphism-faithful, Characteristic central factor of WNSCDIN implies WNSCDIN, Characteristic equals fully invariant in odd-order abelian group, Characteristic equals strictly characteristic in Hopfian, Characteristic equals verbal in free abelian group, Characteristic implies automorph-conjugate, Characteristic implies normal, Characteristic of CDIN implies CDIN, Characteristic upper-hook AEP implies characteristic, Comparable with all normal subgroups implies characteristic in finite nilpotent group, Cyclic characteristic implies hereditarily characteristic, Cyclic-quotient characteristic implies upward-closed characteristic, Fully invariant implies characteristic, Isomorph-containing implies characteristic, Left-transitively complemented normal implies characteristic, Left-transitively permutable implies characteristic, Normality-preserving endomorphism-invariant implies characteristic, Self-centralizing and minimal normal implies characteristic