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Another use of regarding a group (there called $H$) as a subgroup of the symmetric group $S_{|H|}$ is given by Marty Isaacs in Subgroup property stronger than being characteristicSubgroup property stronger than being characteristic
Another use of regarding a group (there called $H$) as a subgroup of the symmetric group $S_{|H|}$ is given by Marty Isaacs in Subgroup property stronger than being characteristic