Radical Republican

The Radical Republicans were a political faction of American politicians within the Republican Party. They existed from 1854 until the end of Reconstruction in 1877. They called themselves "radicals". They were opposed during the War by the Moderate Republicans (led by Abraham Lincoln). One of the fears of the radicals was that if Northern and Southern Democrats came back together again as they had before the Civil War the Republican party would no longer be the dominant political party.
History.
In 1854, the Republican party was formed as a result of the Kansas–Nebraska Act. The act split the Whig Party in two. The Northern Whigs united with the members of the Free Soil Party. Together with the Know-Nothing Party they formed the Republican Party. 
Between its formation in 1854 and 1861, the Republican Party had many different factions or groups. It attracted been Whigs, Anti-Slavery Democrats, Know-Nothings, and Abolitionists, but by the start of the Civil War it had been reduced to just three factions: conservatives, moderates and radicals.
The Republicans generally opposed slavery. At first, many opposed giving African Americans equal rights when and if slavery ended. Radical Republicans believed they should be given equal rights and have the same opportunities as white people. They also wanted the leaders of the Confederate States of America to be punished for any part they played in the Civil War. Many Radical Republicans believed blacks were entitled to the same political rights and opportunities as whites. They also believed that the Confederate leaders should be punished for their roles in the Civil War.