Abstract
Γ is a group of central type if it possesses an irreducible complex character of degree |Γ: Z(Γ)|!/2. This is the largest possible degree for an ordinary irreducible character of a finite group. A group G which is isomorphic to Γ/Z(Γ), where Γ is some group of central type, is called a central type factor group (ctfg). A variety of restrictions on ctfgs are found. These include a local characterization of ctfgs, and restrictions on normal and subnormal structures of ctfgs.
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