German Cockroaches. German cockroaches die younger than any other North American roach species but in only 20 weeks of life, have huge families. They're about 1/2 inch long, light brown in color, with two lengthwise black stripes behind their heads.German cockroaches mature so fast that only a few weeks after hatching, they're ready to make babies of their own.When you take all the different generations into consideration, one female can be the matriarch of up to 35,000 roaches.erman cockroaches mature so fast that only a few weeks after hatching, they're ready to make babies of their own. When you take all the different generations into consideration, one female can be the matriarch of up to 35,000 roaches.