The synchronization behavior of the networks of fast-spiking interneurons is investigated by using one of the phenomenological neural network models, the Izhikevich model. Since electrical and chemical synapses exist within the same networks of inhibitory cells, delayed inhibitory and fast electrical synapses are coupled in the simulations. The effects of hybrid synapses in promoting synchronous activity in neural networks are investigated with short and long time delays. The distinct frequency bands observed in electroencephalography and magnetoencephalography signals are determined using the raster plots of neural networks. For quantitative comparison of activities in networks, the degree of synchrony in the network is calculated. The influences of several network parameters such as inhibitory synaptic strength, electrical synaptic strength, synaptic time constant, and time delay on the network activity are investigated. It is observed that the coupling of electrical and chemical synapses promotes multiple synchronous behaviors in the network. Another important finding is that even though the synchronization measure is highly dependent on inhibitory synaptic strengths at low electrical synaptic strength and synaptic time constant, not much dependence on inhibitory synaptic strengths is observed at high electrical synaptic strength.