Can I obtain a class C address block?

No. Classful addressing (class A, class B, class C, etc) is redundant. The original model for distributing IP addresses, based on classful addressing strategies, did not take into account the massive expansion of Internet use and was unable to scale to meet this expansion.

Classless Inter Domain Routing (CIDR) [PDF]  is one of the fundamental requirements for eligibility to receive IP address ranges.

Address space is referred to by prefix length (or subnet mask). For example, /24 ("slash 24") refers to 256 IP addresses, or the equivalent of a former class C. A /19 refers to 8,192 IP addresses, or the equivalent of 32 former class Cs.