One of the factors is 3684787 = 271 x 13597, so I suspect this is more accidental than malicious. The generator, 2, does not seem to have pathologically small order, but I didn't check very far.

Coincidentally, 13597 base 10 is 351d hex, which in unicode is defined as 'strong resistance'.

http://www.charbase.com/351d-unicode-cjk-unified-ideograph

Wow. 271 is a factor.

Why not try dividing by all 32 bit numbers, to at least filter easy cases. Shouldn't take more than a few seconds.

The following Sage script shows that p has no prime factors less than 2^32 other than 271 and 13597:

  p_list = [0xCC, 0x17, 0xF2, 0xDC, 0x96, 0xDF, 0x59, 0xA4, 0x46, 0xC5, 0x3E, 0x0E, 0xB8, 0x26, 0x55, 0x0C, 0xE3, 0x88, 0xC1, 0xCE, 0xA7, 0xBC, 0xB3, 0xBF, 0x16, 0x94, 0xD8, 0xA9, 0x45, 0xA2, 0xCE, 0xA9, 0x5B, 0x22, 0x25, 0x5F, 0x92, 0x59, 0x94, 0x1C, 0x22, 0xBF, 0xCB, 0xC8, 0xC8, 0x57, 0xCB, 0xBF, 0xBC, 0x0E, 0xE8, 0x40, 0xF9, 0x87, 0x03, 0xBF, 0x60, 0x9B, 0x08, 0xC6, 0x8E, 0x99, 0xC6, 0x05, 0xFC, 0x00, 0xD6, 0x6D, 0x90, 0xA8, 0xF5, 0xF8, 0xD3, 0x8D, 0x43, 0xC8, 0x8F, 0x7A, 0xBD, 0xBB, 0x28, 0xAC, 0x04, 0x69, 0x4A, 0x0B, 0x86, 0x73, 0x37, 0xF0, 0x6D, 0x4F, 0x04, 0xF6, 0xF5, 0xAF, 0xBF, 0xAB, 0x8E, 0xCE, 0x75, 0x53, 0x4D, 0x7F, 0x7D, 0x17, 0x78, 0x0E, 0x12, 0x46, 0x4A, 0xAF, 0x95, 0x99, 0xEF, 0xBC, 0xA6, 0xC5, 0x41, 0x77, 0x43, 0x7A, 0xB9, 0xEC, 0x8E, 0x07, 0x3C, 0x6D]

  p = 0
  for num in p_list: p = (p << 8) + num

  for i, prime in enumerate(primes(2^32)):
      if i % 100 == 0: print str(prime) + '\r',
      if p % prime == 0: print('\n')

Sage also has an is_prime function, which provably show that p is not prime: "is_prime(p)". This takes less than 1ms to run. Proving primality of a 1024 bit prime in Sage takes a few seconds, and for a 2048 bit prime about a minute. Sage uses PARI for this, with sophisticated elliptic curve based algorithms called ECPP("=elliptic curve primality proving"), which are non-deterministic (unlike AKS) but fast in practice and provably correct. https://goo.gl/34uxJl

Have you tried dividing the order by 271 and 13597 and search again on that?

271 is rather small. Which means this fake prime was quite easy to generate.

"Presumably someone constructed it as a product of primes known only to them"

It would be foolish to presume that. And knowing the factors of the Diffie-Hellman parameter isn't all that important.