Based on the alphabetical order, three of the following four letter-clusters are alike in a certain way and thus form a group. Which letter-cluster does not belong to that group?
(Note: The odd one out is not based on the number of consonants/vowels or their position in the letter cluster.)

The correct answer is EGJ.

To determine which letter-cluster does not belong to the group, let us analyze the pattern formed by the positions of the letters in the English alphabet for each option.

First, write down the alphabetical positions of each letter:
A=1, B=2, C=3, D=4, E=5, F=6, G=7, H=8, I=9, J=10, K=11, L=12, M=13, N=14, O=15, P=16, Q=17, R=18, S=19, T=20, U=21, V=22, W=23, X=24, Y=25, Z=26

Now, let us examine the difference between consecutive letters in each cluster:

1. GIM:
G (7) + 2 = I (9)
I (9) + 4 = M (13)
Pattern: (+2, +4)

2. PRV:
P (16) + 2 = R (18)
R (18) + 4 = V (22)
Pattern: (+2, +4)

3. HJN:
H (8) + 2 = J (10)
J (10) + 4 = N (14)
Pattern: (+2, +4)

4. EGJ:
E (5) + 2 = G (7)
G (7) + 3 = J (10)
Pattern: (+2, +3)

All letter-clusters follow a (+2, +4) progression except EGJ, which follows a (+2, +3) pattern. Therefore, EGJ is the odd one out.