"Omnibus test of group" is not some test in itself Ms. Maneesha. Omnibus tests are a class of tests. The word omnibus means someone who can do everything. :)
Therefore, omnibus tests are a class of tests which test all the possible combinations of variables. :)
An omnibus test (also called a combined test) is an overall test for a whole group of results.
For example, the ANOVA is an omnibus test. The t-Test is a special case of the ANOVA. But, the t-Test is a limited test. The t-Test can test the difference in two groups. If you have three variables, then, in order to compare all of them, you would have to perform t-Test three times.
But, as soon as the number of variables becomes four, the total number of t-Tests required would become 3 + 2 + 1 = 6 t-Tests and you would start becoming psychologically unstable. :)
Therefore, the elder brother of the t-Test, the ANOVA takes the matters in his own hands. The ANOVA, run once, would test all six, run once. :)
Therefore, people like ANOVA are called to be having an omnibus personality. :)
Fun explanation. :)