All 5 groups of order 343 are listed and completely calculated.
Small group number 1 of order 343 Cyclic group of order 343
Small group number 2 of order 343 Abelian group C49 x C7
Small group number 3 of order 343 Extraspecial 7-group of order 343 and exponent 7
Small group number 4 of order 343 Extraspecial 7-group of order 343 and exponent 49
Small group number 5 of order 343 Elementary abelian group of order 343