The small groups of order 81

All 15 groups of order 81 are listed and completely calculated.

Small group number 1 of order 81 Cyclic group of order 81

Small group number 2 of order 81 Abelian group C₉ x C₉

Small group number 3 of order 81

Small group number 4 of order 81

Small group number 5 of order 81 Abelian group C₂₇ x C₃

Small group number 6 of order 81

Small group number 7 of order 81 Sylow 3-subgroup of A_9

Small group number 8 of order 81

Small group number 9 of order 81 Sylow 3-subgroup of U_3(8)

Small group number 10 of order 81

Small group number 11 of order 81 Abelian group C₉ x C₃ x C₃

Small group number 12 of order 81 Direct product E27 x C_3

Small group number 13 of order 81 Direct product M27 x C_3

Small group number 14 of order 81 Central product E27 * C_9

Small group number 15 of order 81 Elementary abelian group of order 81