Small group number 55 of order 243

G is the group 243gp55

G has 3 minimal generators, rank 3 and exponent 9. The centre has rank 1.

The 13 maximal subgroups are: 81gp10 (2x), Ab(9,3,3), E27*C9 (3x), Syl3(A9) (3x), 81gp8 (3x), Syl3(U3(8)).

There are 4 conjugacy classes of maximal elementary abelian subgroups. Their ranks are: 2, 2, 2, 3.

At present no information on the cohomology ring.


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