Small group number 52 of order 243

G = 81gp8xC3 is Direct product 81gp8 x C_3

G has 3 minimal generators, rank 3 and exponent 9. The centre has rank 2.

The 13 maximal subgroups are: Ab(9,3,3), E27xC3, M27xC3 (2x), 81gp8 (9x).

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

At present no information on the cohomology ring.


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