# Error when computing Automorphism Group

I am new to Sage. Recently, I tried to compute the Automorphism Group of $\mathbb{Z}_4\times\mathbb{Z}_2$ in the following way:

G = CyclicPermutationGroup(4)
H = CyclicPermutationGroup(2)
D=G.direct_product(H)
D.automorphism_group()


However, there was an error message:

Error in lines 4-4
Traceback (most recent call last):
File "/projects/0aeca2d0-1a41-47c7-b462-f4a4432bfbf3/.sagemathcloud/sage_server.py", line 881, in execute
exec compile(block+'\n', '', 'single') in namespace, locals
File "", line 1, in <module>
AttributeError: 'tuple' object has no attribute 'automorphism_group'


May I know where does the error in the code lie? Thanks!

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Nathann is correct. However, you also used the (slightly) wrong command for what you wanted, and it isn't quite available the way it should be.

sage: d = D[0]
sage: d1 = d._gap_()
sage: d1.AutomorphismGroup()
Group( [ GroupHomomorphismByImages( Group( [ (5,6), (1,2,3,4) ] ), Group(
[ (5,6), (1,2,3,4) ] ), [ (1,2,3,4), (5,6) ], [ (1,2,3,4), (5,6) ] ),
GroupHomomorphismByImages( Group( [ (5,6), (1,2,3,4) ] ), Group(
[ (5,6), (1,2,3,4) ] ), [ (5,6), (1,2,3,4) ], [ (5,6), (1,4,3,2) ] ),
GroupHomomorphismByImages( Group( [ (5,6), (1,2,3,4) ] ), Group(
[ (5,6), (1,2,3,4) ] ), [ (5,6), (1,2,3,4) ],
[ (1,3)(2,4)(5,6), (1,2,3,4) ] ), GroupHomomorphismByImages( Group(
[ (5,6), (1,2,3,4) ] ), Group( [ (5,6), (1,2,3,4) ] ), [ (1,2,3,4), (5,6)
], [ (1,2,3,4)(5,6), (5,6) ] ) ] )


See Trac 19328.

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1

Great ! I was looking how to find the automorphoism of D[0] by changing its representation, and didn not thought to _gap_. Thanks for this hint.

( 2015-10-01 14:34:21 -0500 )edit

The error is that D is a tuple, and not a group. Read the documentation of direct_product, by typing

sage: G.direct_product?

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