This page provides information about the group of outer automorphisms of
G. First we give the order of the group of outer automorphisms,
as well as the minimal number of generators.
For each
generator of this group of outer automorphisms, we
choose an automorphism of G representing it, we
give the order of the class in the outer automorphism group
(which could be higher than the order of the automorphism),
a table describing
the action of the automorphism on the generators of the group G, and
another table describing the map induced by the automorphism in the
cohomology ring of the group G.
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The group of outer automorphisms of G has order
4
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Number of generators:
2
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Automorphism number
1
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Order of the class of the automorphism in the outer automorphism group:
2
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Group generator  Image under automorphism |
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g1
g1
g2
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g2
g2
g4
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g3
g3
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g4
g4
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This automorphism induces the identity homomorphism on cohomology
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Automorphism number
2
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Order of the class of the automorphism in the outer automorphism group:
2
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Group generator Image under automorphism |
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g1
g1
g3
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g2
g2
g4
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g3
g3
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g4
g4
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Cohomology generator Image induced by
automorphism |
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z
z
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y
z +
y
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x
x
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w
w
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