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Add converse tests and example
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src/Groups/group_constructors.jl

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@@ -863,7 +863,7 @@ of order $2^{k+1}, k \geq 2$, and `false` otherwise.
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julia> is_quaternion_group(small_group(8, 3))
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false
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julia> is_quaternion_group(small_group(8, 4))
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julia> is_quaternion_group(transitive_group(8, 5))
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true
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```
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"""

test/Groups/constructors.jl

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@@ -65,7 +65,10 @@ end
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@test isa(dihedral_group(PermGroup, 6), PermGroup)
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@test is_quaternion_group(small_group(8, 4))
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@test ! is_quaternion_group(small_group(12, 3))
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@test is_dicyclic_group(small_group(8, 4))
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@test ! is_dicyclic_group(small_group(13, 1))
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@test small_group_identification(small_group(8, 4)) == (8, 4)
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@test isa(small_group(8, 4), PcGroup)
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@test isa(small_group(60, 5), PermGroup)

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