In the code below g1 and g2 are the same group, where g2 is produced as a
subgroup of g1, and c is the principal character of g1. Still, when it
comes to scalar products, somehow g1 is not considered as a subgroup of
itself:
sage: g1 = SymmetricGroup(2)
....: g2 = g1.conjugacy_classes_subgroups()[-1]
....: c = g1.trivial_character()
....:
....: def test(h):
....: try:
....: x = c.restrict(h)
....: y = h.trivial_character()
....: print('x == y?:', x == y)
....: return x.scalar_product(y)
....: except:
....: return 'GAPError'
....: g1 == g2
....: [test(g2), test(g1)]
....:
True
x == y?: True
x == y?: True
[1, 'GAPError']
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