Dictionary:

impudence

  (ĭm'pyə-dəns) also impudency (-dən-sē)

1. The quality of being offensively bold.
2. Offensively bold behavior.

noun

The state or quality of being impudent or arrogantly self-confident: assumption, audaciousness, audacity, boldness, brashness, brazenness, cheek, cheekiness, chutzpah, discourtesy, disrespect, effrontery, face, familiarity, forwardness, gall¹, impertinence, impudency, incivility, insolence, nerve, nerviness, overconfidence, pertness, presumptuousness, pushiness, rudeness, sassiness, sauciness. Informal brass, crust, sauce, uppishness, uppityness. See attitude/good attitude/bad attitude/neutral attitude, courtesy/discourtesy.

The noun has 2 meanings:

Meaning #1: an impudent statement
  Synonyms: cheek, impertinence

Meaning #2: the trait of being rude and impertinent; inclined to take liberties
  Synonyms: crust, gall, impertinence, insolence, cheekiness, freshness

Quotes:

"Impudence is the worst of all human diseases." - Euripides