Noun, Na-adjective (keiyodoshi), Noun which may take the genitive case particle 'no'
behaving outrageously as though there were no one around; acting without consideration for others; arrogance; audacity; insolence
Yojijukugo (four character compound)
傍若無人の振る舞いだね。They are cutting loose.
Also written 旁若無人【ぼうじゃくぶじん】