Finite Group Databasebeta

← Group #13136916

Character table — Group #13136916

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111111112222222222222222229999999999991212121212121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order122233666666448888121212122424242424242424222266666666336666661212121212121212242424242424242424242424242424244488881212121224242424242424244444444412121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii
χ511111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ711111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii
χ811111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ91-1-1111-1-1-1-1111-1ii−i−i11-1-1iiii−i−i−i−i1-11-111-1-111-1-111-1-1-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1ii−i−i11-1-1iiii−i−i−i−i1-1i−i1-1i−i11-1-1ii−i−i11-1-1ii−i−i
χ101-1-1111-1-1-1-1111-1ii−i−i11-1-1iiii−i−i−i−i1-11-111-1-111-1-111-1-1-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1ii−i−i11-1-1iiii−i−i−i−i-11−ii-11−ii-1-111−i−iii-1-111−i−iii
χ111-1-1111-1-1-1-1111-1ii−i−i11-1-1iiii−i−i−i−i-11-11-1-111-1-11111-1-1-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−i−iii-1-111−i−i−i−iiiiii−i-11−ii1-1ii−i−i-1-111−i−iii11-1-1
χ121-1-1111-1-1-1-1111-1ii−i−i11-1-1iiii−i−i−i−i-11-11-1-111-1-11111-1-1-1-1111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11−i−iii-1-111−i−i−i−iiiii−ii1-1i−i-11−i−iii11-1-1ii−i−i-1-111
χ131-1-1111-1-1-1-1111-1−i−iii11-1-1−i−i−i−iiiii1-11-111-1-111-1-111-1-1-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−i−iii11-1-1−i−i−i−iiiii1-1−ii1-1−ii11-1-1−i−iii11-1-1−i−iii
χ141-1-1111-1-1-1-1111-1−i−iii11-1-1−i−i−i−iiiii1-11-111-1-111-1-111-1-1-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1−i−iii11-1-1−i−i−i−iiiii-11i−i-11i−i-1-111ii−i−i-1-111ii−i−i
χ151-1-1111-1-1-1-1111-1−i−iii11-1-1−i−i−i−iiiii-11-11-1-111-1-11111-1-1-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11ii−i−i-1-111iiii−i−i−i−ii−i1-1−ii-11ii−i−i11-1-1−i−iii-1-111
χ161-1-1111-1-1-1-1111-1−i−iii11-1-1−i−i−i−iiiii-11-11-1-111-1-11111-1-1-1-1111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11ii−i−i-1-111iiii−i−i−i−i−ii-11i−i1-1−i−iii-1-111ii−i−i11-1-1
χ17222222222222-2-20000-2-2-2-20000000022222222222222222222-2-2-2-2-2-2-2-20000000000000000-2-20000-2-2-2-200000000000000000000000000000000
χ18222222222222-2-20000-2-2-2-200000000-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000220000222200000000000000000000000000000000
χ1922-2-22222-2-2-2-2002−22−2000022−2−222−2−222-2-22222-2-2-2-22222-2-2-2-2000000002222−2−2−2−22222−2−2−2−2002−22−2000022−2−222−2−2000000000000000000000000
χ2022-2-22222-2-2-2-2002−22−2000022−2−222−2−2-2-222-2-2-2-222222222-2-2-2-2000000002222−2−2−2−22222−2−2−2−200−22−220000−2−222−2−222000000000000000000000000
χ2122-2-22222-2-2-2-200−22−220000−2−222−2−22222-2-22222-2-2-2-22222-2-2-2-200000000−2−2−2−22222−2−2−2−2222200−22−220000−2−222−2−222000000000000000000000000
χ2222-2-22222-2-2-2-200−22−220000−2−222−2−222-2-222-2-2-2-222222222-2-2-2-200000000−2−2−2−22222−2−2−2−22222002−22−2000022−2−222−2−2000000000000000000000000
χ232-22-222-2-222-2-200−i2i2i2−i20000−i2−i2i2i2i2i2−i2−i22-2-2222-2-2-2-22222-2-222-2-200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200−i2i2i2−i20000−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ242-22-222-2-222-2-200−i2i2i2−i20000−i2−i2i2i2i2i2−i2−i2-222-2-2-22222-2-222-2-222-2-200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200i2−i2−i2i20000i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ252-22-222-2-222-2-200i2−i2−i2i20000i2i2−i2−i2−i2−i2i2i22-2-2222-2-2-2-22222-2-222-2-200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200i2−i2−i2i20000i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ262-22-222-2-222-2-200i2−i2−i2i20000i2i2−i2−i2−i2−i2i2i2-222-2-2-22222-2-222-2-222-2-200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200−i2i2i2−i20000−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ272-2-2222-2-2-2-222-220000-2-222000000002-22-222-2-222-2-222-2-2-2-222-2-2-2-222220000000000000000-220000-2-22200000000000000000000000000000000
χ282-2-2222-2-2-2-222-220000-2-22200000000-22-22-2-222-2-22222-2-2-2-222-2-2-2-2222200000000000000002-2000022-2-200000000000000000000000000000000
χ293333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3200000000000000000000000000000000111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32iiii−i−i−i−iζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22
χ303333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3200000000000000000000000000000000111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−i−i−i−iiiii−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22
χ313333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000000000000000000000000-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i3211111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ323333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000000000000000000000000-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i32
χ333333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233-3-3-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000000000000000000011-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32ii−i−i−i−iiiζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22
χ343333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233-3-3-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i320000000000000000000000000000000011-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32−i−iiiii−i−i−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22
χ353333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233-3-3-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000000000000000000000000-1-111111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ363333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233-3-3-3-3−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3200000000000000000000000000000000-1-111111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ373333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3200000000000000000000000000000000111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32iiii−i−i−i−iζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14
χ383333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3200000000000000000000000000000000111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−i−i−i−iiiii−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14
χ393333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3200000000000000000000000000000000-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i3211111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ403333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32333333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3200000000000000000000000000000000-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i32-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32
χ413333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233-3-3-3-3−3+3i32−3−3i32−3+3i32−3−3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i320000000000000000000000000000000011-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−i321+i321−i321+i32ii−i−i−i−iiiζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14
χ423333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233-3-3-3-3−3+3i32−3−3i32−3+3i32−3−3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i320000000000000000000000000000000011-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−i321+i321−i321+i32−i−iiiii−i−i−ζ22−ζ14−ζ22−ζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14
χ433333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233-3-3-3-3−3+3i32−3−3i32−3+3i32−3−3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3200000000000000000000000000000000-1-111111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-111-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ443333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233-3-3-3-3−3+3i32−3−3i32−3+3i32−3−3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3200000000000000000000000000000000-1-111111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ453-3-33−3−3i32−3+3i323+3i323−3i323+3i323−3i32−3−3i32−3+3i323-33i3i−3i−3i−3−3i32−3+3i323+3i323−3i323ζ223ζ143ζ223ζ14−3ζ22−3ζ14−3ζ22−3ζ141-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32000000000000000000000000000000001-1ii−i−i−1−i32−1+i321+i321−i32ζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14i−i-11−ii1-1ζ14ζ22−ζ14−ζ221−i321+i32−1+i32−1−i32−ζ14−ζ22ζ14ζ22−1+i32−1−i321−i321+i32
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.