Finite Group Databasebeta

← Group #13136914

Character table — Group #13136914

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111111112222222222222222229999999999991212121212121212121212121212121212121212121212121212121212121212181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order123344661212121224668888121224242424242424248888242424242424242433666666121212121212121224242424242424242424242424242424444488121212121212121224242424161616161616161648484848484848484848484848484848
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
χ51111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-111-1-1-1-1-11-1-111-1-1111111-1-1-1-1ii−i−iiiii−i−i−i−i11-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1ii−i−ii−iiiii−i−i−i−iii−i−iζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ101111-1-111-1-1-1-1-11-1-111-1-1111111-1-1-1-1ii−i−iiiii−i−i−i−i11-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1ii−i−ii−iiiii−i−i−i−iii−i−i−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ111111-1-111-1-1-1-1-11-1-111-1-1111111-1-1-1-1−i−iii−i−i−i−iiiii11-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−iii−ii−i−i−i−iiiii−i−iii−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ121111-1-111-1-1-1-1-11-1-111-1-1111111-1-1-1-1−i−iii−i−i−i−iiiii11-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−iii−ii−i−i−i−iiiii−i−iiiζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ131111-1-111-1-1-1-1-11-1-1-1-11111-1-1-1-11111ii−i−iiiii−i−i−i−i11-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iiii−i−i−i−i−iiiiiii−i−iζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13
χ141111-1-111-1-1-1-1-11-1-1-1-11111-1-1-1-11111ii−i−iiiii−i−i−i−i11-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iiii−i−i−i−i−iiiiiii−i−i−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13
χ151111-1-111-1-1-1-1-11-1-1-1-11111-1-1-1-11111−i−iii−i−i−i−iiiii11-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−i−iiiiii−i−i−i−i−i−iii−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23
χ161111-1-111-1-1-1-1-11-1-1-1-11111-1-1-1-11111−i−iii−i−i−i−iiiii11-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−i−iiiiii−i−i−i−i−i−iiiζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23
χ17222222222222-2-2-2-20000-2-20000000022222222222222-2-2-2-2222222-2-2-2-200000000000000000000-2-200000000-2-2-2-2000000000000000000000000
χ18222222222222-2-2-2-20000-2-200000000-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222-2-2-2-20000000000000000000022000000002222000000000000000000000000
χ192222-2-222-2-2-2-22-2220000-2-2000000002i2i−2i−2i2i2i2i2i−2i−2i−2i−2i22222222-2-2-2-2-2-2-2-200000000000000000000−2i2i00000000−2i−2i2i2i000000000000000000000000
χ202222-2-222-2-2-2-22-2220000-2-200000000−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i22222222-2-2-2-2-2-2-2-2000000000000000000002i−2i000000002i2i−2i−2i000000000000000000000000
χ212-2222i−2i-2-22i2i−2i−2i00002−2−i2i20022−2−2−i2−i2i2i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13220000-2-22i2i−2i−2i00002222−2−2−2−2−i2−i2−i2−i2i2i2i2i21+i−1−i1−i−1+i001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000000000000000
χ222-2222i−2i-2-22i2i−2i−2i00002−2−i2i20022−2−2−i2−i2i2i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13220000-2-22i2i−2i−2i00002222−2−2−2−2−i2−i2−i2−i2i2i2i2i2−1−i1+i−1+i1−i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000000000000000
χ232-2222i−2i-2-22i2i−2i−2i0000−22i2−i200−2−222i2i2−i2−i22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ13220000-2-22i2i−2i−2i0000−2−2−2−22222i2i2i2i2−i2−i2−i2−i2−1−i1+i−1+i1−i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000000000000000000000
χ242-2222i−2i-2-22i2i−2i−2i0000−22i2−i200−2−222i2i2−i2−i2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13220000-2-22i2i−2i−2i0000−2−2−2−22222i2i2i2i2−i2−i2−i2−i21+i−1−i1−i−1+i001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000000000000000000000
χ252-222−2i2i-2-2−2i−2i2i2i00002−2i2−i20022−2−2i2i2−i2−i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23220000-2-2−2i−2i2i2i00002222−2−2−2−2i2i2i2i2−i2−i2−i2−i21−i−1+i1+i−1−i001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000000000000000
χ262-222−2i2i-2-2−2i−2i2i2i00002−2i2−i20022−2−2i2i2−i2−i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23220000-2-2−2i−2i2i2i00002222−2−2−2−2i2i2i2i2−i2−i2−i2−i2−1+i1−i−1−i1+i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000000000000000
χ272-222−2i2i-2-2−2i−2i2i2i0000−22−i2i200−2−222−i2−i2i2i2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23220000-2-2−2i−2i2i2i0000−2−2−2−22222−i2−i2−i2−i2i2i2i2i2−1+i1−i−1−i1+i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000000000000000000000
χ282-222−2i2i-2-2−2i−2i2i2i0000−22−i2i200−2−222−i2−i2i2i22ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23220000-2-2−2i−2i2i2i0000−2−2−2−22222−i2−i2−i2−i2i2i2i2i21−i−1+i1+i−1−i001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000000000000000000000
χ2933−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i323333−3−3i32−3+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
χ3033−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i323333−3−3i32−3+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
χ3133−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i323333−3−3i32−3+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
χ3233−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i323333−3−3i32−3+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
χ3333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32-3-3-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3200000000000000000000000000000000-1-1-1-1111+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32ii−i−i−i−iiiζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22
χ3433−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32-3-3-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3200000000000000000000000000000000-1-1-1-1111+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−i−iiiii−i−i−ζ14−ζ22−ζ14−ζ22ζ14ζ22ζ14ζ22ζ14ζ22ζ14ζ22−ζ14−ζ22−ζ14−ζ22
χ3533−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32-3-3-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32000000000000000000000000000000001111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−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
χ3633−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32-3-3-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i323+3i323−3i323+3i323−3i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32000000000000000000000000000000001111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−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
χ3733−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i3233-3-3−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i32ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ1400000000000000000000000000000000ii−i−ii−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14ζ22ζ14−ζ22−ζ14−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ5ζ13−ζ5−ζ13ζ5ζ13−ζ5−ζ13−ζ23−ζ7ζ23ζ7−ζ23−ζ7ζ23ζ7
χ3833−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323−3i323+3i323−3i32-333+3i323−3i3233-3-3−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i323+3i323−3i32ii−i−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ1400000000000000000000000000000000ii−i−ii−iζ22ζ14ζ22ζ14−ζ22−ζ14−ζ22−ζ14ζ22ζ14−ζ22−ζ14ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5ζ13−ζ5−ζ13ζ5ζ13ζ23ζ7−ζ23−ζ7ζ23ζ7−ζ23−ζ7
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.