Finite Group Databasebeta

← Group #10690835

Character table — Group #10690835

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11111111222222222222222222222222222222224444444444444444444444444444448888888888888888888888881212121212121212121212121212121248484848
order12222222344444444444444446666666121212121212121222444466661212121212121212121212121212121212121212888888882424242424242424242424242424242488888888888888884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1-11-1
χ61111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-11-11
χ71111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i-11-11
χ81111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii1-11-1
χ9111111111-1-1-1-11111-1-1-1-11111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ10111111111-1-1-1-11111-1-1-1-11111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ11111111111-1-1-1-11111-1-1-1-11111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ12111111111-1-1-1-11111-1-1-1-11111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ13111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-11
χ14111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-1
χ15111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1
χ16111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11
χ17222222222222222-2-22222-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222-2-2-2-200000000000000000000000000000000000000000000
χ182222222222222-2-222-2-2-2-222-2-2222222222222222-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000
χ19222222222-2-2-2-222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-222-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000000000
χ20222222222-2-2-2-2-2-222222222-2-222222222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000000000000000
χ2122222222-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2222222222-12222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100000000000000000000
χ2322222222-1222222-2-22222-2-222-1-1-1-1-1-1-111111111-2-2-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-111110000000033−3−333−3−333−3−333−3−300000000000000000000
χ2422222222-1222222-2-22222-2-222-1-1-1-1-1-1-111111111-2-2-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-1111100000000−3−333−3−333−3−333−3−33300000000000000000000
χ2522222222-12222-2-222-2-2-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-111111111-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ2622222222-12222-2-222-2-2-2-222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22211111111-1-1-1-111111111-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ2722222222-12222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111112i2i2i2i−2i−2i−2i−2i−i−i−i−i−i−i−i−iiiiiiiii00000000000000000000
χ2822222222-12222-2-2-2-2-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1111111112222-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111−2i−2i−2i−2i2i2i2i2iiiiiiiii−i−i−i−i−i−i−i−i00000000000000000000
χ2922222222-1-2-2-2-22222-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-11111-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-1111100000000000000000000
χ3022222222-1-2-2-2-22222-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222-2-21111-1-1-1-11111-1-1-1-111111111-2-222-2-2221111-1-1-1-11111-1-1-1-100000000000000000000
χ3122222222-1-2-2-2-222-2-2-2-2-2-2-2-222-1-1-1-1-1-1-11111111122-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000033−3−3−3−33333−3−3−3−33300000000000000000000
χ3222222222-1-2-2-2-222-2-2-2-2-2-2-2-222-1-1-1-1-1-1-11111111122-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000−3−33333−3−3−3−33333−3−300000000000000000000
χ3322222222-1-2-2-2-2-2-222222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1111111111111-1-1-1-1111100000000−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ3422222222-1-2-2-2-2-2-222222222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1111111111111-1-1-1-1111100000000i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ3522222222-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-111111111-2-222221111-1-1-1-111111111-1-1-1-1-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ3622222222-1-2-2-2-2-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-111111111-2-222221111-1-1-1-111111111-1-1-1-1-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii00000000000000000000
χ37222-2-2-2-2222i2i−2i−2i002-200002-20022-2-22-2-222-2-222-2-200002i−2i000000002i2i−2i−2i000000002i2i−2i−2i000000000000000000000000−i2−i2i2i222−2−2−i2−i2i2i222−2−20000
χ38222-2-2-2-2222i2i−2i−2i002-200002-20022-2-22-2-222-2-222-2-200002i−2i000000002i2i−2i−2i000000002i2i−2i−2i000000000000000000000000i2i2−i2−i2−2−222i2i2−i2−i2−2−2220000
χ39222-2-2-2-2222i2i−2i−2i00-220000-220022-2-22-2-2-2-222-2-2220000−2i2i000000002i2i−2i−2i00000000−2i−2i2i2i00000000000000000000000022−2−2i2i2−i2−i2−2−222−i2−i2i2i20000
χ40222-2-2-2-2222i2i−2i−2i00-220000-220022-2-22-2-2-2-222-2-2220000−2i2i000000002i2i−2i−2i00000000−2i−2i2i2i000000000000000000000000−2−222−i2−i2i2i222−2−2i2i2−i2−i20000
χ41222-2-2-2-222−2i−2i2i2i002-200002-20022-2-22-2-222-2-222-2-20000−2i2i00000000−2i−2i2i2i00000000−2i−2i2i2i000000000000000000000000−i2−i2i2i2−2−222−i2−i2i2i2−2−2220000
χ42222-2-2-2-222−2i−2i2i2i002-200002-20022-2-22-2-222-2-222-2-20000−2i2i00000000−2i−2i2i2i00000000−2i−2i2i2i000000000000000000000000i2i2−i2−i222−2−2i2i2−i2−i222−2−20000
χ43222-2-2-2-222−2i−2i2i2i00-220000-220022-2-22-2-2-2-222-2-22200002i−2i00000000−2i−2i2i2i000000002i2i−2i−2i00000000000000000000000022−2−2−i2−i2i2i2−2−222i2i2−i2−i20000
χ44222-2-2-2-222−2i−2i2i2i00-220000-220022-2-22-2-2-2-222-2-22200002i−2i00000000−2i−2i2i2i000000002i2i−2i−2i000000000000000000000000−2−222i2i2−i2−i222−2−2−i2−i2i2i20000
χ4522-2-22-22-222i−2i2i−2i2-2002i2i−2i−2i002-22-22-2-22-200000000000000000000002i−2i2i−2i22-2-22i2i−2i−2i00002−2−i2i22−2−i2i22−22−2−i2i2−i2i22−22−2−i2i2−i2i200000000000000000000
χ4622-2-22-22-222i−2i2i−2i2-2002i2i−2i−2i002-22-22-2-22-200000000000000000000002i−2i2i−2i22-2-22i2i−2i−2i0000−22i2−i2−22i2−i2−22−22i2−i2i2−i2−22−22i2−i2i2−i200000000000000000000
χ4722-2-22-22-222i−2i2i−2i-2200−2i−2i2i2i00-222-22-2-22-200000000000000000000002i−2i2i−2i-2-222−2i−2i2i2i0000−i2i2−22i2−i22−2−i2i2−i2i2−22−22i2−i2i2−i22−22−200000000000000000000
χ4822-2-22-22-222i−2i2i−2i-2200−2i−2i2i2i00-222-22-2-22-200000000000000000000002i−2i2i−2i-2-222−2i−2i2i2i0000i2−i22−2−i2i2−22i2−i2i2−i22−22−2−i2i2−i2i2−22−2200000000000000000000
χ4922-2-22-22-22−2i2i−2i2i2-200−2i−2i2i2i002-22-22-2-22-20000000000000000000000−2i2i−2i2i22-2-2−2i−2i2i2i00002−2i2−i22−2i2−i22−22−2i2−i2i2−i22−22−2i2−i2i2−i200000000000000000000
χ5022-2-22-22-22−2i2i−2i2i2-200−2i−2i2i2i002-22-22-2-22-20000000000000000000000−2i2i−2i2i22-2-2−2i−2i2i2i0000−22−i2i2−22−i2i2−22−22−i2i2−i2i2−22−22−i2i2−i2i200000000000000000000
χ5122-2-22-22-22−2i2i−2i2i-22002i2i−2i−2i00-222-22-2-22-20000000000000000000000−2i2i−2i2i-2-2222i2i−2i−2i0000−i2i22−2i2−i2−22−i2i2−i2i22−22−2i2−i2i2−i2−22−2200000000000000000000
χ5222-2-22-22-22−2i2i−2i2i-22002i2i−2i−2i00-222-22-2-22-20000000000000000000000−2i2i−2i2i-2-2222i2i−2i−2i0000i2−i2−22−i2i22−2i2−i2i2−i2−22−22−i2i2−i2i22−22−200000000000000000000
χ5322-2-22-22-2-12i−2i2i−2i2-2002i2i−2i−2i002-2-11-111-113−33−33−33−3000000−i3−i3i3i333−3−3−ii−ii-1-111−i−iii−i3i3−i3i32−2−i2i22−2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ700000000000000000000
χ5422-2-22-22-2-12i−2i2i−2i2-2002i2i−2i−2i002-2-11-111-113−33−33−33−3000000−i3−i3i3i333−3−3−ii−ii-1-111−i−iii−i3i3−i3i3−22i2−i2−22i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ700000000000000000000
χ5522-2-22-22-2-12i−2i2i−2i2-2002i2i−2i−2i002-2-11-111-11−33−33−33−33000000i3i3−i3−i3−3−333−ii−ii-1-111−i−iiii3−i3i3−i32−2−i2i22−2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ2300000000000000000000
χ5622-2-22-22-2-12i−2i2i−2i2-2002i2i−2i−2i002-2-11-111-11−33−33−33−33000000i3i3−i3−i3−3−333−ii−ii-1-111−i−iiii3−i3i3−i3−22i2−i2−22i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ2300000000000000000000
χ5722-2-22-22-2-12i−2i2i−2i-2200−2i−2i2i2i00-22-11-111-113−33−33−33−3000000i3i3−i3−i3−3−333−ii−ii11-1-1ii−i−i−i3i3−i3i3−i2i2−22i2−i22−2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ700000000000000000000
χ5822-2-22-22-2-12i−2i2i−2i-2200−2i−2i2i2i00-22-11-111-113−33−33−33−3000000i3i3−i3−i3−3−333−ii−ii11-1-1ii−i−i−i3i3−i3i3i2−i22−2−i2i2−22−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ700000000000000000000
χ5922-2-22-22-2-12i−2i2i−2i-2200−2i−2i2i2i00-22-11-111-11−33−33−33−33000000−i3−i3i3i333−3−3−ii−ii11-1-1ii−i−ii3−i3i3−i3−i2i2−22i2−i22−2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2300000000000000000000
χ6022-2-22-22-2-12i−2i2i−2i-2200−2i−2i2i2i00-22-11-111-11−33−33−33−33000000−i3−i3i3i333−3−3−ii−ii11-1-1ii−i−ii3−i3i3−i3i2−i22−2−i2i2−22−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ2300000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.