Finite Group Databasebeta

← Group #13145711

Character table — Group #13145711

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
size111122222222222222222222222222222244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444363636363636363636363636363636363636363636363636363636363636363636363636
order1244233346666688881212121212121212242424242424242433333666666666666666661212121212121212121212121212121212121212121224242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242444881212121216161616161616162424242448484848484848484848484848484848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−iii−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ611111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−iii−i−iii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ711111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1111-1111-1-111-1-1111111-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−iii−i−i1-11-1i−ii−iii−i−i11-1-111-1-1ii−i−iii−i−i
χ101111-1111-1111-1-111-1-1111111-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−iii−i−i-11-11−ii−iiii−i−i-1-111-1-111−i−iii−i−iii
χ111111-1111-1111-1-111-1-1111111-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii−i−iii1-11-1−ii−ii−i−iii11-1-111-1-1−i−iii−i−iii
χ121111-1111-1111-1-111-1-1111111-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii−i−iii-11-11i−ii−i−i−iii-1-111-1-111ii−i−iii−i−i
χ131111-1111-1111-1-1-1-111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111i−i−iiii−i−ii−i−ii-111-1−i−iiiii−i−i−i−iii-1-11111-1-1
χ141111-1111-1111-1-1-1-111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111i−i−iiii−i−i−iii−i1-1-11−i−iii−i−iiiii−i−i11-1-1-1-111
χ151111-1111-1111-1-1-1-111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111−iii−i−i−iiii−i−ii1-1-11ii−i−iii−i−i−i−iii11-1-1-1-111
χ161111-1111-1111-1-1-1-111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111−iii−i−i−iii−iii−i-111-1ii−i−i−i−iiiii−i−i-1-11111-1-1
χ172222222-1222-12222222222-1-1222222-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002222000000000000-1-1-1-1-1-1-1-1
χ182222222-1222-12222222222-1-1222222-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-2-2-2-200000000000011111111
χ192222222-1222-122-2-2-2-22222-1-122-2-2-2-211112-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-211-2-2-2-2-2-2-2-21111111111111111-2-2-2-211111111111111110000000000002i2i−2i−2i000000000000−i−i−i−iiiii
χ202222222-1222-122-2-2-2-22222-1-122-2-2-2-211112-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-211-2-2-2-2-2-2-2-21111111111111111-2-2-2-21111111111111111000000000000−2i−2i2i2i000000000000iiii−i−i−i−i
χ21222222-1222-1222222222-1-12222-1-1-1-12222-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000222200000000-1-1-1-1-1-1-1-100000000
χ22222222-1222-1222222222-1-12222-1-1-1-12222-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2000000001111111100000000
χ23222222-1222-1222-2-2-2-222-1-122221111-2-2-2-2-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2111111-2-2-2-21111111111111111-2-2-2-2111111111111000000002i2i−2i−2i00000000−i−i−i−iiiii00000000
χ24222222-1222-1222-2-2-2-222-1-122221111-2-2-2-2-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-2-2-2-2-2-2111111-2-2-2-21111111111111111-2-2-2-211111111111100000000−2i−2i2i2i00000000iiii−i−i−i−i00000000
χ2522222-1222-122-1-12222-1-12222-1-122222222-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-100000000-1-1-1-10000000000000000
χ2622222-1222-122-1-12222-1-12222-1-122222222-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211110000000011110000000000000000
χ2722222-1222-122-1-1-2-2-2-2-1-12222-1-1-2-2-2-2-2-2-2-2-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-111-2-211-2-211111111-2-2-2-21111111111111111-2-2-2-21111111122-2-2-1-1-1-10000000011110000000000000000
χ2822222-1222-122-1-1-2-2-2-2-1-12222-1-1-2-2-2-2-2-2-2-2-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-111-2-211-2-211111111-2-2-2-21111111111111111-2-2-2-211111111-2-222111100000000-1-1-1-10000000000000000
χ292222-222-1-222-1-2-222-2-22222-1-1-2-2222211112-1-1-1-1-21-2-2111111112-1-1-1-1-21-2-21111111122-1-1-1-1-1-1-1-122-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111111110000000000002i−2i2i−2i000000000000−i−iii−i−iii
χ302222-222-1-222-1-2-222-2-22222-1-1-2-2222211112-1-1-1-1-21-2-2111111112-1-1-1-1-21-2-21111111122-1-1-1-1-1-1-1-122-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111000000000000−2i2i−2i2i000000000000ii−i−iii−i−i
χ312222-222-1-222-1-2-2-2-2222222-1-1-2-2-2-2-2-2-1-1-1-12-1-1-1-1-21-2-2111111112-1-1-1-1-21-2-21111111122-1-1-1-1-1-1-1-1-2-2112222-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002-2-22000000000000-1-11111-1-1
χ322222-222-1-222-1-2-2-2-2222222-1-1-2-2-2-2-2-2-1-1-1-12-1-1-1-1-21-2-2111111112-1-1-1-1-21-2-21111111122-1-1-1-1-1-1-1-1-2-2112222-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-222-200000000000011-1-1-1-111
χ332222-22-12-22-12-2-222-2-222-1-122-2-2-1-1-1-1-2-2-2-2-12-1-1-11-211-2-2111111-12-1-1-11-211-2-2111111-1-122-1-1-1-1-1-12222-2-211-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-2111111111111000000002-22-200000000-1-111-1-11100000000
χ342222-22-12-22-12-2-222-2-222-1-122-2-2-1-1-1-1-2-2-2-2-12-1-1-11-211-2-2111111-12-1-1-11-211-2-2111111-1-122-1-1-1-1-1-12222-2-211-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-211111111111100000000-22-220000000011-1-111-1-100000000
χ352222-22-12-22-12-2-2-2-22222-1-122-2-211112222-12-1-1-11-211-2-2111111-12-1-1-11-211-2-2111111-1-122-1-1-1-1-1-1-2-2-2-222-1-11111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000002i−2i−2i2i00000000−i−iiiii−i−i00000000
χ362222-22-12-22-12-2-2-2-22222-1-122-2-211112222-12-1-1-11-211-2-2111111-12-1-1-11-211-2-2111111-1-122-1-1-1-1-1-1-2-2-2-222-1-11111-2-2-2-2111111111111-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000−2i2i2i−2i00000000ii−i−i−i−iii00000000
χ372222-2-122-2-1221122-2-2-1-12222112222-2-2-2-2-1-12-1-1-2-21111-2-21111-1-12-1-1-2-21111-2-21111-1-1-1-122-1-1-1-1-1-12211-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-2111111112i−2i2i−2i−i−iii00000000−i−iii0000000000000000
χ382222-2-122-2-1221122-2-2-1-12222112222-2-2-2-2-1-12-1-1-2-21111-2-21111-1-12-1-1-2-21111-2-21111-1-1-1-122-1-1-1-1-1-12211-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-111111111-2-2-2-211111111−2i2i−2i2iii−i−i00000000ii−i−i0000000000000000
χ392222-2-122-2-12211-2-222-1-1222211-2-2-2-22222-1-12-1-1-2-21111-2-21111-1-12-1-1-2-21111-2-21111-1-1-1-122-1-1-1-111-2-2-1-12211111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12i−2i−2i2i−i−iii00000000ii−i−i0000000000000000
χ402222-2-122-2-12211-2-222-1-1222211-2-2-2-22222-1-12-1-1-2-21111-2-21111-1-12-1-1-2-21111-2-21111-1-1-1-122-1-1-1-111-2-2-1-12211111111-2-2-2-211111111-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1−2i2i2i−2iii−i−i00000000−i−iii0000000000000000
χ4122-2-22222-2222222i−2i2i−2i-2-2-2-2-2-2-2-22i2i−2i−2i2i2i−2i−2i2222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22i−2i2i−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ4222-2-22222-222222−2i2i−2i2i-2-2-2-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i2222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ4322-2-2222-1-222-1222i−2i2i−2i-2-2-2-211-2-22i2i−2i−2i−i−iii2-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-1-21-2-211111111-2-2111111112i−2i−ii2i−2i2i−2i2i2i−2i−2i−i−iii−i−iii−i−i−i−iiiii2i2i−2i−2i−i−iii−i−iii−i−i−i−iiiii0000000000000000000000000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23
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χ4522-2-2222-1-222-122−2i2i−2i2i-2-2-2-211-2-2−2i−2i2i2iii−i−i2-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-1-21-2-211111111-2-211111111−2i2ii−i−2i2i−2i2i−2i−2i2i2iii−i−iii−i−iiiii−i−i−i−i−2i−2i2i2iii−i−iii−i−iiiii−i−i−i−i0000000000000000000000000000−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13
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χ1614-4−4i4i0-2-2-202222i3−2i300002i−2i2i−2i2i−2i23−23−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ232ζ5−2ζ13−2ζ5+2ζ13−2ζ7+2ζ232ζ7−2ζ23111−1−3i32−1+3i3200−i3i3−i3i3-333+i32−3−i323−i32−3+i32-1-1-11+3i321−3i3200−33−333i−3iζ14+2ζ22−ζ14−2ζ222ζ14+ζ22−2ζ14−ζ22−ii−ii−iiζ14−2ζ22−ζ14+2ζ22−2ζ14+ζ222ζ14−ζ2200000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5+2ζ13−ζ5−2ζ13−2ζ5−ζ132ζ5+ζ132ζ7+ζ23−2ζ7−ζ23−ζ7−2ζ23ζ7+2ζ233ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5−2ζ13ζ5+2ζ132ζ5+ζ13−2ζ5−ζ13−2ζ7−ζ232ζ7+ζ23ζ7+2ζ23−ζ7−2ζ23000000000000000000000000000000000000
χ1624-4−4i4i0-2-2-202222i3−2i300002i−2i2i−2i2i−2i23−23−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ23111−1+3i32−1−3i3200−i3i3−i3i33-3−3+i323−i32−3−i323+i32-1-1-11−3i321+3i3200−33−33−3i3i−2ζ14−ζ222ζ14+ζ22−ζ14−2ζ22ζ14+2ζ22−ii−ii−ii−2ζ14+ζ222ζ14−ζ22ζ14−2ζ22−ζ14+2ζ2200000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ233ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−2ζ5−ζ132ζ5+ζ13ζ5+2ζ13−ζ5−2ζ13−ζ7−2ζ23ζ7+2ζ232ζ7+ζ23−2ζ7−ζ233ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−2ζ5−ζ132ζ5+ζ13ζ5+2ζ13−ζ5−2ζ13−ζ7−2ζ23ζ7+2ζ232ζ7+ζ23−2ζ7−ζ23000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.