Finite Group Databasebeta

← Group #13160053

Character table — Group #13160053

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size111122222222222222222222224444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441212121224242424242424242424242424242424363636365454545472727272108108
order12223333344666666666666666333366666666666688121212121212121212121212121212121212121212121212121224242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424242424444412121212121212121212121212121212444422441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1
χ6111111111111111111111111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ7111111111111111111111111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-111
χ8111111111111111111111111111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1-1
χ91-1-11111111-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-1-1-1-1-11111i−i1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−ii−i1-1iiii−i−i−i−i1111-1-1-1-1i−i1-11-11-1i−i1-1i−i
χ101-1-11111111-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-1-1-1-1-11111i−i1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−ii−i1-1iiii−i−i−i−i1111-1-1-1-1−ii-11-11-11−ii-11−ii
χ111-1-11111111-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-1-1-1-1-11111i−i1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−ii-11−i−i−i−iiiii-1-1-1-11111i−i1-1-11-11i−i1-1−ii
χ121-1-11111111-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-1-1-1-1-11111i−i1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−ii-11−i−i−i−iiiii-1-1-1-11111−ii-111-11-1−ii-11i−i
χ131-1-11111111-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-1-1-1-1-11111−ii1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiiiiiiiiii−i-11iiii−i−i−i−i-1-1-1-11111i−i-111-11-1i−i-11−ii
χ141-1-11111111-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-1-1-1-1-11111−ii1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiiiiiiiiii−i-11iiii−i−i−i−i-1-1-1-11111−ii1-1-11-11−ii1-1i−i
χ151-1-11111111-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-1-1-1-1-11111−ii1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiiiiiiiii−ii1-1−i−i−i−iiiii1111-1-1-1-1i−i-11-11-11i−i-11i−i
χ161-1-11111111-1-1-1-1-1-1-1-1-1-11111-111111-1-1-1-1-1-1-1-11111−ii1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiiiiiiiiiiiii−ii1-1−i−i−i−iiiii1111-1-1-1-1−ii1-11-11-1−ii1-1−ii
χ17222222222-2-2222222222222222222222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000000000000000000000000000000022-2-2000000
χ18222222222-2-2222222222222222222222222222222200-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000000000000000000000000000000000000000-2-222000000
χ1922222222-1222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000022220000-1-1-1-100
χ2022222222-1222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000-2-2-2-20000111100
χ2122222222-1222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111111-2-2-2-2-2-2-2-21111111111111111110000000000000000000022-2-20000-1-11100
χ2222222222-1222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111111-2-2-2-2-2-2-2-211111111111111111100000000000000000000-2-222000011-1-100
χ2322222-1-1-12222-1-1-122-1-1-12-1-1-1222-1-1-122-1-1-1-1-1-12-1-1-1222-1-1-1222-1-1-1-1-1-12-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122222-1-1-12-1-1-12-1-1-12-1-1-100000000000000
χ2422222-1-1-12222-1-1-122-1-1-12-1-1-1222-1-1-122-1-1-1-1-1-12-1-1-1222-1-1-1222-1-1-1-1-1-12-1-1-1222-1-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2111-2111-2111-211100000000000000
χ2522222-1-1-12222-1-1-122-1-1-12-1-1-1222-1-1-122-1-1-1-1-1-12-1-1-1-2-22-1-1-1222-1-1-1-1-1-12-1-1-1222-1-1-1-1-1-1-2-2111111-2-2-2-2-2-2111111111111-2-2111111-2-2-2-2-2-211111111111122-2-22-1-1-12-1-1-1-2111-211100000000000000
χ2622222-1-1-12222-1-1-122-1-1-12-1-1-1222-1-1-122-1-1-1-1-1-12-1-1-1-2-22-1-1-1222-1-1-1-1-1-12-1-1-1222-1-1-1-1-1-1-2-2111111-2-2-2-2-2-2111111111111-2-2111111-2-2-2-2-2-2111111111111-2-222-2111-21112-1-1-12-1-1-100000000000000
χ272222-12-1-1222-12-1-12-12-1-1-12-1-122-12-1-1-1-122-1-1-1-1-12-1-122-12-1-12-1-122-1-1-1-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-12-1-1-12-1-1-12-1-1-12-1-100000000000000
χ282222-12-1-1222-12-1-12-12-1-1-12-1-122-12-1-1-1-122-1-1-1-1-12-1-122-12-1-12-1-122-1-1-1-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-21-2111-2111-2111-21100000000000000
χ292222-12-1-1222-12-1-12-12-1-1-12-1-122-12-1-1-1-122-1-1-1-1-12-1-1-2-2-12-1-12-1-122-1-1-1-1-12-1-12-1-122-1-1-1-111-2-21111-2-21111-2-2-2-21111111111-2-21111-2-21111-2-2-2-21111111122-2-2-12-1-1-12-1-11-2111-21100000000000000
χ302222-12-1-1222-12-1-12-12-1-1-12-1-122-12-1-1-1-122-1-1-1-1-12-1-1-2-2-12-1-12-1-122-1-1-1-1-12-1-12-1-122-1-1-1-111-2-21111-2-21111-2-2-2-21111111111-2-21111-2-21111-2-2-2-211111111-2-2221-2111-211-12-1-1-12-1-100000000000000
χ312222-1-12-1222-1-12-12-1-12-1-1-12-122-1-12-1-1-1-1-122-1-1-1-12-122-1-12-12-1-1-1-122-1-1-1-12-12-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-12222-1-12-1-1-12-1-1-12-1-1-12-100000000000000
χ322222-1-12-1222-1-12-12-1-12-1-1-12-122-1-12-1-1-1-1-122-1-1-1-12-122-1-12-12-1-1-1-122-1-1-1-12-12-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-211-2111-2111-2111-2100000000000000
χ332222-1-12-1222-1-12-12-1-12-1-1-12-122-1-12-1-1-1-1-122-1-1-1-12-1-2-2-1-12-12-1-1-1-122-1-1-1-12-12-1-1-1-122-1-11111-2-211-2-211111111-2-2-2-211111111-2-211-2-211111111-2-2-2-2111122-2-2-1-12-1-1-12-111-2111-2100000000000000
χ342222-1-12-1222-1-12-12-1-12-1-1-12-122-1-12-1-1-1-1-122-1-1-1-12-1-2-2-1-12-12-1-1-1-122-1-1-1-12-12-1-1-1-122-1-11111-2-211-2-211111111-2-2-2-211111111-2-211-2-211111111-2-2-2-21111-2-22211-2111-21-1-12-1-1-12-100000000000000
χ352222-1-1-12222-1-1-122-1-1-12-1-1-1222-1-1-12-1-1-1-1-1-122-1-1-1222-1-1-122-1-1-1-1-1-122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-12-1-1-12-1-1-12-1-1-1200000000000000
χ362222-1-1-12222-1-1-122-1-1-12-1-1-1222-1-1-12-1-1-1-1-1-122-1-1-1222-1-1-122-1-1-1-1-1-122-1-1-122-1-1-1-1-1-122-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2111-2111-2111-2111-200000000000000
χ372222-1-1-12222-1-1-122-1-1-12-1-1-1222-1-1-12-1-1-1-1-1-122-1-1-12-2-2-1-1-122-1-1-1-1-1-122-1-1-122-1-1-1-1-1-122111111-2-2-2-2111111111111-2-2-2-2111111-2-2-2-2111111111111-2-2-2-222-2-2-1-1-12-1-1-12111-2111-200000000000000
χ382222-1-1-12222-1-1-122-1-1-12-1-1-1222-1-1-12-1-1-1-1-1-122-1-1-12-2-2-1-1-122-1-1-1-1-1-122-1-1-122-1-1-1-1-1-122111111-2-2-2-2111111111111-2-2-2-2111111-2-2-2-2111111111111-2-2-2-2-2-222111-2111-2-1-1-12-1-1-1200000000000000
χ392-2-2222222-22-2-2-2-2-2-2-2-2-22222-222222-2-2-2-2-2-2-2-2222200-2-2-2-2-2-2-2-2-2-2-2-2-2222222222222200000000000000000000000000000000000000000000000000000000000000000000000000002-2-22000000
χ402-2-2222222-22-2-2-2-2-2-2-2-2-22222-222222-2-2-2-2-2-2-2-2222200-2-2-2-2-2-2-2-2-2-2-2-2-222222222222220000000000000000000000000000000000000000000000000000000000000000000000000000-222-2000000
χ412-2-222222-12-2-2-2-2-21-2-2-2-222221-1-1-1-1-111111111-1-1-1-12i−2i2222-1-1-1-1-1-1-1-1-1-2-2-2-21111111112i2i2i2i2i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−2i−2i−2i−2i−2i−2i−2i−2iiiiiiiiiiiiiiiiiii000000000000000000002i−2i2-20000−ii-1100
χ422-2-222222-12-2-2-2-2-21-2-2-2-222221-1-1-1-1-111111111-1-1-1-12i−2i2222-1-1-1-1-1-1-1-1-1-2-2-2-21111111112i2i2i2i2i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−2i−2i−2i−2i−2i−2i−2i−2iiiiiiiiiiiiiiiiiii00000000000000000000−2i2i-220000i−i1-100
χ432-2-222222-12-2-2-2-2-21-2-2-2-222221-1-1-1-1-111111111-1-1-1-1−2i2i2222-1-1-1-1-1-1-1-1-1-2-2-2-2111111111−2i−2i−2i−2i−2i−2i−2i−2iiiiiiiiiiiiiiiiiii2i2i2i2i2i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i000000000000000000002i−2i-220000−ii1-100
χ442-2-222222-12-2-2-2-2-21-2-2-2-222221-1-1-1-1-111111111-1-1-1-1−2i2i2222-1-1-1-1-1-1-1-1-1-2-2-2-2111111111−2i−2i−2i−2i−2i−2i−2i−2iiiiiiiiiiiiiiiiiii2i2i2i2i2i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i00000000000000000000−2i2i2-20000i−i-1100
χ452-2-222-1-1-122-2-2111-2-21112-1-1-1-222-1-1-1-2-21111112-1-1-12i−2i2-1-1-1222-1-1-1-1-1-1-2111-2-2-21111112i2i−i−i−i−i−i−i2i2i2i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i−2i−2iiiiiii−2i−2i−2i−2i−2i−2iiiiiiiiiiiii2i−2i2-22i−i−i−i−2iiii2-1-1-1-211100000000000000
χ462-2-222-1-1-122-2-2111-2-21112-1-1-1-222-1-1-1-2-21111112-1-1-12i−2i2-1-1-1222-1-1-1-1-1-1-2111-2-2-21111112i2i−i−i−i−i−i−i2i2i2i2i2i2i−i−i−i−i−i−i−i−i−i−i−i−i−2i−2iiiiiii−2i−2i−2i−2i−2i−2iiiiiiiiiiiii−2i2i-22−2iiii2i−i−i−i-21112-1-1-100000000000000
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χ1564-4-44-2-2-24-2-44222-42222-4-2-2-242-2111-2-1-1-1-1-1-122111-200222-42-1-1-1-1-1-122-2-2-24-2111111-2-20000000000-3-333-3-33333-3-30000000000000033-3-333-3-3-3-33300000000000000000000000000000000000000

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