Finite Group Databasebeta

← Group #13173387

Character table — Group #13173387

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168
size111122222222224444444444444444444444444444444444444444444444449999181818181818181818185454545454545454111122222222224444444444444444444444444444444444444444444444449999181818181818181818185454545454545454
order1244234666121212123333336666666666666666661212121212121212121212121212121212121212121212128888882424242424242424161616161616161622442646661212121266666666666666666666666612121212121212121212121212121212121212121212121288888824242424242424241616161616161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111-11-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111-1-11111-11-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111-1-1
χ61111-11-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1111111-11-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-111
χ71111-11-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iii1111-11-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iii
χ81111-11-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i1111-11-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i
χ911-1-111-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−iii−i−iii−i−iζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ1311-1-111-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−iii−i−iii−i−iζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13
χ1011-1-111-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−iii−i−iii−i−i−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ1311-1-111-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−iii−i−iii−i−i−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13
χ1111-1-111-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ii−i−iii−i−iii−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ2311-1-111-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ii−i−iii−i−iii−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23
χ1211-1-111-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ii−i−iii−i−iiiζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ2311-1-111-1111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ii−i−iii−i−iiiζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23
χ1311-1-1-111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111ii−i−i−iiii−i−i−i−iiiζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ1311-1-1-111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111ii−i−i−iiii−i−i−i−iiiζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13
χ1411-1-1-111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111ii−i−i−iiii−i−i−i−iii−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ1311-1-1-111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111ii−i−i−iiii−i−i−i−iii−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13
χ1511-1-1-111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−iiii−i−i−iiiii−i−i−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ2311-1-1-111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−iiii−i−i−iiiii−i−i−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23
χ1611-1-1-111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−iiii−i−i−iiiii−i−iζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ2311-1-1-111-1-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−iiii−i−i−iiiii−i−iζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23
χ1722222-12-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-10000000022222-12-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-100000000
χ1822222-12-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2111111110000000022222-12-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-21111111100000000
χ192222-2-1-211-111-1-122-1-1-1-1-2-2-2-21111111122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2111111112222-2-2-1-1-1-11111000000002222-2-1-211-111-1-122-1-1-1-1-2-2-2-21111111122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2111111112222-2-2-1-1-1-1111100000000
χ202222-2-1-211-111-1-122-1-1-1-1-2-2-2-21111111122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2221111-1-1-1-1000000002222-2-1-211-111-1-122-1-1-1-1-2-2-2-21111111122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2221111-1-1-1-100000000
χ2122-2-22-1-2-1-1-1111122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-2111111112i2i−2i−2i2i−2i−i−iii−i−iii0000000022-2-22-1-2-1-1-1111122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-2111111112i2i−2i−2i2i−2i−i−iii−i−iii00000000
χ2222-2-22-1-2-1-1-1111122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111−2i−2i2i2i−2i2iii−i−iii−i−i0000000022-2-22-1-2-1-1-1111122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111−2i−2i2i2i−2i2iii−i−iii−i−i00000000
χ2322-2-2-2-1211-1-1-11122-1-1-1-1-2-2-2-21111111122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-12i2i−2i−2i−2i2i−i−iiiii−i−i0000000022-2-2-2-1211-1-1-11122-1-1-1-1-2-2-2-21111111122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-12i2i−2i−2i−2i2i−i−iiiii−i−i00000000
χ2422-2-2-2-1211-1-1-11122-1-1-1-1-2-2-2-21111111122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1−2i−2i2i2i2i−2iii−i−i−i−iii0000000022-2-2-2-1211-1-1-11122-1-1-1-1-2-2-2-21111111122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1−2i−2i2i2i2i−2iii−i−i−i−iii00000000
χ252-22i−2i02000-2002i−2i222222000000000000-2-2-2-2-2-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000002-22i−2i02000-2002i−2i222222000000000000-2-2-2-2-2-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000000
χ262-22i−2i02000-2002i−2i222222000000000000-2-2-2-2-2-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000002-22i−2i02000-2002i−2i222222000000000000-2-2-2-2-2-22i2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000000
χ272-22i−2i0-10−i3i313−3−ii22-1-1-1-10000−i3−i3−i3−i3i3i3i3i3-2-211112i2i−2i−2i−i−i−i−iiiii00003333−3−3−3−32ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000002-22i−2i0-10−i3i313−3−ii22-1-1-1-10000−i3−i3−i3−i3i3i3i3i3-2-211112i2i−2i−2i−i−i−i−iiiii00003333−3−3−3−32ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ282-22i−2i0-10−i3i313−3−ii22-1-1-1-10000−i3−i3−i3−i3i3i3i3i3-2-211112i2i−2i−2i−i−i−i−iiiii00003333−3−3−3−3−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000002-22i−2i0-10−i3i313−3−ii22-1-1-1-10000−i3−i3−i3−i3i3i3i3i3-2-211112i2i−2i−2i−i−i−i−iiiii00003333−3−3−3−3−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ292-22i−2i0-10i3−i31−33−ii22-1-1-1-10000i3i3i3i3−i3−i3−i3−i3-2-211112i2i−2i−2i−i−i−i−iiiii0000−3−3−3−333332ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000002-22i−2i0-10i3−i31−33−ii22-1-1-1-10000i3i3i3i3−i3−i3−i3−i3-2-211112i2i−2i−2i−i−i−i−iiiii0000−3−3−3−333332ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ302-22i−2i0-10i3−i31−33−ii22-1-1-1-10000i3i3i3i3−i3−i3−i3−i3-2-211112i2i−2i−2i−i−i−i−iiiii0000−3−3−3−33333−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000002-22i−2i0-10i3−i31−33−ii22-1-1-1-10000i3i3i3i3−i3−i3−i3−i3-2-211112i2i−2i−2i−i−i−i−iiiii0000−3−3−3−33333−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ312-2−2i2i02000-200−2i2i222222000000000000-2-2-2-2-2-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000002-2−2i2i02000-200−2i2i222222000000000000-2-2-2-2-2-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000000
χ322-2−2i2i02000-200−2i2i222222000000000000-2-2-2-2-2-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000002-2−2i2i02000-200−2i2i222222000000000000-2-2-2-2-2-2−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000000
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χ1684-4−4i4i0-202i3−2i3223−232i−2i-2111−1+3i32−1−3i32003-3−i3−i3−3+i323+i32i3i33−i32−3−i322-1-1-11−3i321+3i322i−i−2ii−i−i−2ζ14+ζ22ζ14−2ζ22ii2ζ14−ζ22−ζ14+2ζ2200−3i3i−3−3−2ζ14−ζ22ζ14+2ζ22332ζ14+ζ22−ζ14−2ζ220000000000000000000000-444i−4i020−2i32i3-2−2323−2i2i2-1-1-11−3i321+3i3200-33i3i33−i32−3−i32−i3−i3−3+i323+i32-2111−1+3i32−1−3i32−2ii2i−iii2ζ14−ζ22−ζ14+2ζ22−i−i−2ζ14+ζ22ζ14−2ζ22003i−3i332ζ14+ζ22−ζ14−2ζ22−3−3−2ζ14−ζ22ζ14+2ζ220000000000000000000000

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