Finite Group Databasebeta

← Group #13173441

Character table — Group #13173441

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168
size111122222222224444444444444444444444444444444444444444444444449999181818181818181818185454545454545454111122222222224444444444444444444444444444444444444444444444449999181818181818181818185454545454545454
order1222223666666633333366666666666666666666666666666666666666666644444412121212121212128888888822222266666666666666666666666666666666666666666666666666666666444444121212121212121288888888
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
χ51111-1-1111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111-1-11111-1-1111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111-1-1
χ61111-1-1111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1111111-1-1111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-111
χ71111-1-1111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iii1111-1-1111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111ii−i−i−i−iii
χ81111-1-1111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i1111-1-1111-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111−i−iiiii−i−i
χ911-1-11-111-111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−iii−i−iii−i−iζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ1311-1-11-111-111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−iii−i−iii−i−iζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13
χ1011-1-11-111-111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−iii−i−iii−i−i−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ1311-1-11-111-111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−ii−iii−i−iii−i−i−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23ζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13
χ1111-1-11-111-111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ii−i−iii−i−iii−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ2311-1-11-111-111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ii−i−iii−i−iii−ζ5−ζ13ζ5+ζ13−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ7+ζ23−ζ7−ζ23
χ1211-1-11-111-111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ii−i−iii−i−iiiζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ2311-1-11-111-111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−ii−i−iii−i−iiiζ5+ζ13−ζ5−ζ13ζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ7−ζ23ζ7+ζ23
χ1311-1-1-1111-1-1-111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111ii−i−i−iiii−i−i−i−iiiζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ1311-1-1-1111-1-1-111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111ii−i−i−iiii−i−i−i−iiiζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13
χ1411-1-1-1111-1-1-111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111ii−i−i−iiii−i−i−i−iii−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ1311-1-1-1111-1-1-111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111ii−i−i−iiii−i−i−i−iii−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13
χ1511-1-1-1111-1-1-111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−iiii−i−i−iiiii−i−i−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ2311-1-1-1111-1-1-111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−iiii−i−i−iiiii−i−i−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ7+ζ23
χ1611-1-1-1111-1-1-111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−iiii−i−i−iiiii−i−iζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ2311-1-1-1111-1-1-111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−iiii−i−i−iiiii−i−iζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ7−ζ23
χ17222222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-100000000222222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-100000000
χ18222222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-21111111100000000222222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-21111111100000000
χ192222-2-2-1-1-11111-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-2-2-1-1-1-11111000000002222-2-2-1-1-11111-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-2-2-1-1-1-1111100000000
χ202222-2-2-1-1-11111-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2221111-1-1-1-1000000002222-2-2-1-1-11111-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-2221111-1-1-1-100000000
χ2122-2-22-2-1-11-1-111122-1-1-1-122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-2111111112i2i−2i−2i2i−2i−i−iii−i−iii0000000022-2-22-2-1-11-1-111122-1-1-1-122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-2111111112i2i−2i−2i2i−2i−i−iii−i−iii00000000
χ2222-2-22-2-1-11-1-111122-1-1-1-122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-211111111−2i−2i2i2i−2i2iii−i−iii−i−i0000000022-2-22-2-1-11-1-111122-1-1-1-122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-2-2-211111111−2i−2i2i2i−2i2iii−i−iii−i−i00000000
χ2322-2-2-22-1-1111-1-1122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-12i2i−2i−2i−2i2i−i−iiiii−i−i0000000022-2-2-22-1-1111-1-1122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-12i2i−2i−2i−2i2i−i−iiiii−i−i00000000
χ2422-2-2-22-1-1111-1-1122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-1−2i−2i2i2i2i−2iii−i−i−i−iii0000000022-2-2-22-1-1111-1-1122-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-2111111112222-1-1-1-1-1-1-1-1−2i−2i2i2i2i−2iii−i−i−i−iii00000000
χ252-22-2002-220000-2222222-2-2-2-2-2-222-2-22222-2-2-2-20000000000000000000000002i−2i2i−2i002i−2i2i−2i0000000000002-22-2002-220000-2222222-2-2-2-2-2-222-2-22222-2-2-2-20000000000000000000000002i−2i2i−2i002i−2i2i−2i000000000000
χ262-22-2002-220000-2222222-2-2-2-2-2-222-2-22222-2-2-2-2000000000000000000000000−2i2i−2i2i00−2i2i−2i2i0000000000002-22-2002-220000-2222222-2-2-2-2-2-222-2-22222-2-2-2-2000000000000000000000000−2i2i−2i2i00−2i2i−2i2i000000000000
χ272-22-200-11-1−i3i3−i3i3122-1-1-1-1-2-2111122-2-2-1-1-1-111110000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i32i−2i2i−2i00−ii−ii3−33−3000000002-22-200-11-1−i3i3−i3i3122-1-1-1-1-2-2111122-2-2-1-1-1-111110000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i32i−2i2i−2i00−ii−ii3−33−300000000
χ282-22-200-11-1−i3i3−i3i3122-1-1-1-1-2-2111122-2-2-1-1-1-111110000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i3−2i2i−2i2i00i−ii−i−33−33000000002-22-200-11-1−i3i3−i3i3122-1-1-1-1-2-2111122-2-2-1-1-1-111110000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i3−2i2i−2i2i00i−ii−i−33−3300000000
χ292-22-200-11-1i3−i3i3−i3122-1-1-1-1-2-2111122-2-2-1-1-1-111110000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i32i−2i2i−2i00−ii−ii−33−33000000002-22-200-11-1i3−i3i3−i3122-1-1-1-1-2-2111122-2-2-1-1-1-111110000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i32i−2i2i−2i00−ii−ii−33−3300000000
χ302-22-200-11-1i3−i3i3−i3122-1-1-1-1-2-2111122-2-2-1-1-1-111110000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i3−2i2i−2i2i00i−ii−i3−33−3000000002-22-200-11-1i3−i3i3−i3122-1-1-1-1-2-2111122-2-2-1-1-1-111110000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i3−2i2i−2i2i00i−ii−i3−33−300000000
χ312-2-22002-2-200002222222-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000002-2-22002-2-220000000000002-2-22002-2-200002222222-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000002-2-22002-2-22000000000000
χ322-2-22002-2-200002222222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000-222-200-222-20000000000002-2-22002-2-200002222222-2-2-2-2-2-2-2-222-2-2-2-22222000000000000000000000000-222-200-222-2000000000000
χ332-2-2200-111−i3i3i3−i3-122-1-1-1-1-2-21111-2-2221111-1-1-1-10000−i3−i3−i3−i3i3i3i3i30000i3i3i3i3−i3−i3−i3−i32-2-2200-111-1−i3i3i3−i3000000002-2-2200-111−i3i3i3−i3-122-1-1-1-1-2-21111-2-2221111-1-1-1-10000−i3−i3−i3−i3i3i3i3i30000i3i3i3i3−i3−i3−i3−i32-2-2200-111-1−i3i3i3−i300000000
χ342-2-2200-111−i3i3i3−i3-122-1-1-1-1-2-21111-2-2221111-1-1-1-10000−i3−i3−i3−i3i3i3i3i30000i3i3i3i3−i3−i3−i3−i3-222-2001-1-11i3−i3−i3i3000000002-2-2200-111−i3i3i3−i3-122-1-1-1-1-2-21111-2-2221111-1-1-1-10000−i3−i3−i3−i3i3i3i3i30000i3i3i3i3−i3−i3−i3−i3-222-2001-1-11i3−i3−i3i300000000
χ352-2-2200-111i3−i3−i3i3-122-1-1-1-1-2-21111-2-2221111-1-1-1-10000i3i3i3i3−i3−i3−i3−i30000−i3−i3−i3−i3i3i3i3i32-2-2200-111-1i3−i3−i3i3000000002-2-2200-111i3−i3−i3i3-122-1-1-1-1-2-21111-2-2221111-1-1-1-10000i3i3i3i3−i3−i3−i3−i30000−i3−i3−i3−i3i3i3i3i32-2-2200-111-1i3−i3−i3i300000000
χ362-2-2200-111i3−i3−i3i3-122-1-1-1-1-2-21111-2-2221111-1-1-1-10000i3i3i3i3−i3−i3−i3−i30000−i3−i3−i3−i3i3i3i3i3-222-2001-1-11−i3i3i3−i3000000002-2-2200-111i3−i3−i3i3-122-1-1-1-1-2-21111-2-2221111-1-1-1-10000i3i3i3i3−i3−i3−i3−i30000−i3−i3−i3−i3i3i3i3i3-222-2001-1-11−i3i3i3−i300000000
χ37444444444444441-211-2-21-211-2-21-21-211-2-211-2-211-2-211-2-211-2-211-2-211-2-211-2-20000000000000000000000444444444444441-211-2-21-211-2-21-21-211-2-211-2-211-2-211-2-211-2-211-2-211-2-211-2-20000000000000000000000
χ3844444444444444-21-2-211-21-2-211-21-21-2-211-2-211-2-211-2-211-2-211-2-211-2-211-2-211000000000000000000000044444444444444-21-2-211-21-2-211-21-21-2-211-2-211-2-211-2-211-2-211-2-211-2-211-2-2110000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.