Finite Group Databasebeta

← Group #13176642

Character table — Group #13176642

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
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χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-11111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1
χ41111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11
χ5111111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11-1111-1-1111111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11-1111-1-1
χ6111111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-11-1-1-111111111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-11-1-1-111
χ7111111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-11-11111111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-11-11
χ8111111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1111-11-1111111111111111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1111-11-1
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χ18222-1-1-1222-1-1-122-1-1-12-1-1-1-22-1-1-1222-1-1-1-1-1-1-2-2111111-2-2-2-2-2-2111111111111-22-21112-1-1-10000000222-1-1-1222-1-1-122-1-1-12-1-1-1-22-1-1-1222-1-1-1-1-1-1-2-2111111-2-2-2-2-2-2111111111111-22-21112-1-1-10000000
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χ3022-1-1-1222-1-1-122-1-1-12-1-1-12-2-1-1-122-1-1-1-1-1-122111111-2-2-2-2111111111111-2-2-2-2-22111-2-1-1-12000000022-1-1-1222-1-1-122-1-1-12-1-1-12-2-1-1-122-1-1-1-1-1-122111111-2-2-2-2111111111111-2-2-2-2-22111-2-1-1-120000000
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χ1454-4-2-24-24022-42-4-2-24-222-4200000000000000i6−i6−i6i600i6−i600i6−i6−i6i6−i6i6i6−i60000i6−i6−i6i600000000000000000-4422-42-40-2-24-2422-42-2-24-200000000000000−i6i6i6−i600−i6i600−i6i6i6−i6i6−i6−i6i60000−i6i6i6−i600000000000000000
χ1464-4-2-24-24022-42-4-2-24-222-4200000000000000−i6i6i6−i600−i6i600−i6i6i6−i6i6−i6−i6i60000−i6i6i6−i600000000000000000-4422-42-40-2-24-2422-42-2-24-200000000000000i6−i6−i6i600i6−i600i6−i6−i6i6−i6i6i6−i60000i6−i6−i6i600000000000000000
χ1474-4-2-24-2-2022-42211-21-1-12-10000003i−3i−3i3i003i−3ii6−i6−i6i600i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ136−66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000000-4422-4220-2-24-2-2-1-12-111-21000000−3i3i3i−3i00−3i3i−i6i6i6−i600−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−66−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000000
χ1484-4-2-24-2-2022-42211-21-1-12-10000003i−3i−3i3i003i−3i−i6i6i6−i600−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−66−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000000-4422-4220-2-24-2-2-1-12-111-21000000−3i3i3i−3i00−3i3ii6−i6−i6i600i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ136−66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000000000000
χ1494-4-2-24-2-2022-42211-21-1-12-1000000−3i3i3i−3i00−3i3ii6−i6−i6i600i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−66−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000000-4422-4220-2-24-2-2-1-12-111-210000003i−3i−3i3i003i−3i−i6i6i6−i600−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ236−66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000000
χ1504-4-2-24-2-2022-42211-21-1-12-1000000−3i3i3i−3i00−3i3i−i6i6i6−i600−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ236−66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000000-4422-4220-2-24-2-2-1-12-111-210000003i−3i−3i3i003i−3ii6−i6−i6i600i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−66−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000000000000
χ1514-4-2-2-2440222-4-4-2-2-24222-400000000000000i6−i6i6−i6−i6i60000i6−i6−i6i6i6−i6−i6i6−i6i6i6−i6000000000000000000000-44222-4-40-2-2-244222-4-2-2-2400000000000000−i6i6−i6i6i6−i60000−i6i6i6−i6−i6i6i6−i6i6−i6−i6i6000000000000000000000
χ1524-4-2-2-2440222-4-4-2-2-24222-400000000000000−i6i6−i6i6i6−i60000−i6i6i6−i6−i6i6i6−i6i6−i6−i6i6000000000000000000000-44222-4-40-2-2-244222-4-2-2-2400000000000000i6−i6i6−i6−i6i60000i6−i6−i6i6i6−i6−i6i6−i6i6i6−i6000000000000000000000
χ1534-4-2-2-24-20222-42111-2-1-1-120000003i−3i3i−3i−3i3i00i6−i6i6−i6−i6i6006−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ136−66−600000000000000000-44222-420-2-2-24-2-1-1-12111-2000000−3i3i−3i3i3i−3i00−i6i6−i6i6i6−i600−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−66−6600000000000000000
χ1544-4-2-2-24-20222-42111-2-1-1-120000003i−3i3i−3i−3i3i00−i6i6−i6i6i6−i600−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−66−6600000000000000000-44222-420-2-2-24-2-1-1-12111-2000000−3i3i−3i3i3i−3i00i6−i6i6−i6−i6i6006−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ136−66−600000000000000000
χ1554-4-2-2-24-20222-42111-2-1-1-12000000−3i3i−3i3i3i−3i00i6−i6i6−i6−i6i600−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−66−6600000000000000000-44222-420-2-2-24-2-1-1-12111-20000003i−3i3i−3i−3i3i00−i6i6−i6i6i6−i6006−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ236−66−600000000000000000
χ1564-4-2-2-24-20222-42111-2-1-1-12000000−3i3i−3i3i3i−3i00−i6i6−i6i6i6−i6006−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ236−66−600000000000000000-44222-420-2-2-24-2-1-1-12111-20000003i−3i3i−3i−3i3i00i6−i6i6−i6−i6i600−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−66−6600000000000000000

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