Finite Group Databasebeta

← Group #359352

Character table — Group #359352

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128
size11111111111111111111111111111111222222222222222244444444444444444444444444444444444444444444444488888888888888888888888888888888
order12222222222222224444444444444444888888888888888844444444444444444444444488888888888888888888888844444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ1011111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ1211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ171111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ181111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-1-111-1-111-1-111-1-111−i−iii−i−iii−i−iii−i−iii
χ191111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ201111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-1-1-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i
χ211111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ221111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ231111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ241111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ251111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ261111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i
χ271111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ281111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii
χ291111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ301111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ311111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ321111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111-1-1-1-111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i
χ3322222-2-2222-2-2-2-2-2-22222-2-22222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000000000002-22-20000000000002-22-2000000000000
χ3422222-2-2222-2-2-2-2-2-22222-2-22222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000-22-22000000000000-22-22000000000000
χ3522222-2-2222-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000000000002-22-2000000000000-22-22000000000000
χ3622222-2-2222-2-2-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000-22-220000000000002-22-2000000000000
χ3722222-2-2222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000000000002-2-220000000000002i−2i−2i2i000000000000
χ3822222-2-2222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000000000000000-222-2000000000000−2i2i2i−2i000000000000
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χ42222-2-2222-2-222-2-2-2-222-2-22222-2-222-2-2-2-222-2-222-2-222-2-222-2-2-2-222-2-2220000000000000000-2-222-2-222000000000000000000000000000000000000000000000000
χ43222-2-2222-2-222-2-2-2-222-2-22222-2-222-2-2-2-2-2-222-2-222-2-222-2-22222-2-222-2-20000000000000000-2-222-2-222000000000000000000000000000000000000000000000000
χ44222-2-2222-2-222-2-2-2-222-2-22222-2-222-2-2-2-2-2-222-2-222-2-222-2-222-2-222-2-222000000000000000022-2-222-2-2000000000000000000000000000000000000000000000000
χ45222-2-2222-2-222-2-2-2-2-2-222-2-2-2-222-2-222222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i22-2-2-2-22200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
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χ48222-2-2222-2-222-2-2-2-2-2-222-2-2-2-222-2-22222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i-2-22222-2-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
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χ52222-2-2-2-22-2-2-2-2222222-2-2-2-222-2-2-2-22222-2-22222-2-2-2-22222-2-20000000000000000000000000000000000000000000000000000-22-220000000000002-22-200000000
χ53222-2-2-2-22-2-2-2-22222-2-22222-2-22222-2-2-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000000000002-2-220000000000002i−2i−2i2i00000000
χ54222-2-2-2-22-2-2-2-22222-2-22222-2-22222-2-2-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000-222-2000000000000−2i2i2i−2i00000000
χ55222-2-2-2-22-2-2-2-22222-2-22222-2-22222-2-2-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000000000002-2-22000000000000−2i2i2i−2i00000000
χ56222-2-2-2-22-2-2-2-22222-2-22222-2-22222-2-2-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000-222-20000000000002i−2i−2i2i00000000
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χ5822-22-22-2-22-22-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000022-2-22i2i−2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000000000000000000000000000
χ5922-22-22-2-22-22-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000-2-222−2i−2i2i2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000000000000000000000000000
χ6022-22-22-2-22-22-22-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000-2-222−2i−2i2i2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000000000000000000000000000
χ6122-22-22-2-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000022-2-2−2i−2i2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000000000000000000000000000
χ6222-22-22-2-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000022-2-2−2i−2i2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000000000000000000000000000
χ6322-22-22-2-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000-2-2222i2i−2i−2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000000000000000000000000000
χ6422-22-22-2-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000-2-2222i2i−2i−2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000000000000000000000000000
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χ6622-2-222-2-2-222-2-22-222i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i0000000000000000000000002i2i−2i−2i22-2-200000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ00000000000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.