Finite Group Databasebeta

← Group #199169

Character table — Group #199169

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12224444222222444444444422224444444444444444448888888888888888888888888888888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-11-1-1-1-1-11-1-1-111-1-111-1-11111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i11-1-1
χ101111111111-1-1-1-11-1-1-1-1-11-1-1-111-1-111-1-11111-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-111−i−iii-1-111
χ111111111111-1-1-1-11-1-1-1-1-11-1-1-111-1-111-1-11111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-111ii−i−i-1-111
χ121111111111-1-1-1-11-1-1-1-1-11-1-1-111-1-111-1-11111-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii11-1-1−i−iii11-1-1
χ131111111111-1-1-1-11-1-1-1-1-11-1-1-1-1-111-1-1111111-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i11-1-1−i−iii-1-111
χ141111111111-1-1-1-11-1-1-1-1-11-1-1-1-1-111-1-1111111-1-1-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii-1-111ii−i−i11-1-1
χ151111111111-1-1-1-11-1-1-1-1-11-1-1-1-1-111-1-1111111-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i-1-111−i−iii11-1-1
χ161111111111-1-1-1-11-1-1-1-1-11-1-1-1-1-111-1-1111111-1-1-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii11-1-1ii−i−i-1-111
χ171111-1-1-1-1-1-111-1-1111-1111-1-1-111-1-1-1-11111-1-11-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1i−ii−i1-11-1
χ181111-1-1-1-1-1-111-1-1111-1111-1-1-111-1-1-1-11111-1-11-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11-11−ii−ii-11-11
χ191111-1-1-1-1-1-111-1-1111-1111-1-1-111-1-1-1-11111-1-11-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11-11i−ii−i-11-11
χ201111-1-1-1-1-1-111-1-1111-1111-1-1-111-1-1-1-11111-1-11-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-1−ii−ii1-11-1
χ211111-1-1-1-1-1-111-1-1111-1111-1-1-1-1-11111-1-111-1-11-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i1-11-1−ii−ii-11-11
χ221111-1-1-1-1-1-111-1-1111-1111-1-1-1-1-11111-1-111-1-11-1-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii-11-11i−ii−i1-11-1
χ231111-1-1-1-1-1-111-1-1111-1111-1-1-1-1-11111-1-111-1-11-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i-11-11−ii−ii1-11-1
χ241111-1-1-1-1-1-111-1-1111-1111-1-1-1-1-11111-1-111-1-11-1-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii1-11-1i−ii−i-11-11
χ251111-1-1-1-1-1-1-1-1111-1-11-1-111111111-1-1-1-111-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-111-1-111-1-11
χ261111-1-1-1-1-1-1-1-1111-1-11-1-111111111-1-1-1-111-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1-111-1-111-1
χ271111-1-1-1-1-1-1-1-1111-1-11-1-111111111-1-1-1-111-1-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-111-11-1-11-111-1
χ281111-1-1-1-1-1-1-1-1111-1-11-1-111111111-1-1-1-111-1-1-1111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11-111-11-1-11
χ291111-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1-1-1111111-1-1-11-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1111-1-11-111-1-111-1
χ301111-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1-1-1111111-1-1-11-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-111-11-1-111-1-11
χ311111-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1-1-1111111-1-1-11-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-111-1-111-11-1-11
χ321111-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1-1-1111111-1-1-11-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11-1-111-1-11-111-1
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χ8422-2-2-2-222-222-2-2222-2-200-2200-222-22-2-2200000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000000000000000
χ8522-2-2-2-222-22-222-22-22200-2-2002-22-2-22-22000000000000002−22−2−22−22−22−222−22−22−22−2−22−22−22−222−22−200000000000000000000
χ8622-2-2-2-222-22-222-22-22200-2-2002-22-2-22-2200000000000000−22−222−22−22−22−2−22−22−22−222−22−22−22−2−22−2200000000000000000000
χ8722-2-2-2-222-22-222-22-22200-2-200-22-222-22-2000000000000002−22−2−22−22−22−222−22−2−22−222−22−22−22−2−22−2200000000000000000000
χ8822-2-2-2-222-22-222-22-22200-2-200-22-222-22-200000000000000−22−222−22−22−22−2−22−222−22−2−22−22−22−222−22−200000000000000000000
χ894-44-44i−4i4i−4i00000000004-4004i−4i0000000000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000
χ904-44-44i−4i4i−4i00000000004-4004i−4i000000000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000
χ914-44-44i−4i4i−4i0000000000-4400−4i4i0000000000000000000000000000000000000000000000000000002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ000000000000
χ924-44-44i−4i4i−4i0000000000-4400−4i4i000000000000000000000000000000000000000000000000000000−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ000000000000
χ934-44-4−4i4i−4i4i00000000004-400−4i4i0000000000000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000
χ944-44-4−4i4i−4i4i00000000004-400−4i4i000000000000000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000
χ954-44-4−4i4i−4i4i0000000000-44004i−4i0000000000000000000000000000000000000000000000000000002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ3000000000000
χ964-44-4−4i4i−4i4i0000000000-44004i−4i000000000000000000000000000000000000000000000000000000−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3000000000000
χ978-8-888i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.