Finite Group Databasebeta

← Group #378121

Character table — Group #378121

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128
size11111111111111111111111111111111222222222222222244444444444444444444444444444444444444444444444488888888888888888888888888888888
order12222222222222224444444444444444888888888888888822224444444444444444444488888888888888888888888822224444444444448888888888888888
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
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
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
χ1111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ1211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-11111-1-11111111111-1-1-1-1-1-1-1-1
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ171111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i111111-1-111-1-1-1-1-1-1ii−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−i11111111-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-1-1-111-1-1111111−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−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−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−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1iiii−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-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1111-1-111-1-111-1-1-1-1ii−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-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111-1-111-1-11111−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-1-1-1-1-1-1-1-111111111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-11111-1-1-1-111ii−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-1-1-1-1-1-1-1-111111111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1-1-11111-1-1−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−iiiiiiiii11111111-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii111111-1-111-1-1-1-1-1-1−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−iiiiiiiii11111111-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1-1-111-1-1111111ii−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−iiiiiiiii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−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−iiiiiiiii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−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-1-1-1-11111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-111-1-111-1-1-1-1−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-1-1-1-11111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111-1-111-1-11111ii−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-1-1-1-1-1-1-1-111111111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-11111-1-1-1-111−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-1-1-1-1-1-1-1-111111111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ332222222-2-2-2-2-2-2-2-222222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000002i2i−2i−2i2i2i−2i−2i000000000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ342222222-2-2-2-2-2-2-2-222222-2-2-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-2000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ352222222-2-2-2-2-2-2-2-222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ362222222-2-2-2-2-2-2-2-222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ372222222-2-2-2-2-2-2-2-22-2-2-2-22222-2-2-2-222222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000-2-22222-2-200000000000000000000000000000000
χ382222222-2-2-2-2-2-2-2-22-2-2-2-22222-2-2-2-222222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000022-2-2-2-22200000000000000000000000000000000
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χ402222222-2-2-2-2-2-2-2-22-2-2-2-22222-2-2-2-22222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000-2-22222-2-200000000000000000000000000000000
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χ422222-2-2-22222-2-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000002i−2i2i−2i2-22-20000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000000000000000000000000000
χ432222-2-2-22222-2-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000−2i2i−2i2i-22-2200002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000000000000000000000000000
χ442222-2-2-22222-2-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000−2i2i−2i2i-22-220000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000000000000000000000000000
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χ462222-2-2-22222-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000002i−2i2i−2i-22-220000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000000000000000000000000000
χ472222-2-2-22222-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000−2i2i−2i2i2-22-200002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000000000000000000000000000
χ482222-2-2-22222-2-2-2-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000−2i2i−2i2i2-22-20000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000000000000000000000000000
χ492222-2-2-2-2-2-2-22222-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000022-2-222-2-22i2i−2i−2i2-2-22−2i2i2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ502222-2-2-2-2-2-2-22222-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000022-2-2-2-222−2i−2i2i2i-222-22i−2i−2i2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ512222-2-2-2-2-2-2-22222-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000-2-22222-2-22i2i−2i−2i-222-22i−2i−2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ522222-2-2-2-2-2-2-22222-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000-2-222-2-222−2i−2i2i2i2-2-22−2i2i2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ532222-2-2-2-2-2-2-22222-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000022-2-222-2-2−2i−2i2i2i2-2-222i−2i−2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ542222-2-2-2-2-2-2-22222-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000022-2-2-2-2222i2i−2i−2i-222-2−2i2i2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ552222-2-2-2-2-2-2-22222-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000-2-22222-2-2−2i−2i2i2i-222-2−2i2i2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-22222-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000-2-222-2-2222i2i−2i−2i2-2-222i−2i−2i2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ5722-2-222-222-2-222-2-2-22i−2i2i−2i2i2i−2i−2i2i−2i2i−2i−2i−2i2i2i2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ300002-22-22i−2i2i−2i000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000000000000000000000
χ5822-2-222-222-2-222-2-2-22i−2i2i−2i2i2i−2i−2i2i−2i2i−2i−2i−2i2i2i2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ30000-22-22−2i2i−2i2i00000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000000000000000000000
χ5922-2-222-222-2-222-2-2-22i−2i2i−2i2i2i−2i−2i2i−2i2i−2i−2i−2i2i2i−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ300002-22-22i−2i2i−2i00000000000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000000000000000000000
χ6022-2-222-222-2-222-2-2-22i−2i2i−2i2i2i−2i−2i2i−2i2i−2i−2i−2i2i2i−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ30000-22-22−2i2i−2i2i000000000000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.