Finite Group Databasebeta

← Group #134378

Character table — Group #134378

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111111111111222222222222222222222222222222224444444444444444444444444444444444444444444488888888888888881616161616161616
order12224444888888882244444444444444888888888888888844444444444444444444448888888888888888888888161616161616161616161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii
χ171111-1-1-1-1ii−i−iii−i−i-1-111-1-1iiii−i−i−i−i11ii−i−i1111-1-1-1-1ii−i−i1-11111-1-1-1-1ii−i−iiiii−i−i−i−ii−iiiii−i−i−i−i11-1-11111-1-1-1-1ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ−ζζ3−ζ3ζ3−ζ3ζ−ζ
χ181111-1-1-1-1ii−i−iii−i−i-1-111-1-1iiii−i−i−i−i11ii−i−i1111-1-1-1-1ii−i−i1-11111-1-1-1-1ii−i−iiiii−i−i−i−ii−iiiii−i−i−i−i11-1-11111-1-1-1-1−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζζ−ζ3ζ3−ζ3ζ3−ζζ
χ191111-1-1-1-1ii−i−iii−i−i-1-111-1-1iiii−i−i−i−i11ii−i−i1111-1-1-1-1ii−i−i1-1-1-1-1-11111ii−i−i−i−i−i−iiiiii−i−i−i−i−iiiii11-1-1-1-1-1-11111ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζζ−ζ3ζ3−ζ3ζ3−ζζ
χ201111-1-1-1-1ii−i−iii−i−i-1-111-1-1iiii−i−i−i−i11ii−i−i1111-1-1-1-1ii−i−i1-1-1-1-1-11111ii−i−i−i−i−i−iiiiii−i−i−i−i−iiiii11-1-1-1-1-1-11111−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζζ−ζζ3−ζ3ζ3−ζ3ζ−ζ
χ211111-1-1-1-1ii−i−iii−i−i-1-111-1-1−i−i−i−iiiii11ii−i−i-1-1-1-11111ii−i−i1-11111-1-1-1-1−i−iii−i−i−i−iiiiii−iiiii−i−i−i−i-1-111-1-1-1-11111ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζζ−ζζ3−ζ3−ζ3ζ3−ζζ
χ221111-1-1-1-1ii−i−iii−i−i-1-111-1-1−i−i−i−iiiii11ii−i−i-1-1-1-11111ii−i−i1-11111-1-1-1-1−i−iii−i−i−i−iiiiii−iiiii−i−i−i−i-1-111-1-1-1-11111−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζζ−ζ3ζ3ζ3−ζ3ζ−ζ
χ231111-1-1-1-1ii−i−iii−i−i-1-111-1-1−i−i−i−iiiii11ii−i−i-1-1-1-11111ii−i−i1-1-1-1-1-11111−i−iiiiiii−i−i−i−ii−i−i−i−i−iiiii-1-1111111-1-1-1-1ζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζζ−ζ3ζ3ζ3−ζ3ζ−ζ
χ241111-1-1-1-1ii−i−iii−i−i-1-111-1-1−i−i−i−iiiii11ii−i−i-1-1-1-11111ii−i−i1-1-1-1-1-11111−i−iiiiiii−i−i−i−ii−i−i−i−i−iiiii-1-1111111-1-1-1-1−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζ−ζζ3−ζ3−ζ3ζ3−ζζ
χ251111-1-1-1-1−i−iii−i−iii-1-111-1-1iiii−i−i−i−i11−i−iii-1-1-1-11111−i−iii1-11111-1-1-1-1ii−i−iiiii−i−i−i−i−ii−i−i−i−iiiii-1-111-1-1-1-11111ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ3−ζ3ζ−ζ−ζζ−ζ3ζ3
χ261111-1-1-1-1−i−iii−i−iii-1-111-1-1iiii−i−i−i−i11−i−iii-1-1-1-11111−i−iii1-11111-1-1-1-1ii−i−iiiii−i−i−i−i−ii−i−i−i−iiiii-1-111-1-1-1-11111−ζ3−ζ3ζ3ζ3−ζ−ζζζζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3ζ3−ζζζ−ζζ3−ζ3
χ271111-1-1-1-1−i−iii−i−iii-1-111-1-1iiii−i−i−i−i11−i−iii-1-1-1-11111−i−iii1-1-1-1-1-11111ii−i−i−i−i−i−iiiii−iiiiii−i−i−i−i-1-1111111-1-1-1-1ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3ζ3−ζζζ−ζζ3−ζ3
χ281111-1-1-1-1−i−iii−i−iii-1-111-1-1iiii−i−i−i−i11−i−iii-1-1-1-11111−i−iii1-1-1-1-1-11111ii−i−i−i−i−i−iiiii−iiiiii−i−i−i−i-1-1111111-1-1-1-1−ζ3−ζ3ζ3ζ3−ζ−ζζζζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3−ζ3ζ−ζ−ζζ−ζ3ζ3
χ291111-1-1-1-1−i−iii−i−iii-1-111-1-1−i−i−i−iiiii11−i−iii1111-1-1-1-1−i−iii1-11111-1-1-1-1−i−iii−i−i−i−iiiii−ii−i−i−i−iiiii11-1-11111-1-1-1-1ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3−ζ3ζ−ζζ−ζζ3−ζ3
χ301111-1-1-1-1−i−iii−i−iii-1-111-1-1−i−i−i−iiiii11−i−iii1111-1-1-1-1−i−iii1-11111-1-1-1-1−i−iii−i−i−i−iiiii−ii−i−i−i−iiiii11-1-11111-1-1-1-1−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3ζ3−ζζ−ζζ−ζ3ζ3
χ311111-1-1-1-1−i−iii−i−iii-1-111-1-1−i−i−i−iiiii11−i−iii1111-1-1-1-1−i−iii1-1-1-1-1-11111−i−iiiiiii−i−i−i−i−iiiiii−i−i−i−i11-1-1-1-1-1-11111ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3ζ3−ζζ−ζζ−ζ3ζ3
χ321111-1-1-1-1−i−iii−i−iii-1-111-1-1−i−i−i−iiiii11−i−iii1111-1-1-1-1−i−iii1-1-1-1-1-11111−i−iiiiiii−i−i−i−i−iiiiii−i−i−i−i11-1-1-1-1-1-11111−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ3−ζ3ζ−ζζ−ζζ3−ζ3
χ33222222222222222222-2-2-2-22222222222222222222222-2-2-2-2-2-200000000-2-2-2-200000000-2-200000000-2-2-2-200000000000000000000000000000000
χ34222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000222200000000-2-200000000222200000000000000000000000000000000
χ352222222222222222-2-2222200000000-2-2-2-2-2-2000000002222-2-222-2-222-2-2000000000000-2-222-2-222-2-2000000000000000000000000000000000000
χ362222222222222222-2-2222200000000-2-2-2-2-2-2000000002222-2-2-2-222-2-222000000000000-2-2-2-222-2-222000000000000000000000000000000000000
χ372222222222222222-2-2-2-2-2-200000000-2-2-2-2-2-200000000-2-2-2-2220000000000002i2i−2i−2i2i2i−2i−2i220000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ382222222222222222-2-2-2-2-2-200000000-2-2-2-2-2-200000000-2-2-2-222000000000000−2i−2i2i2i−2i−2i2i2i22000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-200000000-2-2-2-2000000002200000000222200000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2222222222222-2-2000000002222000000002200000000-2-2-2-200000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-2-2-2222200000000-2-2222200000000-2-2-2-2-2-222-2-222-2-200000000000022-2-222-2-222000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-2-2-2222200000000-2-2222200000000-2-2-2-2-2-2-2-222-2-2220000000000002222-2-222-2-2000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-22222000000002222220000000000002i2i−2i−2i2i2i−2i−2i-2-2000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2222200000000222222000000000000−2i−2i2i2i−2i−2i2i2i-2-20000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ452222-2-2-2-22i2i−2i−2i2i2i−2i−2i2222-2-200000000-2-2−2i−2i2i2i000000002i2i−2i−2i-2222-2-2-2-222000000000000−2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ462222-2-2-2-22i2i−2i−2i2i2i−2i−2i2222-2-200000000-2-2−2i−2i2i2i000000002i2i−2i−2i-22-2-22222-2-2000000000000−2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ472222-2-2-2-22i2i−2i−2i2i2i−2i−2i22-2-22200000000-2-2−2i−2i2i2i00000000−2i−2i2i2i2-200000000000022-2-2-2-2222i−2i000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ482222-2-2-2-22i2i−2i−2i2i2i−2i−2i22-2-22200000000-2-2−2i−2i2i2i00000000−2i−2i2i2i2-2000000000000-2-22222-2-22i−2i0000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ492222-2-2-2-22i2i−2i−2i2i2i−2i−2i-2-2-2-2222i2i2i2i−2i−2i−2i−2i222i2i−2i−2i2222-2-2-2-2−2i−2i2i2i-2200000000−2i−2i2i2i00000000−2i2i00000000-2-22200000000000000000000000000000000
χ502222-2-2-2-22i2i−2i−2i2i2i−2i−2i-2-2-2-222−2i−2i−2i−2i2i2i2i2i222i2i−2i−2i-2-2-2-22222−2i−2i2i2i-22000000002i2i−2i−2i00000000−2i2i0000000022-2-200000000000000000000000000000000
χ512222-2-2-2-2−2i−2i2i2i−2i−2i2i2i2222-2-200000000-2-22i2i−2i−2i00000000−2i−2i2i2i-2222-2-2-2-2220000000000002i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ522222-2-2-2-2−2i−2i2i2i−2i−2i2i2i2222-2-200000000-2-22i2i−2i−2i00000000−2i−2i2i2i-22-2-22222-2-20000000000002i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ532222-2-2-2-2−2i−2i2i2i−2i−2i2i2i22-2-22200000000-2-22i2i−2i−2i000000002i2i−2i−2i2-200000000000022-2-2-2-222−2i2i0000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ542222-2-2-2-2−2i−2i2i2i−2i−2i2i2i22-2-22200000000-2-22i2i−2i−2i000000002i2i−2i−2i2-2000000000000-2-22222-2-2−2i2i000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ552222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-2-2-2-2222i2i2i2i−2i−2i−2i−2i22−2i−2i2i2i-2-2-2-222222i2i−2i−2i-2200000000−2i−2i2i2i000000002i−2i0000000022-2-200000000000000000000000000000000
χ562222-2-2-2-2−2i−2i2i2i−2i−2i2i2i-2-2-2-222−2i−2i−2i−2i2i2i2i2i22−2i−2i2i2i2222-2-2-2-22i2i−2i−2i-22000000002i2i−2i−2i000000002i−2i00000000-2-22200000000000000000000000000000000
χ5722-2-222-2-22222-2-2-2-22-2000022-2-222-2-22-22-22-222-2-222-2-20000000000000000000000000000000000000000000000002−22−22−22−22−22−22−22−200000000
χ5822-2-222-2-22222-2-2-2-22-2000022-2-222-2-22-22-22-222-2-222-2-2000000000000000000000000000000000000000000000000−22−22−22−22−22−22−22−2200000000
χ5922-2-222-2-22222-2-2-2-22-20000-2-222-2-2222-22-22-2-2-222-2-2220000000000000000000000000000000000000000000000002−22−22−22−2−22−22−22−2200000000
χ6022-2-222-2-22222-2-2-2-22-20000-2-222-2-2222-22-22-2-2-222-2-222000000000000000000000000000000000000000000000000−22−22−22−222−22−22−22−200000000
χ6122-2-222-2-2-2-2-2-222222-2000022-2-222-2-22-2-22-22-2-222-2-222000000000000000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ6222-2-222-2-2-2-2-2-222222-2000022-2-222-2-22-2-22-22-2-222-2-222000000000000000000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ6322-2-222-2-2-2-2-2-222222-20000-2-222-2-2222-2-22-2222-2-222-2-2000000000000000000000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ6422-2-222-2-2-2-2-2-222222-20000-2-222-2-2222-2-22-2222-2-222-2-2000000000000000000000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ6522-2-2-2-2222i2i−2i−2i−2i−2i2i2i-2200002i2i−2i−2i−2i−2i2i2i2-22i−2i−2i2i22-2-2-2-2220000000000000000000000000000000000000000000000001+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ6622-2-2-2-2222i2i−2i−2i−2i−2i2i2i-2200002i2i−2i−2i−2i−2i2i2i2-22i−2i−2i2i22-2-2-2-222000000000000000000000000000000000000000000000000−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
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χ1134-4-44−4i4i4i−4i4ζ3−4ζ34ζ−4ζ−4ζ34ζ3−4ζ4ζ0000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i000000−222222−222i2−2i2−2i22i2000000000000000000000000000000000000000000000000000000000000000000000000
χ1144-4-44−4i4i4i−4i4ζ3−4ζ34ζ−4ζ−4ζ34ζ3−4ζ4ζ000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i00000022−22−2222−2i22i22i2−2i2000000000000000000000000000000000000000000000000000000000000000000000000
χ1154-4-44−4i4i4i−4i−4ζ34ζ3−4ζ4ζ4ζ3−4ζ34ζ−4ζ0000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i00000022−22−2222−2i22i22i2−2i2000000000000000000000000000000000000000000000000000000000000000000000000
χ1164-4-44−4i4i4i−4i−4ζ34ζ3−4ζ4ζ4ζ3−4ζ34ζ−4ζ000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i000000−222222−222i2−2i2−2i22i2000000000000000000000000000000000000000000000000000000000000000000000000

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