Finite Group Databasebeta

← Group #147102

Character table — Group #147102

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111112222222222222222222222222222222222224444444444444444444444444444444444444444444416161616161616161616161616161616
order122244442222224444448888888816161616161616161616161616161616444444448888888888881616161616161616161616161616161616161616161616164444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111-1-1-1-111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-111-1-1-1-111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-111-1-1-1-111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ1711-1-111-1-11-11-1-111-11-11-111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−i1-11-1ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−ii−ii−i
χ1811-1-111-1-11-11-1-111-11-11-111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−i1-11-1ii−i−iii−i−i11-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii
χ1911-1-111-1-11-11-1-111-11-11-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii1-11-1−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii−ii−ii
χ2011-1-111-1-11-11-1-111-11-11-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii1-11-1−i−iii−i−iii11-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i
χ2111-1-111-1-11-11-1-111-11-11-111-1-111-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i1-11-1ii−i−iii−i−i-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii1-11-1-11-11i−ii−i−ii−ii
χ2211-1-111-1-11-11-1-111-11-11-111-1-111-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i1-11-1ii−i−iii−i−i-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii-11-111-11-1−ii−iii−ii−i
χ2311-1-111-1-11-11-1-111-11-11-111-1-111-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iii1-11-1−i−iii−i−iii-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i1-11-1-11-11−ii−iii−ii−i
χ2411-1-111-1-11-11-1-111-11-11-111-1-111-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iii1-11-1−i−iii−i−iii-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i-11-111-11-1i−ii−i−ii−ii
χ2511-1-1-1-1111-1-111-11-1-111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iii1-1-11ii−i−i−i−iii11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiii−i−iii−i−ii-111-1-111-1
χ2611-1-1-1-1111-1-111-11-1-111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iii1-1-11ii−i−i−i−iii11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−iii−i−iii−i1-1-111-1-11
χ2711-1-1-1-1111-1-111-11-1-111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−i1-1-11−i−iiiii−i−i11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−ii−i−iii−i−ii1-1-111-1-11
χ2811-1-1-1-1111-1-111-11-1-111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−i1-1-11−i−iiiii−i−i11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−iii−i−iii−i-111-1-111-1
χ2911-1-1-1-1111-1-111-11-1-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii1-1-11ii−i−i−i−iii-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−ii−i−ii−iii−i-111-11-1-11
χ3011-1-1-1-1111-1-111-11-1-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii1-1-11ii−i−i−i−iii-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i−iii−ii−i−ii1-1-11-111-1
χ3111-1-1-1-1111-1-111-11-1-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i1-1-11−i−iiiii−i−i-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiiii−i−ii−iii−i1-1-11-111-1
χ3211-1-1-1-1111-1-111-11-1-111-1-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−i1-1-11−i−iiiii−i−i-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−iii−ii−i−ii-111-11-1-11
χ3322222222222222222222-2-2-2-2-2-2-2-2000000000000000022222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ352222222222-2-2-2-2-2-222-2-20000000022−2−222−2−222−2−222−2−20000000000002i−2i2i−2i2i−2i2i−2i2−22−22−22−2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ362222222222-2-2-2-2-2-222-2-20000000022−2−222−2−222−2−222−2−2000000000000−2i2i−2i2i−2i2i−2i2i2−22−22−22−2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ372222222222-2-2-2-2-2-222-2-200000000−2−222−2−222−2−222−2−2220000000000002i−2i2i−2i2i−2i2i−2i−22−22−22−22−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ382222222222-2-2-2-2-2-222-2-200000000−2−222−2−222−2−222−2−222000000000000−2i2i−2i2i−2i2i−2i2i−22−22−22−22i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3922222222-2-222-2-2-2-2-2-22222222222222222222222222200000000-2-2-2-200000000-2-2-2-2-2-2-2-200000000000000000000000000000000
χ4022222222-2-222-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-2000000002222222200000000000000000000000000000000
χ4122222222-2-222-2-2-2-2-2-222-2-2-2-2-2-2-2-2000000000000000000000000222200000000000000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000
χ4222222222-2-222-2-2-2-2-2-222-2-2-2-2-2-2-2-200000000000000000000000022220000000000000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000
χ4322222222-2-2-2-22222-2-2-2-20000000022−2−222−2−222−2−222−2−22-22-22-22-2000000000000−22−22−22−222−2−222−2−222−2−222−2−220000000000000000
χ4422222222-2-2-2-22222-2-2-2-20000000022−2−222−2−222−2−222−2−2-22-22-22-22000000000000−22−22−22−22−222−2−222−2−222−2−222−20000000000000000
χ4522222222-2-2-2-22222-2-2-2-200000000−2−222−2−222−2−222−2−2222-22-22-22-20000000000002−22−22−22−2−222−2−222−2−222−2−222−20000000000000000
χ4622222222-2-2-2-22222-2-2-2-200000000−2−222−2−222−2−222−2−222-22-22-22-220000000000002−22−22−22−22−2−222−2−222−2−222−2−220000000000000000
χ472222-2-2-2-2222222-2-2-2-2-2-20000000022−2−222−2−2−2−222−2−2220000000000002i−2i2i−2i−2i2i−2i2i2−22−2−22−22i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ482222-2-2-2-2222222-2-2-2-2-2-20000000022−2−222−2−2−2−222−2−222000000000000−2i2i−2i2i2i−2i2i−2i2−22−2−22−22−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ492222-2-2-2-2222222-2-2-2-2-2-200000000−2−222−2−22222−2−222−2−20000000000002i−2i2i−2i−2i2i−2i2i−22−222−22−2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ502222-2-2-2-2222222-2-2-2-2-2-200000000−2−222−2−22222−2−222−2−2000000000000−2i2i−2i2i2i−2i2i−2i−22−222−22−2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000
χ512222-2-2-2-222-2-2-2-222-2-2222222-2-2-2-200000000000000002222-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000000000000000
χ522222-2-2-2-222-2-2-2-222-2-2222222-2-2-2-20000000000000000-2-2-2-22222-2-2222222-2-2-2-20000000000000000000000000000000000000000
χ532222-2-2-2-2-2-222-2-22222-2-20000000022−2−222−2−2−2−222−2−2222-22-2-22-22000000000000−22−222−22−22−2−222−2−22−222−2−222−20000000000000000
χ542222-2-2-2-2-2-222-2-22222-2-20000000022−2−222−2−2−2−222−2−222-22-222-22-2000000000000−22−222−22−2−222−2−222−22−2−222−2−220000000000000000
χ552222-2-2-2-2-2-222-2-22222-2-200000000−2−222−2−22222−2−222−2−22-22-2-22-220000000000002−22−2−22−22−222−2−222−22−2−222−2−220000000000000000
χ562222-2-2-2-2-2-222-2-22222-2-200000000−2−222−2−22222−2−222−2−2-22-222-22-20000000000002−22−2−22−222−2−222−2−22−222−2−222−20000000000000000
χ572222-2-2-2-2-2-2-2-222-2-222222222-2-2-2-200000000000000000000000022-2-200000000000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i0000000000000000
χ582222-2-2-2-2-2-2-2-222-2-222222222-2-2-2-200000000000000000000000022-2-20000000000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i0000000000000000
χ592222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2222222222222-2-2-2-2-2-2-2-200000000-2-22200000000-2-2-2-2222200000000000000000000000000000000
χ602222-2-2-2-2-2-2-2-222-2-22222-2-2-2-22222-2-2-2-2-2-2-2-22222222200000000-2-222000000002222-2-2-2-200000000000000000000000000000000
χ6122-2-222-2-22-22-2-222-22-22-2-2-222-2-22200000000000000002i2i−2i−2i2i2i−2i−2i-22-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ6222-2-222-2-22-22-2-222-22-22-2-2-222-2-2220000000000000000−2i−2i2i2i−2i−2i2i2i-22-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ6322-2-222-2-22-2-222-2-222-2-220000000022−2−2−2−22222−2−2−2−2220000000000002-2-222-2-222−2−222−2−2222−2−2−2−22222−2−2−2−2220000000000000000
χ6422-2-222-2-22-2-222-2-222-2-220000000022−2−2−2−22222−2−2−2−222000000000000-222-2-222-22−2−222−2−22−2−22222−2−2−2−22222−2−20000000000000000
χ6522-2-222-2-22-2-222-2-222-2-2200000000−2−22222−2−2−2−22222−2−20000000000002-2-222-2-22−222−2−222−2−2−22222−2−2−2−22222−2−20000000000000000
χ6622-2-222-2-22-2-222-2-222-2-2200000000−2−22222−2−2−2−22222−2−2000000000000-222-2-222-2−222−2−222−222−2−2−2−22222−2−2−2−2220000000000000000
χ6722-2-222-2-2-222-22-2-22-222-222-2-222-2-22222-2-2-2-22222-2-2-2-200000000-22-2200000000-2-222-2-22200000000000000000000000000000000
χ6822-2-222-2-2-222-22-2-22-222-222-2-222-2-2-2-2-2-22222-2-2-2-2222200000000-22-220000000022-2-222-2-200000000000000000000000000000000
χ6922-2-222-2-2-222-22-2-22-222-2-2-222-2-2220000000000000000000000002-22-200000000000000002-22-2-22-222-22-2-22-220000000000000000
χ7022-2-222-2-2-222-22-2-22-222-2-2-222-2-2220000000000000000000000002-22-20000000000000000-22-222-22-2-22-222-22-20000000000000000
χ7122-2-222-2-2-22-22-222-2-22-220000000022−2−2−2−22222−2−2−2−2222i−2i−2i2i2i−2i−2i2i000000000000−222−2−222−2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ7222-2-222-2-2-22-22-222-2-22-220000000022−2−2−2−22222−2−2−2−222−2i2i2i−2i−2i2i2i−2i000000000000−222−2−222−2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ7322-2-222-2-2-22-22-222-2-22-2200000000−2−22222−2−2−2−22222−2−22i−2i−2i2i2i−2i−2i2i0000000000002−2−222−2−22−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i20000000000000000
χ7422-2-222-2-2-22-22-222-2-22-2200000000−2−22222−2−2−2−22222−2−2−2i2i2i−2i−2i2i2i−2i0000000000002−2−222−2−22i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i20000000000000000
χ7522-2-2-2-2222-22-2-22-22-22-220000000022−2−2−2−222−2−22222−2−20000000000002-2-22-222-22−2−22−222−222−2−2−2−222−2−22222−2−20000000000000000
χ7622-2-2-2-2222-22-2-22-22-22-220000000022−2−2−2−222−2−22222−2−2000000000000-222-22-2-222−2−22−222−2−2−22222−2−222−2−2−2−2220000000000000000
χ7722-2-2-2-2222-22-2-22-22-22-2200000000−2−22222−2−222−2−2−2−2220000000000002-2-22-222-2−222−22−2−22−2−22222−2−222−2−2−2−2220000000000000000
χ7822-2-2-2-2222-22-2-22-22-22-2200000000−2−22222−2−222−2−2−2−222000000000000-222-22-2-22−222−22−2−2222−2−2−2−222−2−22222−2−20000000000000000
χ7922-2-2-2-2222-2-222-22-2-222-222-2-2-2-22200000000000000002i2i−2i−2i−2i−2i2i2i-222-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ8022-2-2-2-2222-2-222-22-2-222-222-2-2-2-2220000000000000000−2i−2i2i2i2i2i−2i−2i-222-22i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.