Finite Group Databasebeta

← Group #495246

Character table — Group #495246

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222444444444444444444444444444488888888888888888888888888881616161616161616
order12224444222222444444888888884444444488881616161616161616161616161616161688888888888888888888161616161616161622224444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-111-1-1
χ91111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11-11-11-11-1
χ101111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-11-11-11-11
χ111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-11-11-11-11
χ121111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-111111-11-11-11-1
χ131111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111-1-111-1-11
χ141111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-111-1-111-1
χ151111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-111-1-111-1
χ161111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-11-1-111-1-11
χ171111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−iii−i−iii−i−i1-11-1ii−i−iii−i−i111-1-1-1-11
χ181111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii−i−iii−i−iii1-11-1ii−i−iii−i−i-1-1-11111-1
χ191111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−iii−i−iii−i−i1-11-1−i−iii−i−iii-1-1-11111-1
χ201111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii−i−iii−i−iii1-11-1−i−iii−i−iii111-1-1-1-11
χ211111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i−i−iii−i−iii-11-11−i−iii−i−iii11-11-1-11-1
χ221111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iiiii−i−iii−i−i-11-11−i−iii−i−iii-1-11-111-11
χ231111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i−i−iii−i−iii-11-11ii−i−iii−i−i-1-11-111-11
χ241111-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iiiii−i−iii−i−i-11-11ii−i−iii−i−i11-11-1-11-1
χ251111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iiiii−i−i−i−iii1-1-11ii−i−i−i−iii1-111-11-1-1
χ261111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i−i−iiiii−i−i1-1-11ii−i−i−i−iii-11-1-11-111
χ271111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iiiii−i−i−i−iii1-1-11−i−iiiii−i−i-11-1-11-111
χ281111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i−i−iiiii−i−i1-1-11−i−iiiii−i−i1-111-11-1-1
χ291111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii−i−iiiii−i−i-111-1−i−iiiii−i−i1-1-1-1-1111
χ301111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−iii−i−i−i−iii-111-1−i−iiiii−i−i-11111-1-1-1
χ311111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii−i−iiiii−i−i-111-1ii−i−i−i−iii-11111-1-1-1
χ321111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−iii−i−i−i−iii-111-1ii−i−i−i−iii1-1-1-1-1111
χ3322222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-200000000000000000000000000000000-2-2-2-20000000000000000
χ3422222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000022220000000000000000
χ352222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000-2-2220000000000000000
χ362222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000022-2-20000000000000000
χ3722222222-2-222-2-2-2-222-2-2000000002-22-22-22-2000022−2−222−2−222−2−222−2−2000000000000000000002−22−22−22−200000000
χ3822222222-2-222-2-2-2-222-2-2000000002-22-22-22-20000−2−222−2−222−2−222−2−22200000000000000000000−22−22−22−2200000000
χ3922222222-2-222-2-2-2-222-2-200000000-22-22-22-22000022−2−222−2−222−2−222−2−200000000000000000000−22−22−22−2200000000
χ4022222222-2-222-2-2-2-222-2-200000000-22-22-22-220000−2−222−2−222−2−222−2−222000000000000000000002−22−22−22−200000000
χ4122222222-2-2-2-22222-2-2-2-2000000002-22-2-22-22000022−2−222−2−2−2−222−2−222000000000000000000002−22−2−22−2200000000
χ4222222222-2-2-2-22222-2-2-2-2000000002-22-2-22-220000−2−222−2−22222−2−222−2−200000000000000000000−22−222−22−200000000
χ4322222222-2-2-2-22222-2-2-2-200000000-22-222-22-2000022−2−222−2−2−2−222−2−22200000000000000000000−22−222−22−200000000
χ4422222222-2-2-2-22222-2-2-2-200000000-22-222-22-20000−2−222−2−22222−2−222−2−2000000000000000000002−22−2−22−2200000000
χ452222-2-2-2-2222222-2-2-2-2-2-2000000002-2-222-2-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ462222-2-2-2-2222222-2-2-2-2-2-2000000002-2-222-2-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ472222-2-2-2-2222222-2-2-2-2-2-200000000-222-2-222-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000000000000000−i2i2i2−i2−i2i2i2−i200000000
χ482222-2-2-2-2222222-2-2-2-2-2-200000000-222-2-222-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000000000000000i2−i2−i2i2i2−i2−i2i200000000
χ492222-2-2-2-222-2-2-2-22222-2-2000000002-2-22-222-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000i2−i2−i2i2−i2i2i2−i200000000
χ502222-2-2-2-222-2-2-2-22222-2-2000000002-2-22-222-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ512222-2-2-2-222-2-2-2-22222-2-200000000-222-22-2-220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000−i2i2i2−i2i2−i2−i2i200000000
χ522222-2-2-2-222-2-2-2-22222-2-200000000-222-22-2-220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000i2−i2−i2i2−i2i2i2−i200000000
χ532222-2-2-2-2-2-222-2-222-2-222-2-2-2-2222222-2-222-2-2-2-22200000000000000000000000000000000-22-220000000000000000
χ542222-2-2-2-2-2-222-2-222-2-222-2-2-2-22222-2-222-2-222-2-222000000000000000000000000000000002-22-20000000000000000
χ552222-2-2-2-2-2-2-2-222-2-22222-2-2-2-2222222-2-2-2-22222-2-200000000000000000000000000000000-222-20000000000000000
χ562222-2-2-2-2-2-2-2-222-2-22222-2-2-2-22222-2-22222-2-222-2-2000000000000000000000000000000002-2-220000000000000000
χ572-2-2222-2-22-22-22-22-22-22-222-2-222-2-2000000002-22-20000000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ582-2-2222-2-22-22-22-22-22-22-222-2-222-2-2000000002-22-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ592-2-2222-2-22-22-22-22-22-22-2-2-222-2-22200000000-22-2200000000000000002-22-22-22-20000000000000000000000000000
χ602-2-2222-2-22-22-22-22-22-22-2-2-222-2-22200000000-22-220000000000000000-22-22-22-220000000000000000000000000000
χ612-2-2222-2-22-2-22-22-22-222-222-2-222-2-200000000-22-220000000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ622-2-2222-2-22-2-22-22-22-222-222-2-222-2-200000000-22-22000000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ632-2-2222-2-22-2-22-22-22-222-2-2-222-2-222000000002-22-200000000000000002-22-2-22-220000000000000000000000000000
χ642-2-2222-2-22-2-22-22-22-222-2-2-222-2-222000000002-22-20000000000000000-22-222-22-20000000000000000000000000000
χ652-2-22-2-222-222-2-222-2-222-222-2-2-2-222000000002-2-220000000000000000000000002-2-222-2-2200000000000000000000
χ662-2-22-2-222-222-2-222-2-222-222-2-2-2-222000000002-2-22000000000000000000000000-222-2-222-200000000000000000000
χ672-2-22-2-222-222-2-222-2-222-2-2-22222-2-200000000-222-200000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ682-2-22-2-222-222-2-222-2-222-2-2-22222-2-200000000-222-20000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ692-2-22-2-222-22-222-2-222-22-222-2-2-2-22200000000-222-20000000000000000000000002-2-22-222-200000000000000000000
χ702-2-22-2-222-22-222-2-222-22-222-2-2-2-22200000000-222-2000000000000000000000000-222-22-2-2200000000000000000000
χ712-2-22-2-222-22-222-2-222-22-2-2-22222-2-2000000002-2-2200000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ722-2-22-2-222-22-222-2-222-22-2-2-22222-2-2000000002-2-220000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ7344-4-44i−4i4i−4i00000000000022−2222−222i2−2i22i2−2i2000000000000000000002ζ+2ζ3−2ζ−2ζ32ζ5−2ζ7−2ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ−2ζ3−2ζ+2ζ3000000000000000000000000000000000000
χ7444-4-44i−4i4i−4i00000000000022−2222−222i2−2i22i2−2i200000000000000000000−2ζ−2ζ32ζ+2ζ3−2ζ5+2ζ72ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ+2ζ32ζ−2ζ3000000000000000000000000000000000000
χ7544-4-44i−4i4i−4i000000000000−2222−2222−2i22i2−2i22i2000000000000000000002ζ5−2ζ7−2ζ5+2ζ7−2ζ−2ζ32ζ+2ζ3−2ζ+2ζ32ζ−2ζ32ζ5+2ζ7−2ζ5−2ζ7000000000000000000000000000000000000
χ7644-4-44i−4i4i−4i000000000000−2222−2222−2i22i2−2i22i200000000000000000000−2ζ5+2ζ72ζ5−2ζ72ζ+2ζ3−2ζ−2ζ32ζ−2ζ3−2ζ+2ζ3−2ζ5−2ζ72ζ5+2ζ7000000000000000000000000000000000000
χ7744-4-4−4i4i−4i4i00000000000022−2222−22−2i22i2−2i22i2000000000000000000002ζ5+2ζ7−2ζ5−2ζ7−2ζ+2ζ32ζ−2ζ32ζ+2ζ3−2ζ−2ζ3−2ζ5+2ζ72ζ5−2ζ7000000000000000000000000000000000000
χ7844-4-4−4i4i−4i4i00000000000022−2222−22−2i22i2−2i22i200000000000000000000−2ζ5−2ζ72ζ5+2ζ72ζ−2ζ3−2ζ+2ζ3−2ζ−2ζ32ζ+2ζ32ζ5−2ζ7−2ζ5+2ζ7000000000000000000000000000000000000
χ7944-4-4−4i4i−4i4i000000000000−2222−22222i2−2i22i2−2i2000000000000000000002ζ−2ζ3−2ζ+2ζ32ζ5+2ζ7−2ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ−2ζ32ζ+2ζ3000000000000000000000000000000000000
χ8044-4-4−4i4i−4i4i000000000000−2222−22222i2−2i22i2−2i200000000000000000000−2ζ+2ζ32ζ−2ζ3−2ζ5−2ζ72ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ+2ζ3−2ζ−2ζ3000000000000000000000000000000000000
χ814-44-44i−4i−4i4i00000000000022−22−22222i2−2i2−2i22i20000000000002ζ5−2ζ7−2ζ5+2ζ72ζ+2ζ3−2ζ−2ζ32ζ−2ζ3−2ζ+2ζ32ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000000000000000000000
χ824-44-44i−4i−4i4i00000000000022−22−22222i2−2i2−2i22i2000000000000−2ζ5+2ζ72ζ5−2ζ7−2ζ−2ζ32ζ+2ζ3−2ζ+2ζ32ζ−2ζ3−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000000000000000000000
χ834-44-44i−4i−4i4i000000000000−222222−22−2i22i22i2−2i20000000000002ζ+2ζ3−2ζ−2ζ3−2ζ5+2ζ72ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ72ζ−2ζ3−2ζ+2ζ300000000000000000000000000000000000000000000
χ844-44-44i−4i−4i4i000000000000−222222−22−2i22i22i2−2i2000000000000−2ζ−2ζ32ζ+2ζ32ζ5−2ζ7−2ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ7−2ζ+2ζ32ζ−2ζ300000000000000000000000000000000000000000000
χ854-44-4−4i4i4i−4i00000000000022−22−2222−2i22i22i2−2i20000000000002ζ−2ζ3−2ζ+2ζ3−2ζ5−2ζ72ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ7−2ζ−2ζ32ζ+2ζ300000000000000000000000000000000000000000000
χ864-44-4−4i4i4i−4i00000000000022−22−2222−2i22i22i2−2i2000000000000−2ζ+2ζ32ζ−2ζ32ζ5+2ζ7−2ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ72ζ+2ζ3−2ζ−2ζ300000000000000000000000000000000000000000000
χ874-44-4−4i4i4i−4i000000000000−222222−222i2−2i2−2i22i20000000000002ζ5+2ζ7−2ζ5−2ζ72ζ−2ζ3−2ζ+2ζ3−2ζ−2ζ32ζ+2ζ3−2ζ5+2ζ72ζ5−2ζ700000000000000000000000000000000000000000000
χ884-44-4−4i4i4i−4i000000000000−222222−222i2−2i2−2i22i2000000000000−2ζ5−2ζ72ζ5+2ζ7−2ζ+2ζ32ζ−2ζ32ζ+2ζ3−2ζ−2ζ32ζ5−2ζ7−2ζ5+2ζ700000000000000000000000000000000000000000000
χ894-4-4444-4-4-444-4-44-444-4-44000000000000000000000000000000000000000000000000000000000000000000000000
χ904-4-4444-4-4-44-444-44-4-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ914-4-44-4-4444-44-44-4-44-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4-4444-4-44-444-44-4-44000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.