Finite Group Databasebeta

← Group #126839

Character table — Group #126839

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122222222222222222222222222224444444444444444888888888888888888888888888888881616161616161616
order122244442222444444444444444488888888244488888888888888888888888888881616161616161616161616161616161644444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111-1-11111-1-1-1-1-1-1-1-111-1-111111111-111-11111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ61111111111-1-11111-1-1-1-1-1-1-1-111-1-111111111-111-11111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-111111111−i−i−i−iiiii
χ71111111111-1-11111-1-1-1-1-1-1-1-111-1-111111111-111-11111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ81111111111-1-11111-1-1-1-1-1-1-1-111-1-111111111-111-11111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-111111111iiii−i−i−i−i
χ911111111-1-11111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-11111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1111111111-1-11111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ1211111111-1-11111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-111-1-1-1-1-1-1111111-1-1111111111-1-11-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ1411111111-1-1-1-111-1-1-1-1-1-1111111-1-1111111111-1-11-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−iiiii−i−i
χ1511111111-1-1-1-111-1-1-1-1-1-1111111-1-1111111111-1-11-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ1611111111-1-1-1-111-1-1-1-1-1-1111111-1-1111111111-1-11-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1ii−i−i−i−iii
χ171111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i1-11-11-11-1
χ181111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii-11-11-11-11
χ191111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i-11-11-11-11
χ201111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii1-11-11-11-1
χ211111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-11-1111-1-1-1-111-1-11111-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii−ii−iii−ii−i
χ221111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-11-1111-1-1-1-111-1-11111-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−ii−ii−i−ii−ii
χ231111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-11-1111-1-1-1-111-1-111-1-111-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iiii−ii−i−ii−ii
χ241111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-11-1111-1-1-1-111-1-111-1-111-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i−ii−iii−ii−i
χ251111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii1-1-111-1-11
χ261111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i-111-1-111-1
χ271111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii-111-1-111-1
χ281111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i1-1-111-1-11
χ291111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111111111-1-1-1-11-11-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i−iii−ii−i−ii
χ301111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111111111-1-1-1-11-11-1-1-111-1-11111-1-111-1-1-1-111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iiii−i−ii−iii−i
χ311111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111111111-1-1-1-11-11-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−ii−i−ii−iii−i
χ321111-1-1-1-1-1-1-1-1-1-111-1-11111-1-111111111-1-1-1-11-11-1-1-111-1-11111-1-1-1-11111-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii−iii−ii−i−ii
χ332222222222222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ34222222222222-2-222-2-222-2-2-2-2-2-2-2-2000000002-2-220000000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ35222222222222-2-222-2-222-2-2-2-2-2-2-2-2000000002-2-220000000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ362222222222-2-22222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2222222220000000000000000000000000000000000000000
χ372222222222-2-2-2-22222-2-22222-2-22200000000-2-2-2-20000000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ382222222222-2-2-2-22222-2-22222-2-22200000000-2-2-2-20000000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ3922222222-2-22222-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ4022222222-2-222-2-2-2-2-2-2222222-2-2-2-200000000-222-20000000000000000000000000000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000
χ4122222222-2-222-2-2-2-2-2-2222222-2-2-2-200000000-222-20000000000000000000000000000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000
χ4222222222-2-2-2-222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-22-2-2222222222-2-2-2-20000000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2220000000022220000000000000000000000000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000
χ4422222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2220000000022220000000000000000000000000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000
χ452222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-222000000002-22-200000000000000000000000000002−2−222−2−222−2−222−2−2200000000
χ462222-2-2-2-2222222-2-2-2-2-2-2-2-222-2-222000000002-22-20000000000000000000000000000−222−2−222−2−222−2−222−200000000
χ472222-2-2-2-22222-2-2-2-222-2-222-2-222-2-2-2-2-2-2222222-2-2-2-222-2-222-2-2220000000000000000000000000000000000000000
χ482222-2-2-2-222-2-222-2-2222222-2-2-2-2-2-200000000-2-22200000000000000000000000000002−2−222−2−22−222−2−222−200000000
χ492222-2-2-2-222-2-222-2-2222222-2-2-2-2-2-200000000-2-2220000000000000000000000000000−222−2−222−22−2−222−2−2200000000
χ502222-2-2-2-222-2-2-2-2-2-2-2-222-2-2222222-2-2-2-22222-22-22-2-22222-2-222-2-20000000000000000000000000000000000000000
χ512222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-22200000000-22-2200000000000000000000000000002−2−22−222−22−2−22−222−200000000
χ522222-2-2-2-2-2-2222222-2-2-2-222-2-2-2-22200000000-22-220000000000000000000000000000−222−22−2−22−222−22−2−2200000000
χ532222-2-2-2-2-2-222-2-22222-2-2-2-22222-2-2-2-2-2-22222-2-22222-2-2-2-22222-2-20000000000000000000000000000000000000000
χ542222-2-2-2-2-2-2-2-222222222-2-222-2-2-2-20000000022-2-200000000000000000000000000002−2−22−222−2−222−22−2−2200000000
χ552222-2-2-2-2-2-2-2-222222222-2-222-2-2-2-20000000022-2-20000000000000000000000000000−222−22−2−222−2−22−222−200000000
χ562222-2-2-2-2-2-2-2-2-2-222-2-22222-2-22222-2-2-2-222222-22-222-2-222-2-2-2-2220000000000000000000000000000000000000000
χ5722-2-22i2i−2i−2i002-22i−2i002-22i−2i00002-22i−2i22-2-22i2i−2i−2i000000002-22i−2i000000002ζ−2ζ2ζ3−2ζ300002ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ5822-2-22i2i−2i−2i002-22i−2i002-22i−2i00002-22i−2i22-2-22i2i−2i−2i000000002-22i−2i00000000−2ζ2ζ−2ζ32ζ30000−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ5922-2-22i2i−2i−2i002-22i−2i002-22i−2i00002-22i−2i-2-222−2i−2i2i2i00000000-22−2i2i00002ζ−2ζ2ζ3−2ζ300002ζ−2ζ2ζ3−2ζ30000000000000000000000000000
χ6022-2-22i2i−2i−2i002-22i−2i002-22i−2i00002-22i−2i-2-222−2i−2i2i2i00000000-22−2i2i0000−2ζ2ζ−2ζ32ζ30000−2ζ2ζ−2ζ32ζ30000000000000000000000000000
χ6122-2-22i2i−2i−2i00-222i−2i00-22−2i2i00002-2−2i2i22-2-22i2i−2i−2i00000000-22−2i2i000000002ζ3−2ζ3−2ζ2ζ0000−2ζ32ζ32ζ−2ζ000000000000000000000000
χ6222-2-22i2i−2i−2i00-222i−2i00-22−2i2i00002-2−2i2i22-2-22i2i−2i−2i00000000-22−2i2i00000000−2ζ32ζ32ζ−2ζ00002ζ3−2ζ3−2ζ2ζ000000000000000000000000
χ6322-2-22i2i−2i−2i00-222i−2i00-22−2i2i00002-2−2i2i-2-222−2i−2i2i2i000000002-22i−2i00002ζ3−2ζ3−2ζ2ζ0000−2ζ32ζ32ζ−2ζ0000000000000000000000000000
χ6422-2-22i2i−2i−2i00-222i−2i00-22−2i2i00002-2−2i2i-2-222−2i−2i2i2i000000002-22i−2i0000−2ζ32ζ32ζ−2ζ00002ζ3−2ζ3−2ζ2ζ0000000000000000000000000000
χ6522-2-2−2i−2i2i2i002-2−2i2i002-2−2i2i00002-2−2i2i22-2-2−2i−2i2i2i000000002-2−2i2i000000002ζ3−2ζ32ζ−2ζ00002ζ3−2ζ32ζ−2ζ000000000000000000000000
χ6622-2-2−2i−2i2i2i002-2−2i2i002-2−2i2i00002-2−2i2i22-2-2−2i−2i2i2i000000002-2−2i2i00000000−2ζ32ζ3−2ζ2ζ0000−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ6722-2-2−2i−2i2i2i002-2−2i2i002-2−2i2i00002-2−2i2i-2-2222i2i−2i−2i00000000-222i−2i00002ζ3−2ζ32ζ−2ζ00002ζ3−2ζ32ζ−2ζ0000000000000000000000000000
χ6822-2-2−2i−2i2i2i002-2−2i2i002-2−2i2i00002-2−2i2i-2-2222i2i−2i−2i00000000-222i−2i0000−2ζ32ζ3−2ζ2ζ0000−2ζ32ζ3−2ζ2ζ0000000000000000000000000000
χ6922-2-2−2i−2i2i2i00-22−2i2i00-222i−2i00002-22i−2i22-2-2−2i−2i2i2i00000000-222i−2i000000002ζ−2ζ−2ζ32ζ30000−2ζ2ζ2ζ3−2ζ3000000000000000000000000
χ7022-2-2−2i−2i2i2i00-22−2i2i00-222i−2i00002-22i−2i22-2-2−2i−2i2i2i00000000-222i−2i00000000−2ζ2ζ2ζ3−2ζ300002ζ−2ζ−2ζ32ζ3000000000000000000000000
χ7122-2-2−2i−2i2i2i00-22−2i2i00-222i−2i00002-22i−2i-2-2222i2i−2i−2i000000002-2−2i2i00002ζ−2ζ−2ζ32ζ30000−2ζ2ζ2ζ3−2ζ30000000000000000000000000000
χ7222-2-2−2i−2i2i2i00-22−2i2i00-222i−2i00002-22i−2i-2-2222i2i−2i−2i000000002-2−2i2i0000−2ζ2ζ2ζ3−2ζ300002ζ−2ζ−2ζ32ζ30000000000000000000000000000
χ7344-4-44i4i−4i−4i004-4−4i4i00-444i−4i0000-44−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ7444-4-44i4i−4i−4i00-44−4i4i004-4−4i4i0000-444i−4i0000000000000000000000000000000000000000000000000000000000000000
χ7544-4-4−4i−4i4i4i004-44i−4i00-44−4i4i0000-444i−4i0000000000000000000000000000000000000000000000000000000000000000
χ7644-4-4−4i−4i4i4i00-444i−4i004-44i−4i0000-44−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ774-44-44-44-44-400004-40000000000002i2−2i22i2−2i22i2−2i22i2−2i200002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ784-44-44-44-44-400004-4000000000000−2i22i2−2i22i2−2i22i2−2i22i20000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ794-44-44-44-4-440000-440000000000002i2−2i22i2−2i22i2−2i22i2−2i20000−2i22i2−2i22i2000000000000000000000000000000000000000000000000
χ804-44-44-44-4-440000-44000000000000−2i22i2−2i22i2−2i22i2−2i22i200002i2−2i22i2−2i2000000000000000000000000000000000000000000000000
χ814-44-4-44-444-40000-440000000000002i2−2i22i2−2i2−2i22i2−2i22i200002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ824-44-4-44-444-40000-44000000000000−2i22i2−2i22i22i2−2i22i2−2i20000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ834-44-4-44-44-4400004-40000000000002i2−2i22i2−2i2−2i22i2−2i22i20000−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ844-44-4-44-44-4400004-4000000000000−2i22i2−2i22i22i2−2i22i2−2i200002i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ854-4-444i−4i−4i4i0000000000004i−4i4-400002i2−2i2−2i22i2−222222−2200000000000022−222i2−2i20000000000000000000000000000000000000000
χ864-4-444i−4i−4i4i0000000000004i−4i4-40000−2i22i22i2−2i222−22−2222000000000000−2222−2i22i20000000000000000000000000000000000000000
χ874-4-444i−4i−4i4i000000000000−4i4i-4400002i2−2i2−2i22i2−222222−22000000000000−2222−2i22i20000000000000000000000000000000000000000
χ884-4-444i−4i−4i4i000000000000−4i4i-440000−2i22i22i2−2i222−22−222200000000000022−222i2−2i20000000000000000000000000000000000000000
χ894-4-44−4i4i4i−4i0000000000004i−4i-4400002i2−2i2−2i22i222−22−222200000000000022−22−2i22i20000000000000000000000000000000000000000
χ904-4-44−4i4i4i−4i0000000000004i−4i-440000−2i22i22i2−2i2−222222−22000000000000−22222i2−2i20000000000000000000000000000000000000000
χ914-4-44−4i4i4i−4i000000000000−4i4i4-400002i2−2i2−2i22i222−22−2222000000000000−22222i2−2i20000000000000000000000000000000000000000
χ924-4-44−4i4i4i−4i000000000000−4i4i4-40000−2i22i22i2−2i2−222222−2200000000000022−22−2i22i20000000000000000000000000000000000000000

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