Finite Group Databasebeta

← Group #206058

Character table — Group #206058

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122222222222222222244444444444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222444444444444442444444444444444444444888888888888888888888888888888882224444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-11111
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111-1-1-1-1
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111
χ9111111111-1-1-1-1-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-11-1111-1-111-1-1
χ10111111111-1-1-1-1-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-111-11-1-1-111-1-111
χ11111111111-1-1-1-1-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-1-1111-1-111-1-1-1-111
χ12111111111-1-1-1-1-1-1-1-11111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-111-1-1-111-1-11111-1-1
χ13111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111-1-1-1-11111-1-1
χ14111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-11111-1-1-1-111
χ15111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11-11-1-11-11-1-111-1-111
χ16111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-111-11-111-1-111-1-1
χ17111111-1-111111-1-1-1-1-1-11-1-1-11-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-11111-1-1-1-1i−ii−ii−ii−i
χ18111111-1-111111-1-1-1-1-1-11-1-1-11-1-111iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1-1-1-1-11111−ii−ii−ii−ii
χ19111111-1-111111-1-1-1-1-1-11-1-1-11-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-1111111-1-11-1-11i−ii−i−ii−ii
χ20111111-1-111111-1-1-1-1-1-11-1-1-11-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-1-111-111-1−ii−iii−ii−i
χ21111111-1-111111-1-1-1-1-1-11-1-1-11-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-1111111-1-11-1-11−ii−iii−ii−i
χ22111111-1-111111-1-1-1-1-1-11-1-1-11-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111-1-1-1-11111-1-111-111-1i−ii−i−ii−ii
χ23111111-1-111111-1-1-1-1-1-11-1-1-11-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-11111-1-1-1-1−ii−ii−ii−ii
χ24111111-1-111111-1-1-1-1-1-11-1-1-11-1-111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1-1-1-1-11111i−ii−ii−ii−i
χ25111111-1-11-1-1-1-11111-1-11-1-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-111111-11-11-11-1i−i−iii−i−ii
χ26111111-1-11-1-1-1-11111-1-11-1-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-11-11-11-11−iii−i−iii−i
χ27111111-1-11-1-1-1-11111-1-11-1-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-11-1-11-1-111i−i−ii−iii−i
χ28111111-1-11-1-1-1-11111-1-11-1-1-1111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1-111-111-1-1−iii−ii−i−ii
χ29111111-1-11-1-1-1-11111-1-11-1-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-11-1-11-1-111−iii−ii−i−ii
χ30111111-1-11-1-1-1-11111-1-11-1-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1-111-111-1-1i−i−ii−iii−i
χ31111111-1-11-1-1-1-11111-1-11-1-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-111111-11-11-11-1−iii−i−iii−i
χ32111111-1-11-1-1-1-11111-1-11-1-1-1111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-11-11-11-11i−i−iii−i−ii
χ3322222222-22222-2-2-2-2-2-2-2-2-22-222-2-200000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ3422222222-22222-2-2-2-2-2-2-2-2-22-222-2-20000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ3522222222-2-2-2-2-22222-2-2-2-2-22-2-2-22200000000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ3622222222-2-2-2-2-22222-2-2-2-2-22-2-2-2220000000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ37222222-2-2-22222222222-222-2-2-2-2-2-2000000000000000022-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ38222222-2-2-22222222222-222-2-2-2-2-2-20000000000000000-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ39222222-2-2-2-2-2-2-2-2-2-2-222-222-2-22222000000000000000022-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ40222222-2-2-2-2-2-2-2-2-2-2-222-222-2-222220000000000000000-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ412222-2-222222-2-222-2-2222-2-2-2-22-22-20000000000000000000000000000000022-2-222-2-222-2-222-2-20000000000000000
χ422222-2-222222-2-222-2-2222-2-2-2-22-22-200000000000000000000000000000000-2-222-2-222-2-222-2-2220000000000000000
χ432222-2-2222-2-222-2-222222-2-2-2-2-22-220000000000000000000000000000000022-2-222-2-2-2-222-2-2220000000000000000
χ442222-2-2222-2-222-2-222222-2-2-2-2-22-2200000000000000000000000000000000-2-222-2-22222-2-222-2-20000000000000000
χ452222-2-222-222-2-2-2-222-2-2-222-222-2-2222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ462222-2-222-222-2-2-2-222-2-2-222-222-2-22-2-222-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ472222-2-222-2-2-22222-2-2-2-2-222-22-222-222-2-222-2-2-2-222-2-222000000000000000000000000000000000000000000000000
χ482222-2-222-2-2-22222-2-2-2-2-222-22-222-2-2-222-2-22222-2-222-2-2000000000000000000000000000000000000000000000000
χ492222-2-2-2-2222-2-2-2-222-2-22222-2-222-20000000000000000000000000000000022-2-2-2-22222-2-2-2-2220000000000000000
χ502222-2-2-2-2222-2-2-2-222-2-22222-2-222-200000000000000000000000000000000-2-22222-2-2-2-22222-2-20000000000000000
χ512222-2-2-2-22-2-22222-2-2-2-22222-22-2-220000000000000000000000000000000022-2-2-2-222-2-22222-2-20000000000000000
χ522222-2-2-2-22-2-22222-2-2-2-22222-22-2-2200000000000000000000000000000000-2-22222-2-222-2-2-2-2220000000000000000
χ532222-2-2-2-2-222-2-222-2-222-2-2-222-22-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ542222-2-2-2-2-222-2-222-2-222-2-2-222-22-22−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ552222-2-2-2-2-2-2-222-2-22222-2-2-2222-22-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ562222-2-2-2-2-2-2-222-2-22222-2-2-2222-22-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ5722-2-22-20002-22-22i−2i2i−2i2i−2i02i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ−2ζ2ζ3−2ζ300002ζ−2ζ2ζ3−2ζ3002−22−2i2−i2i2−i22−22−2i2−i2i2−i20000000000000000
χ5822-2-22-20002-22-22i−2i2i−2i2i−2i02i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ2ζ−2ζ32ζ30000−2ζ2ζ−2ζ32ζ300−22−22−i2i2−i2i2−22−22−i2i2−i2i20000000000000000
χ5922-2-22-20002-22-22i−2i2i−2i2i−2i02i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ−2ζ2ζ3−2ζ300002ζ−2ζ2ζ3−2ζ300−22−22−i2i2−i2i2−22−22−i2i2−i2i20000000000000000
χ6022-2-22-20002-22-22i−2i2i−2i2i−2i02i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ2ζ−2ζ32ζ30000−2ζ2ζ−2ζ32ζ3002−22−2i2−i2i2−i22−22−2i2−i2i2−i20000000000000000
χ6122-2-22-20002-22-2−2i2i−2i2i−2i2i0−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ3−2ζ32ζ−2ζ00002ζ3−2ζ32ζ−2ζ00−22−22i2−i2i2−i2−22−22i2−i2i2−i20000000000000000
χ6222-2-22-20002-22-2−2i2i−2i2i−2i2i0−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ32ζ3−2ζ2ζ0000−2ζ32ζ3−2ζ2ζ002−22−2−i2i2−i2i22−22−2−i2i2−i2i20000000000000000
χ6322-2-22-20002-22-2−2i2i−2i2i−2i2i0−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ3−2ζ32ζ−2ζ00002ζ3−2ζ32ζ−2ζ002−22−2−i2i2−i2i22−22−2−i2i2−i2i20000000000000000
χ6422-2-22-20002-22-2−2i2i−2i2i−2i2i0−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ32ζ3−2ζ2ζ0000−2ζ32ζ3−2ζ2ζ00−22−22i2−i2i2−i2−22−22i2−i2i2−i20000000000000000
χ6522-2-22-2000-22-222i−2i2i−2i−2i2i0−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ3−2ζ32ζ−2ζ0000−2ζ32ζ3−2ζ2ζ00−22−22i2−i2i2−i22−22−2−i2i2−i2i20000000000000000
χ6622-2-22-2000-22-222i−2i2i−2i−2i2i0−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ32ζ3−2ζ2ζ00002ζ3−2ζ32ζ−2ζ002−22−2−i2i2−i2i2−22−22i2−i2i2−i20000000000000000
χ6722-2-22-2000-22-222i−2i2i−2i−2i2i0−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ3−2ζ32ζ−2ζ0000−2ζ32ζ3−2ζ2ζ002−22−2−i2i2−i2i2−22−22i2−i2i2−i20000000000000000
χ6822-2-22-2000-22-222i−2i2i−2i−2i2i0−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ32ζ3−2ζ2ζ00002ζ3−2ζ32ζ−2ζ00−22−22i2−i2i2−i22−22−2−i2i2−i2i20000000000000000
χ6922-2-22-2000-22-22−2i2i−2i2i2i−2i02i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ−2ζ2ζ3−2ζ30000−2ζ2ζ−2ζ32ζ3002−22−2i2−i2i2−i2−22−22−i2i2−i2i20000000000000000
χ7022-2-22-2000-22-22−2i2i−2i2i2i−2i02i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ2ζ−2ζ32ζ300002ζ−2ζ2ζ3−2ζ300−22−22−i2i2−i2i22−22−2i2−i2i2−i20000000000000000
χ7122-2-22-2000-22-22−2i2i−2i2i2i−2i02i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ−2ζ2ζ3−2ζ30000−2ζ2ζ−2ζ32ζ300−22−22−i2i2−i2i22−22−2i2−i2i2−i20000000000000000
χ7222-2-22-2000-22-22−2i2i−2i2i2i−2i02i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ2ζ−2ζ32ζ300002ζ−2ζ2ζ3−2ζ3002−22−2i2−i2i2−i2−22−22−i2i2−i2i20000000000000000
χ7322-2-2-220002-2-222i−2i−2i2i2i−2i0−2i2i0000001−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i2ζ3−2ζ300002ζ−2ζ2ζ3−2ζ300002ζ−2ζ2−2−22i2−i2−i2i22−2−22i2−i2−i2i20000000000000000
χ7422-2-2-220002-2-222i−2i−2i2i2i−2i0−2i2i0000001−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−2ζ32ζ30000−2ζ2ζ−2ζ32ζ30000−2ζ2ζ−222−2−i2i2i2−i2−222−2−i2i2i2−i20000000000000000
χ7522-2-2-220002-2-222i−2i−2i2i2i−2i0−2i2i000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i2ζ3−2ζ300002ζ−2ζ2ζ3−2ζ300002ζ−2ζ−222−2−i2i2i2−i2−222−2−i2i2i2−i20000000000000000
χ7622-2-2-220002-2-222i−2i−2i2i2i−2i0−2i2i000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−2ζ32ζ30000−2ζ2ζ−2ζ32ζ30000−2ζ2ζ2−2−22i2−i2−i2i22−2−22i2−i2−i2i20000000000000000
χ7722-2-2-220002-2-22−2i2i2i−2i−2i2i02i−2i0000001+i−1−i−1−i1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i2ζ−2ζ00002ζ3−2ζ32ζ−2ζ00002ζ3−2ζ3−222−2i2−i2−i2i2−222−2i2−i2−i2i20000000000000000
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χ7922-2-2-220002-2-22−2i2i2i−2i−2i2i02i−2i000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i2ζ−2ζ00002ζ3−2ζ32ζ−2ζ00002ζ3−2ζ32−2−22−i2i2i2−i22−2−22−i2i2i2−i20000000000000000
χ8022-2-2-220002-2-22−2i2i2i−2i−2i2i02i−2i000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−2ζ2ζ0000−2ζ32ζ3−2ζ2ζ0000−2ζ32ζ3−222−2i2−i2−i2i2−222−2i2−i2−i2i20000000000000000
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χ8822-2-2-22000-222-2−2i2i2i−2i2i−2i0−2i2i000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1+i−1−i−1−i1+i−2ζ32ζ30000−2ζ2ζ2ζ3−2ζ300002ζ−2ζ2−2−22i2−i2−i2i2−222−2−i2i2i2−i20000000000000000
χ898-88-8000080000000000-8000000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-80000-800000000008000000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-88008-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-8800-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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