Finite Group Databasebeta

← Group #141790

Character table — Group #141790

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111222222222222222222222222222222222244444444444444444444444444444444444444444444443232323232323232
order122222444444448888888816161616161616161616161616161616444444444488888888888816161616161616161616161616161616161616161616161624448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1
χ91111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111iiii−i−i−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1i−ii−i
χ101111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111iiii−i−i−i−i11-1-1iiii−i−i−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11−ii−ii
χ111111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111−i−i−i−iiiii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1−ii−ii
χ121111-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111−i−i−i−iiiii11-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11i−ii−i
χ131111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111iiii−i−i−i−i11-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii1-1-11i−i−ii
χ141111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111iiii−i−i−i−i11-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-111-1−iii−i
χ151111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−iiiii11-1-1−i−i−i−iiiii-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i1-1-11−iii−i
χ161111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−iiiii11-1-1−i−i−i−iiiii-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-111-1i−i−ii
χ1722222222222222-2-2-2-2-2-2-2-200000000000000002222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2000000000000000022-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ1922222222-2-2-2-2-2-2000000002222−2−2−2−22222−2−2−2−22-20000000000002i2i−2i−2i2i2i−2i−2i22−2−222−2−2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200000000
χ2022222222-2-2-2-2-2-2000000002222−2−2−2−22222−2−2−2−22-2000000000000−2i−2i2i2i−2i−2i2i2i22−2−222−2−2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200000000
χ2122222222-2-2-2-2-2-200000000−2−2−2−22222−2−2−2−222222-20000000000002i2i−2i−2i2i2i−2i−2i−2−222−2−222−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i200000000
χ2222222222-2-2-2-2-2-200000000−2−2−2−22222−2−2−2−222222-2000000000000−2i−2i2i2i−2i−2i2i2i−2−222−2−222i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i200000000
χ23222222-2-22222-2-2222222222222222222222222-2-200000000-2-2-2-200000000-2-2-2-2-2-2-2-2000000000000000000000000
χ24222222-2-22222-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-2-2-20000000022222222000000000000000000000000
χ25222222-2-22222-2-2-2-2-2-2-2-2-2-20000000000000000-2-200000000222200000000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000
χ26222222-2-22222-2-2-2-2-2-2-2-2-2-20000000000000000-2-20000000022220000000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000
χ27222222-2-2-2-2-2-222000000002222−2−2−2−22222−2−2−2−2-2222-2-222-2-2000000000000−2−222−2−22222−2−2−2−22222−2−2−2−22200000000
χ28222222-2-2-2-2-2-222000000002222−2−2−2−22222−2−2−2−2-22-2-222-2-222000000000000−2−222−2−222−2−22222−2−2−2−22222−2−200000000
χ29222222-2-2-2-2-2-22200000000−2−2−2−22222−2−2−2−22222-2222-2-222-2-200000000000022−2−222−2−2−2−22222−2−2−2−22222−2−200000000
χ30222222-2-2-2-2-2-22200000000−2−2−2−22222−2−2−2−22222-22-2-222-2-22200000000000022−2−222−2−222−2−2−2−22222−2−2−2−22200000000
χ312222-2-22222-2-2222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-200000000-2-22200000000-2-2-2-22222000000000000000000000000
χ322222-2-22222-2-2222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-200000000-2-222000000002222-2-2-2-2000000000000000000000000
χ332222-2-22222-2-222-2-2-2-222220000000000000000-2-20000000022-2-2000000000000000022-2-222-2-2-2-222-2-22200000000
χ342222-2-22222-2-222-2-2-2-222220000000000000000-2-20000000022-2-20000000000000000-2-222-2-22222-2-222-2-200000000
χ352222-2-222-2-222-2-2000000002222−2−2−2−2−2−2−2−22222-222i2i−2i−2i−2i−2i2i2i000000000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000
χ362222-2-222-2-222-2-2000000002222−2−2−2−2−2−2−2−22222-22−2i−2i2i2i2i2i−2i−2i000000000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000
χ372222-2-222-2-222-2-200000000−2−2−2−222222222−2−2−2−2-222i2i−2i−2i−2i−2i2i2i00000000000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000
χ382222-2-222-2-222-2-200000000−2−2−2−222222222−2−2−2−2-22−2i−2i2i2i2i2i−2i−2i00000000000022−2−2−2−222i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000
χ392222-2-2-2-222-2-2-2-2-2-2-2-222220000000000000000222i2i2i2i−2i−2i−2i−2i-2-222−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ402222-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000022−2i−2i−2i−2i2i2i2i2i-2-2222i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ412222-2-2-2-2-2-22222000000002222−2−2−2−2−2−2−2−222222-200000000000022-2-2-2-22222−2−2−2−2222222−2−2−2−2−2−2−2−2222200000000
χ422222-2-2-2-2-2-22222000000002222−2−2−2−2−2−2−2−222222-2000000000000-2-22222-2-222−2−2−2−222−2−2−2−222222222−2−2−2−200000000
χ432222-2-2-2-2-2-2222200000000−2−2−2−222222222−2−2−2−22-200000000000022-2-2-2-222−2−22222−2−2−2−2−2−222222222−2−2−2−200000000
χ442222-2-2-2-2-2-2222200000000−2−2−2−222222222−2−2−2−22-2000000000000-2-22222-2-2−2−22222−2−22222−2−2−2−2−2−2−2−2222200000000
χ4522-2-2002i−2i2-2002i−2i00002i2i−2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−2001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+ii2−i2i2−i22−22−2002ζ6−2ζ6002ζ6−2ζ62ζ2−2ζ2002ζ2−2ζ20000000000
χ4622-2-2002i−2i2-2002i−2i00002i2i−2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−200−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−ii2−i2i2−i22−22−200−2ζ62ζ600−2ζ62ζ6−2ζ22ζ200−2ζ22ζ20000000000
χ4722-2-2002i−2i2-2002i−2i00002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−222001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i−i2i2−i2i2−22−2200−2ζ62ζ600−2ζ62ζ6−2ζ22ζ200−2ζ22ζ20000000000
χ4822-2-2002i−2i2-2002i−2i00002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−22200−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−i2i2−i2i2−22−22002ζ6−2ζ6002ζ6−2ζ62ζ2−2ζ2002ζ2−2ζ20000000000
χ4922-2-2002i−2i2-2002i−2i0000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−222001+i−1−i1+i−1−i1−i−1+i1−i−1+i-2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−i2i2−i2i22−22−22ζ6−2ζ6002ζ6−2ζ600002ζ2−2ζ2002ζ2−2ζ200000000
χ5022-2-2002i−2i2-2002i−2i0000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−22200−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22001+i−1−i1+i−1−i1−i−1+i1−i−1+i−i2i2−i2i22−22−2−2ζ62ζ600−2ζ62ζ60000−2ζ22ζ200−2ζ22ζ200000000
χ5122-2-2002i−2i2-2002i−2i0000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−2001+i−1−i1+i−1−i1−i−1+i1−i−1+i-2200−1−i1+i−1−i1+i−1+i1−i−1+i1−ii2−i2i2−i2−22−22−2ζ62ζ600−2ζ62ζ60000−2ζ22ζ200−2ζ22ζ200000000
χ5222-2-2002i−2i2-2002i−2i0000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−200−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22001+i−1−i1+i−1−i1−i−1+i1−i−1+ii2−i2i2−i2−22−222ζ6−2ζ6002ζ6−2ζ600002ζ2−2ζ2002ζ2−2ζ200000000
χ5322-2-2002i−2i-2200−2i2i22-2-200000000000022-2-2-2-222001−i−1+i−1+i1−i1+i−1−i−1−i1+i002i−2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i2i−2i−2i2i00001+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i00000000
χ5422-2-2002i−2i-2200−2i2i22-2-200000000000022-2-2-2-22200−1+i1−i1−i−1+i−1−i1+i1+i−1−i002i−2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i2i−2i−2i2i0000−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i00000000
χ5522-2-2002i−2i-2200−2i2i22-2-2000000000000-2-22222-2-2001−i−1+i−1+i1−i1+i−1−i−1−i1+i002i−2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−2i2i2i−2i0000−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i00000000
χ5622-2-2002i−2i-2200−2i2i22-2-2000000000000-2-22222-2-200−1+i1−i1−i−1+i−1−i1+i1+i−1−i002i−2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−2i2i2i−2i00001+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i00000000
χ5722-2-2002i−2i-2200−2i2i-2-22200002i2i−2i−2i−2i−2i2i2i00000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00−2i2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i00002-2-221+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i00000000
χ5822-2-2002i−2i-2200−2i2i-2-22200002i2i−2i−2i−2i−2i2i2i0000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00−2i2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i00002-2-22−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i00000000
χ5922-2-2002i−2i-2200−2i2i-2-2220000−2i−2i2i2i2i2i−2i−2i00000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00−2i2i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000-222-2−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1+i1−i1−i−1+i00000000
χ6022-2-2002i−2i-2200−2i2i-2-2220000−2i−2i2i2i2i2i−2i−2i0000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00−2i2i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000-222-21+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1−i−1+i−1+i1−i00000000
χ6122-2-200−2i2i2-200−2i2i00002i2i−2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−2001−i−1+i1−i−1+i1+i−1−i1+i−1−i-2200−1+i1−i−1+i1−i−1−i1+i−1−i1+i−i2i2−i2i2−22−222ζ2−2ζ2002ζ2−2ζ200002ζ6−2ζ6002ζ6−2ζ600000000
χ6222-2-200−2i2i2-200−2i2i00002i2i−2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−200−1+i1−i−1+i1−i−1−i1+i−1−i1+i-22001−i−1+i1−i−1+i1+i−1−i1+i−1−i−i2i2−i2i2−22−22−2ζ22ζ200−2ζ22ζ20000−2ζ62ζ600−2ζ62ζ600000000
χ6322-2-200−2i2i2-200−2i2i00002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−222001−i−1+i1−i−1+i1+i−1−i1+i−1−i-2200−1+i1−i−1+i1−i−1−i1+i−1−i1+ii2−i2i2−i22−22−2−2ζ22ζ200−2ζ22ζ20000−2ζ62ζ600−2ζ62ζ600000000
χ6422-2-200−2i2i2-200−2i2i00002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−22200−1+i1−i−1+i1−i−1−i1+i−1−i1+i-22001−i−1+i1−i−1+i1+i−1−i1+i−1−ii2−i2i2−i22−22−22ζ2−2ζ2002ζ2−2ζ200002ζ6−2ζ6002ζ6−2ζ600000000
χ6522-2-200−2i2i2-200−2i2i0000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−222001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−ii2−i2i2−i2−22−22002ζ2−2ζ2002ζ2−2ζ22ζ6−2ζ6002ζ6−2ζ60000000000
χ6622-2-200−2i2i2-200−2i2i0000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−22200−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+ii2−i2i2−i2−22−2200−2ζ22ζ200−2ζ22ζ2−2ζ62ζ600−2ζ62ζ60000000000
χ6722-2-200−2i2i2-200−2i2i0000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−2001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i−i2i2−i2i22−22−200−2ζ22ζ200−2ζ22ζ2−2ζ62ζ600−2ζ62ζ60000000000
χ6822-2-200−2i2i2-200−2i2i0000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−200−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i−i2i2−i2i22−22−2002ζ2−2ζ2002ζ2−2ζ22ζ6−2ζ6002ζ6−2ζ60000000000
χ6922-2-200−2i2i-22002i−2i22-2-200000000000022-2-2-2-222001+i−1−i−1−i1+i1−i−1+i−1+i1−i00−2i2i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−2i2i2i−2i00001−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i00000000
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Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.