Finite Group Databasebeta

← Group #200414

Character table — Group #200414

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122222222222222222244444444444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222224444444444442222444444444444444444888888888888888888888888888888882444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ111111111111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ121111111111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ131111111111-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ141111111111-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1
χ151111111111-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ161111111111-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ17111111-1-1-1-1111111-1-1-1-1-1-111-1-111-11-1-111-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1i−ii−ii−ii−i
χ18111111-1-1-1-1111111-1-1-1-1-1-111-1-111-11-1-111-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11-11-11−ii−ii−ii−ii
χ19111111-1-1-1-1111111-1-1-1-1-1-111-1-111-11-1-111-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−ii−ii−ii−ii
χ20111111-1-1-1-1111111-1-1-1-1-1-111-1-111-11-1-111-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-11-11-11-11i−ii−ii−ii−i
χ21111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii1-11-1-11-11i−ii−i−ii−ii
χ22111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-1-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-11-111-11-1−ii−iii−ii−i
χ23111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i1-11-1-11-11−ii−iii−ii−i
χ24111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-1-1-11111-1-1-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-11-111-11-1i−ii−i−ii−ii
χ25111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11111-1-1-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-111-1-11i−i−iii−i−ii
χ26111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11111-1-1-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-111-1-111-1−iii−i−iii−i
χ27111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11111-1-1-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-111-1-11−iii−i−iii−i
χ28111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-11111-1-1-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-111-1-111-1i−i−iii−i−ii
χ29111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i1-1-11-111-1i−i−ii−iii−i
χ30111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-11-1-11−iii−ii−i−ii
χ31111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii1-1-11-111-1−iii−ii−i−ii
χ32111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-11-1-11i−i−ii−iii−i
χ3322222222222222-2-22222-2-222-2-2-2-2-2-2-2-2-2-222-2-222-2-222000000000000000000000000000000000000000000000000
χ3422222222222222-2-22222-2-2-2-222-2-2-2-2-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ352222222222-2-2-2-222-2-2-2-2-2-22222-2-2-2222-2-222-2-2-2-222-2-2000000000000000000000000000000000000000000000000
χ362222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-222222-2-22222-2-222000000000000000000000000000000000000000000000000
χ37222222-2-2-2-22222-2-2-2-2-2-2222222-2-22-222-2-2-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ38222222-2-2-2-22222-2-2-2-2-2-222-2-2-2-2-2-22-2222222-2-2-2-22222000000000000000000000000000000000000000000000000
χ39222222-2-2-2-2-2-2-2-22222222222-2-2-2-222-2-2-2-2-2-222-2-22222000000000000000000000000000000000000000000000000
χ40222222-2-2-2-2-2-2-2-222222222-2-222-2-222-2-22222-2-222-2-2-2-2000000000000000000000000000000000000000000000000
χ412222-2-222-2-222-2-22222-2-22200002-2-2-22-2000000000000000000000000000022-2-222-2-222-2-222-2-20000000000000000
χ422222-2-222-2-222-2-22222-2-22200002-2-2-22-20000000000000000000000000000-2-222-2-222-2-222-2-2220000000000000000
χ432222-2-222-2-222-2-2-2-222-2-2-2-20000-2222-220000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ442222-2-222-2-222-2-2-2-222-2-2-2-20000-2222-22000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ452222-2-222-2-2-2-22222-2-222-2-20000-222-22-20000000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ462222-2-222-2-2-2-22222-2-222-2-20000-222-22-2000000000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ472222-2-222-2-2-2-222-2-2-2-2222200002-2-22-22000000000000000000000000000022-2-222-2-2-2-222-2-2220000000000000000
χ482222-2-222-2-2-2-222-2-2-2-2222200002-2-22-220000000000000000000000000000-2-222-2-22222-2-222-2-20000000000000000
χ492222-2-2-2-22222-2-222-2-222-2-200002-22-2-2200000000000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ502222-2-2-2-22222-2-222-2-222-2-200002-22-2-220000000000000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ512222-2-2-2-22222-2-2-2-2-2-222220000-22-222-200000000000022-2-2-2-22222-2-2-2-22200000000000000000000000000000000
χ522222-2-2-2-22222-2-2-2-2-2-222220000-22-222-2000000000000-2-22222-2-2-2-22222-2-200000000000000000000000000000000
χ532222-2-2-2-222-2-2222222-2-2220000-22-2-2-2200000000000022-2-2-2-222-2-22222-2-200000000000000000000000000000000
χ542222-2-2-2-222-2-2222222-2-2220000-22-2-2-22000000000000-2-22222-2-222-2-2-2-22200000000000000000000000000000000
χ552222-2-2-2-222-2-222-2-222-2-2-2-200002-2222-200000000000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ562222-2-2-2-222-2-222-2-222-2-2-2-200002-2222-20000000000000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ5722-2-22-22-22-22i−2i2i−2i002i−2i2i−2i00002-20000002i−2i002i−2i002-200i2−i2i2−i2i2−i2i2−i22−22−22−22−22−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ5822-2-22-22-22-22i−2i2i−2i002i−2i2i−2i00002-20000002i−2i002i−2i002-200−i2i2−i2i2−i2i2−i2i2−22−22−22−22−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ5922-2-22-22-22-22i−2i2i−2i002i−2i2i−2i0000-22000000−2i2i00−2i2i00-2200i2−i2i2−i2i2−i2i2−i22−22−22−22−2−22−22−22−22−i2i2−i2i2−i2i2−i2i20000000000000000
χ6022-2-22-22-22-22i−2i2i−2i002i−2i2i−2i0000-22000000−2i2i00−2i2i00-2200−i2i2−i2i2−i2i2−i2i2−22−22−22−222−22−22−22−2i2−i2i2−i2i2−i2i2−i20000000000000000
χ6122-2-22-22-22-2−2i2i−2i2i00−2i2i−2i2i00002-2000000−2i2i00−2i2i002-200i2−i2i2−i2i2−i2i2−i2−22−22−22−22−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ6222-2-22-22-22-2−2i2i−2i2i00−2i2i−2i2i00002-2000000−2i2i00−2i2i002-200−i2i2−i2i2−i2i2−i2i22−22−22−22−22−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ6322-2-22-22-22-2−2i2i−2i2i00−2i2i−2i2i0000-220000002i−2i002i−2i00-2200i2−i2i2−i2i2−i2i2−i2−22−22−22−222−22−22−22−2−i2i2−i2i2−i2i2−i2i20000000000000000
χ6422-2-22-22-22-2−2i2i−2i2i00−2i2i−2i2i0000-220000002i−2i002i−2i00-2200−i2i2−i2i2−i2i2−i2i22−22−22−22−2−22−22−22−22i2−i2i2−i2i2−i2i2−i20000000000000000
χ6522-2-22-2-22-222i−2i2i−2i00−2i2i−2i2i00002-2000000−2i2i002i−2i00-22002−22−2−22−22−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ6622-2-22-2-22-222i−2i2i−2i00−2i2i−2i2i00002-2000000−2i2i002i−2i00-2200−22−222−22−2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ6722-2-22-2-22-222i−2i2i−2i00−2i2i−2i2i0000-220000002i−2i00−2i2i002-2002−22−2−22−22−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000000000
χ6822-2-22-2-22-222i−2i2i−2i00−2i2i−2i2i0000-220000002i−2i00−2i2i002-200−22−222−22−2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
χ6922-2-22-2-22-22−2i2i−2i2i002i−2i2i−2i00002-20000002i−2i00−2i2i00-22002−22−2−22−22i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
χ7022-2-22-2-22-22−2i2i−2i2i002i−2i2i−2i00002-20000002i−2i00−2i2i00-2200−22−222−22−2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ7122-2-22-2-22-22−2i2i−2i2i002i−2i2i−2i0000-22000000−2i2i002i−2i002-2002−22−2−22−22i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000000000
χ7222-2-22-2-22-22−2i2i−2i2i002i−2i2i−2i0000-22000000−2i2i002i−2i002-200−22−222−22−2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000000000
χ7322-2-2-222-2-222i−2i−2i2i002i−2i−2i2i002-200000000002-2002i−2i002i−2i2−2−222−2−22−i2i2i2−i2−i2i2i2−i22−2−222−2−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ7422-2-2-222-2-222i−2i−2i2i002i−2i−2i2i002-200000000002-2002i−2i002i−2i−222−2−222−2i2−i2−i2i2i2−i2−i2i2−222−2−222−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ7522-2-2-222-2-222i−2i−2i2i002i−2i−2i2i00-220000000000-2200−2i2i00−2i2i2−2−222−2−22−i2i2i2−i2−i2i2i2−i2−222−2−222−2−i2i2i2−i2−i2i2i2−i20000000000000000
χ7622-2-2-222-2-222i−2i−2i2i002i−2i−2i2i00-220000000000-2200−2i2i00−2i2i−222−2−222−2i2−i2−i2i2i2−i2−i2i22−2−222−2−22i2−i2−i2i2i2−i2−i2i20000000000000000
χ7722-2-2-222-2-22−2i2i2i−2i00−2i2i2i−2i002-200000000002-200−2i2i00−2i2i2−2−222−2−22i2−i2−i2i2i2−i2−i2i22−2−222−2−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ7822-2-2-222-2-22−2i2i2i−2i00−2i2i2i−2i002-200000000002-200−2i2i00−2i2i−222−2−222−2−i2i2i2−i2−i2i2i2−i2−222−2−222−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ7922-2-2-222-2-22−2i2i2i−2i00−2i2i2i−2i00-220000000000-22002i−2i002i−2i2−2−222−2−22i2−i2−i2i2i2−i2−i2i2−222−2−222−2i2−i2−i2i2i2−i2−i2i20000000000000000
χ8022-2-2-222-2-22−2i2i2i−2i00−2i2i2i−2i00-220000000000-22002i−2i002i−2i−222−2−222−2−i2i2i2−i2−i2i2i2−i22−2−222−2−22−i2i2i2−i2−i2i2i2−i20000000000000000
χ8122-2-2-22-222-22i−2i−2i2i00−2i2i2i−2i002-20000000000-22002i−2i00−2i2ii2−i2−i2i2−i2i2i2−i22−2−22−222−2i2−i2−i2i2−i2i2i2−i2−222−22−2−220000000000000000
χ8222-2-2-22-222-22i−2i−2i2i00−2i2i2i−2i002-20000000000-22002i−2i00−2i2i−i2i2i2−i2i2−i2−i2i2−222−22−2−22−i2i2i2−i2i2−i2−i2i22−2−22−222−20000000000000000
χ8322-2-2-22-222-22i−2i−2i2i00−2i2i2i−2i00-2200000000002-200−2i2i002i−2ii2−i2−i2i2−i2i2i2−i22−2−22−222−2−i2i2i2−i2i2−i2−i2i22−2−22−222−20000000000000000
χ8422-2-2-22-222-22i−2i−2i2i00−2i2i2i−2i00-2200000000002-200−2i2i002i−2i−i2i2i2−i2i2−i2−i2i2−222−22−2−22i2−i2−i2i2−i2i2i2−i2−222−22−2−220000000000000000
χ8522-2-2-22-222-2−2i2i2i−2i002i−2i−2i2i002-20000000000-2200−2i2i002i−2ii2−i2−i2i2−i2i2i2−i2−222−22−2−22i2−i2−i2i2−i2i2i2−i22−2−22−222−20000000000000000
χ8622-2-2-22-222-2−2i2i2i−2i002i−2i−2i2i002-20000000000-2200−2i2i002i−2i−i2i2i2−i2i2−i2−i2i22−2−22−222−2−i2i2i2−i2i2−i2−i2i2−222−22−2−220000000000000000
χ8722-2-2-22-222-2−2i2i2i−2i002i−2i−2i2i00-2200000000002-2002i−2i00−2i2ii2−i2−i2i2−i2i2i2−i2−222−22−2−22−i2i2i2−i2i2−i2−i2i2−222−22−2−220000000000000000
χ8822-2-2-22-222-2−2i2i2i−2i002i−2i−2i2i00-2200000000002-2002i−2i00−2i2i−i2i2i2−i2i2−i2−i2i22−2−22−222−2i2−i2−i2i2−i2i2i2−i22−2−22−222−20000000000000000
χ898-88-800000000000000008i−8i0000000000000000000000000000000000000000000000000000000000000000000000
χ908-88-80000000000000000−8i8i0000000000000000000000000000000000000000000000000000000000000000000000
χ918-8-8800000000008i−8i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-880000000000−8i8i0000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).