Finite Group Databasebeta

← Group #188749

Character table — Group #188749

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111111111111222222222222222222222222222222224444444444444444444444444444444444444444444488888888888888881616161616161616
order12222222444444444444444444444444888888888888888822222244444444444444888888888888888888888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ101111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ121111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ131111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ141111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ151111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ161111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111
χ1711111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−ii−ii−ii−ii−i
χ1811111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii−ii−ii−ii−ii
χ1911111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i−ii−ii−ii−ii
χ2011111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iii−i−iii−i−iiii−ii−ii−ii−i
χ2111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iiii−ii−i−ii−ii
χ2211111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i−ii−iii−ii−i
χ2311111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii−ii−iii−ii−i
χ2411111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−ii−ii−i−ii−ii
χ2511111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iiii−i−iii−i−ii
χ2611111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i−iii−i−iii−i
χ2711111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii−iii−i−iii−i
χ2811111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iii−i−iiiii−i−iii−i−ii−i−iii−i−ii
χ2911111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−ii−i−ii−iii−i
χ3011111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii−iii−ii−i−ii
χ3111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i−iii−ii−i−ii
χ3211111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111−i−iiiii−i−iii−i−i−i−iiii−i−ii−iii−i
χ332222222222222222-2-2-2-2-2-222222222-2-20000000000000000-2-22222-2-2-2-222-2-222-2-2-2-2000000000000000000000000000000000000000000000000
χ342222222222222222-2-2-2-2-2-222222222-2-20000000000000000-2-2-2-2-2-2-2-222-2-222-2-22222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222-2-222-2-222-2-2-2-22222000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022-2-2222222-2-22222-2-2-2-2000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-20000000000000000-2-222-2-222-2-2-2-22222-2-222000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-20000000000000000-2-2-2-222222222-2-2-2-222-2-2000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-20000000000000000222222-2-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2000000000000000022-2-2-2-2-2-22222-2-222-2-222000000000000000000000000000000000000000000000000
χ41222-2-22-2-22i2i−2i−2i2i2i−2i−2i0000002i2i−2i−2i22-2-200i2i2i2i2−i2−i2−i2−i22222−2−2−2−2000000002i−2i002-2002-22i−2i22−2−2i2i2−i2−i222−2−2i2i2−i2−i2i2i2−i2−i222−2−2000000000000000000000000
χ42222-2-22-2-22i2i−2i−2i2i2i−2i−2i0000002i2i−2i−2i22-2-200i2i2i2i2−i2−i2−i2−i22222−2−2−2−200000000−2i2i00-2200-22−2i2i22−2−2i2i2−i2−i2−2−222−i2−i2i2i2−i2−i2i2i2−2−222000000000000000000000000
χ43222-2-22-2-22i2i−2i−2i2i2i−2i−2i0000002i2i−2i−2i22-2-200−i2−i2−i2−i2i2i2i2i2−2−2−2−22222000000002i−2i002-2002-22i−2i−2−222−i2−i2i2i2−2−222−i2−i2i2i2−i2−i2i2i2−2−222000000000000000000000000
χ44222-2-22-2-22i2i−2i−2i2i2i−2i−2i0000002i2i−2i−2i22-2-200−i2−i2−i2−i2i2i2i2i2−2−2−2−2222200000000−2i2i00-2200-22−2i2i−2−222−i2−i2i2i222−2−2i2i2−i2−i2i2i2−i2−i222−2−2000000000000000000000000
χ45222-2-22-2-22i2i−2i−2i2i2i−2i−2i000000−2i−2i2i2i-2-22200i2i2i2i2−i2−i2−i2−i22222−2−2−2−2000000002i−2i002-200-22−2i2i−2−222−i2−i2i2i222−2−2i2i2−i2−i2−i2−i2i2i2−2−222000000000000000000000000
χ46222-2-22-2-22i2i−2i−2i2i2i−2i−2i000000−2i−2i2i2i-2-22200i2i2i2i2−i2−i2−i2−i22222−2−2−2−200000000−2i2i00-22002-22i−2i−2−222−i2−i2i2i2−2−222−i2−i2i2i2i2i2−i2−i222−2−2000000000000000000000000
χ47222-2-22-2-22i2i−2i−2i2i2i−2i−2i000000−2i−2i2i2i-2-22200−i2−i2−i2−i2i2i2i2i2−2−2−2−22222000000002i−2i002-200-22−2i2i22−2−2i2i2−i2−i2−2−222−i2−i2i2i2i2i2−i2−i222−2−2000000000000000000000000
χ48222-2-22-2-22i2i−2i−2i2i2i−2i−2i000000−2i−2i2i2i-2-22200−i2−i2−i2−i2i2i2i2i2−2−2−2−2222200000000−2i2i00-22002-22i−2i22−2−2i2i2−i2−i222−2−2i2i2−i2−i2−i2−i2i2i2−2−222000000000000000000000000
χ49222-2-22-2-2−2i−2i2i2i−2i−2i2i2i0000002i2i−2i−2i-2-22200i2i2i2i2−i2−i2−i2−i2−2−2−2−22222000000002i−2i00-22002-2−2i2i22−2−2−i2−i2i2i222−2−2−i2−i2i2i2i2i2−i2−i2−2−222000000000000000000000000
χ50222-2-22-2-2−2i−2i2i2i−2i−2i2i2i0000002i2i−2i−2i-2-22200i2i2i2i2−i2−i2−i2−i2−2−2−2−2222200000000−2i2i002-200-222i−2i22−2−2−i2−i2i2i2−2−222i2i2−i2−i2−i2−i2i2i222−2−2000000000000000000000000
χ51222-2-22-2-2−2i−2i2i2i−2i−2i2i2i0000002i2i−2i−2i-2-22200−i2−i2−i2−i2i2i2i2i22222−2−2−2−2000000002i−2i00-22002-2−2i2i−2−222i2i2−i2−i2−2−222i2i2−i2−i2−i2−i2i2i222−2−2000000000000000000000000
χ52222-2-22-2-2−2i−2i2i2i−2i−2i2i2i0000002i2i−2i−2i-2-22200−i2−i2−i2−i2i2i2i2i22222−2−2−2−200000000−2i2i002-200-222i−2i−2−222i2i2−i2−i222−2−2−i2−i2i2i2i2i2−i2−i2−2−222000000000000000000000000
χ53222-2-22-2-2−2i−2i2i2i−2i−2i2i2i000000−2i−2i2i2i22-2-200i2i2i2i2−i2−i2−i2−i2−2−2−2−22222000000002i−2i00-2200-222i−2i−2−222i2i2−i2−i222−2−2−i2−i2i2i2−i2−i2i2i222−2−2000000000000000000000000
χ54222-2-22-2-2−2i−2i2i2i−2i−2i2i2i000000−2i−2i2i2i22-2-200i2i2i2i2−i2−i2−i2−i2−2−2−2−2222200000000−2i2i002-2002-2−2i2i−2−222i2i2−i2−i2−2−222i2i2−i2−i2i2i2−i2−i2−2−222000000000000000000000000
χ55222-2-22-2-2−2i−2i2i2i−2i−2i2i2i000000−2i−2i2i2i22-2-200−i2−i2−i2−i2i2i2i2i22222−2−2−2−2000000002i−2i00-2200-222i−2i22−2−2−i2−i2i2i2−2−222i2i2−i2−i2i2i2−i2−i2−2−222000000000000000000000000
χ56222-2-22-2-2−2i−2i2i2i−2i−2i2i2i000000−2i−2i2i2i22-2-200−i2−i2−i2−i2i2i2i2i22222−2−2−2−200000000−2i2i002-2002-2−2i2i22−2−2−i2−i2i2i222−2−2−i2−i2i2i2−i2−i2i2i222−2−2000000000000000000000000
χ5722-22-2-22-22i2i−2i−2i−2i−2i2i2i2-22i2i−2i−2i000000002-22i2i−2i−2i2i2i−2i−2i22-2-222-2-2000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ0000000000000000
χ5822-22-2-22-22i2i−2i−2i−2i−2i2i2i2-22i2i−2i−2i000000002-22i2i−2i−2i2i2i−2i−2i22-2-222-2-200000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ0000000000000000
χ5922-22-2-22-22i2i−2i−2i−2i−2i2i2i2-22i2i−2i−2i000000002-2−2i−2i2i2i−2i−2i2i2i-2-222-2-222000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ0000000000000000
χ6022-22-2-22-22i2i−2i−2i−2i−2i2i2i2-22i2i−2i−2i000000002-2−2i−2i2i2i−2i−2i2i2i-2-222-2-22200000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ0000000000000000
χ6122-22-2-22-2−2i−2i2i2i2i2i−2i−2i2-2−2i−2i2i2i000000002-22i2i−2i−2i2i2i−2i−2i-2-222-2-222000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ30000000000000000
χ6222-22-2-22-2−2i−2i2i2i2i2i−2i−2i2-2−2i−2i2i2i000000002-22i2i−2i−2i2i2i−2i−2i-2-222-2-22200000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ30000000000000000
χ6322-22-2-22-2−2i−2i2i2i2i2i−2i−2i2-2−2i−2i2i2i000000002-2−2i−2i2i2i−2i−2i2i2i22-2-222-2-2000000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ30000000000000000
χ6422-22-2-22-2−2i−2i2i2i2i2i−2i−2i2-2−2i−2i2i2i000000002-2−2i−2i2i2i−2i−2i2i2i22-2-222-2-200000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ30000000000000000
χ652-22-22-22-22i−2i2i−2i2i−2i2i−2i2-22i−2i2i−2i00000000-222-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ300000000
χ662-22-22-22-22i−2i2i−2i2i−2i2i−2i2-22i−2i2i−2i00000000-222-22-22-22-22i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ300000000
χ672-22-22-22-22i−2i2i−2i2i−2i2i−2i2-22i−2i2i−2i00000000-22-22-22-22-22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ300000000
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χ1164-44-44-44-4−4i4i−4i4i−4i4i−4i4i-444i−4i4i−4i000000004-4000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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