Finite Group Databasebeta

← Group #367757

Character table — Group #367757

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111111111111222222222222222222222222222222224444444444444444444444444444444444444444444488888888888888881616161616161616
order12222222222222224444444444444444888888888888888844444444444444444444888888888888888888888888444444444444444444444444
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
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ91111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ101111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ121111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ131111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-1-111
χ141111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ161111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111
χ17111-1-1-111-1-11-11-11-11111-1-1-1-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−iii−i−iii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-111-1-1ii−i−i11-1-1ii−i−ii−i1-11-1i−i
χ18111-1-1-111-1-11-11-11-11111-1-1-1-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−iii−i−iii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-11111-1-1-1-1-1-111−i−iii-1-111−i−iii−ii-11-11−ii
χ19111-1-1-111-1-11-11-11-11111-1-1-1-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1−i−iii−i−iii−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111-1-1-1-1111111-1-1ii−i−i11-1-1ii−i−i−ii-11-11−ii
χ20111-1-1-111-1-11-11-11-11111-1-1-1-111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1−i−iii−i−iii−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111-1-1-1-11111-1-111−i−iii-1-111−i−iiii−i1-11-1i−i
χ21111-1-1-111-1-11-11-11-11111-1-1-1-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1ii−i−iii−i−iii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111-1-1-1-1111111-1-1−i−iii11-1-1−i−iiii−i-11-11i−i
χ22111-1-1-111-1-11-11-11-11111-1-1-1-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1ii−i−iii−i−iii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111-1-1-1-11111-1-111ii−i−i-1-111ii−i−i−ii1-11-1−ii
χ23111-1-1-111-1-11-11-11-11111-1-1-1-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii−i−iii−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-111-1-1−i−iii11-1-1−i−iii−ii1-11-1−ii
χ24111-1-1-111-1-11-11-11-11111-1-1-1-111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii−i−iii−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1-1-111ii−i−i-1-111ii−i−ii−i-11-11i−i
χ25111-1-1-111-1-11-11-11-1-1-1-1-1111111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111ii−i−i−i−iiiii−i−i−i−iii−i−i−i−iiiii1111-1-1-1-1-1-1-1-1111111-1-1ii−i−i-1-111−i−iii−ii-111-1i−i
χ26111-1-1-111-1-11-11-11-1-1-1-1-1111111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111ii−i−i−i−iiiii−i−i−i−iii−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111-1-111−i−iii11-1-1ii−i−ii−i1-1-11−ii
χ27111-1-1-111-1-11-11-11-1-1-1-1-1111111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-111-1-1ii−i−i-1-111−i−iiii−i1-1-11−ii
χ28111-1-1-111-1-11-11-11-1-1-1-1-1111111-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1-1-111−i−iii11-1-1ii−i−i−ii-111-1i−i
χ29111-1-1-111-1-11-11-11-1-1-1-1-1111111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-111-1-1−i−iii-1-111ii−i−i−ii1-1-11i−i
χ30111-1-1-111-1-11-11-11-1-1-1-1-1111111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1-1-111ii−i−i11-1-1−i−iiii−i-111-1−ii
χ31111-1-1-111-1-11-11-11-1-1-1-1-1111111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111−i−iiiii−i−i−i−iiiii−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-1111111-1-1−i−iii-1-111ii−i−ii−i-111-1−ii
χ32111-1-1-111-1-11-11-11-1-1-1-1-1111111-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111−i−iiiii−i−i−i−iiiii−i−iiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111-1-111ii−i−i11-1-1−i−iii−ii1-1-11i−i
χ33222222222222222222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000
χ34222222222222222222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022222222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000002222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
χ3722222-22-222-2-2-2-2-2-222-2-222-2-2000000002222−2−2−2−22222−2−2−2−200002-22-22-22-20000000022−2−222−2−222−2−222−2−222−2−222−2−2000000000000000000000000
χ3822222-22-222-2-2-2-2-2-222-2-222-2-2000000002222−2−2−2−22222−2−2−2−20000-22-22-22-220000000022−2−222−2−2−2−222−2−222−2−222−2−222000000000000000000000000
χ3922222-22-222-2-2-2-2-2-222-2-222-2-200000000−2−2−2−22222−2−2−2−2222200002-22-22-22-200000000−2−222−2−222−2−222−2−222−2−222−2−222000000000000000000000000
χ4022222-22-222-2-2-2-2-2-222-2-222-2-200000000−2−2−2−22222−2−2−2−222220000-22-22-22-2200000000−2−222−2−22222−2−222−2−222−2−222−2−2000000000000000000000000
χ4122222-22-222-2-2-2-2-2-2-2-222-2-222000000002222−2−2−2−22222−2−2−2−200002-22-2-22-2200000000−2−222−2−22222−2−222−2−2−2−222−2−222000000000000000000000000
χ4222222-22-222-2-2-2-2-2-2-2-222-2-222000000002222−2−2−2−22222−2−2−2−20000-22-222-22-200000000−2−222−2−222−2−222−2−22222−2−222−2−2000000000000000000000000
χ4322222-22-222-2-2-2-2-2-2-2-222-2-22200000000−2−2−2−22222−2−2−2−2222200002-22-2-22-220000000022−2−222−2−2−2−222−2−22222−2−222−2−2000000000000000000000000
χ4422222-22-222-2-2-2-2-2-2-2-222-2-22200000000−2−2−2−22222−2−2−2−222220000-22-222-22-20000000022−2−222−2−222−2−222−2−2−2−222−2−222000000000000000000000000
χ45222-2-222-2-2-2-22-22-2222-2-2-2-22200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200002i−2i−2i2i2i−2i−2i2i00000000i2i2−i2−i2−i2−i2i2i222−2−2−2−22222−2−2−2−222000000000000000000000000
χ46222-2-222-2-2-2-22-22-2222-2-2-2-22200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000−2i2i2i−2i−2i2i2i−2i00000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−2−2−22222−2−2000000000000000000000000
χ47222-2-222-2-2-2-22-22-2222-2-2-2-22200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200002i−2i−2i2i2i−2i−2i2i00000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−2−2−22222−2−2000000000000000000000000
χ48222-2-222-2-2-2-22-22-2222-2-2-2-22200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i20000−2i2i2i−2i−2i2i2i−2i00000000−i2−i2i2i2i2i2−i2−i222−2−2−2−22222−2−2−2−222000000000000000000000000
χ49222-2-222-2-2-2-22-22-22-2-22222-2-200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i200002i−2i−2i2i−2i2i2i−2i00000000−i2−i2i2i2i2i2−i2−i222−2−2−2−222−2−22222−2−2000000000000000000000000
χ50222-2-222-2-2-2-22-22-22-2-22222-2-200000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i20000−2i2i2i−2i2i−2i−2i2i00000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−222−2−2−2−222000000000000000000000000
χ51222-2-222-2-2-2-22-22-22-2-22222-2-200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i200002i−2i−2i2i−2i2i2i−2i00000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−222−2−2−2−222000000000000000000000000
χ52222-2-222-2-2-2-22-22-22-2-22222-2-200000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i20000−2i2i2i−2i2i−2i−2i2i00000000i2i2−i2−i2−i2−i2i2i222−2−2−2−222−2−22222−2−2000000000000000000000000
χ53222-2-2-222-2-22-22-22-22222-2-2-2-2-2-222-2-2220000000000000000-2-2222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ54222-2-2-222-2-22-22-22-22222-2-2-2-2-2-222-2-2220000000000000000-2-222−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ55222-2-2-222-2-22-22-22-2-2-2-2-22222-2-222-2-222000000000000000022-2-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ56222-2-2-222-2-22-22-22-2-2-2-2-22222-2-222-2-222000000000000000022-2-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ5722-2222-2-2-2-2-222-22-200000000-2-22-2222-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000002-22-22i−2i2i−2i00000000
χ5822-2222-2-2-2-2-222-22-200000000-2-22-2222-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000000000-22-22−2i2i−2i2i00000000
χ5922-2222-2-2-2-2-222-22-200000000-2-22-2222-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000002-22-2−2i2i−2i2i00000000
χ6022-2222-2-2-2-2-222-22-200000000-2-22-2222-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000000000-22-222i−2i2i−2i00000000
χ6122-2-2-2-2-2-222-2-2222200000000-2-2-2222-2222-2-222-2-2-2-222-2-22200000000000000000000000000000000000000000000000000002-2-222-2-2200000000
χ6222-2-2-2-2-2-222-2-2222200000000-2-2-2222-2222-2-222-2-2-2-222-2-2220000000000000000000000000000000000000000000000000000-222-2-222-200000000
χ6322-2-2-2-2-2-222-2-2222200000000-2-2-2222-22-2-222-2-22222-2-222-2-200000000000000000000000000000000000000000000000000002-2-22-222-200000000
χ6422-2-2-2-2-2-222-2-2222200000000-2-2-2222-22-2-222-2-22222-2-222-2-20000000000000000000000000000000000000000000000000000-222-22-2-2200000000
χ652-222-22-222-2-2-2-2-2222i−2i2i−2i2i−2i2i−2i000000002−22−22−22−22−22−22−22−20000000000002i−2i2i−2i2-22-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000000000000000
χ662-222-22-222-2-2-2-2-2222i−2i2i−2i2i−2i2i−2i000000002−22−22−22−22−22−22−22−2000000000000−2i2i−2i2i-22-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000000000000000
χ672-222-22-222-2-2-2-2-2222i−2i2i−2i2i−2i2i−2i00000000−22−22−22−22−22−22−22−220000000000002i−2i2i−2i2-22-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000000000000000
χ682-222-22-222-2-2-2-2-2222i−2i2i−2i2i−2i2i−2i00000000−22−22−22−22−22−22−22−22000000000000−2i2i−2i2i-22-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000000000000000
χ692-222-22-222-2-2-2-2-222−2i2i−2i2i−2i2i−2i2i000000002−22−22−22−22−22−22−22−20000000000002i−2i2i−2i-22-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000000000000000
χ702-222-22-222-2-2-2-2-222−2i2i−2i2i−2i2i−2i2i000000002−22−22−22−22−22−22−22−2000000000000−2i2i−2i2i2-22-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000000000000000
χ712-222-22-222-2-2-2-2-222−2i2i−2i2i−2i2i−2i2i00000000−22−22−22−22−22−22−22−220000000000002i−2i2i−2i-22-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000000000000000
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χ10744-444-4-44-4-44-4-44-440000000000000000−2i2−2i22i22i22i22i2−2i2−2i2−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000000000000000000000000000000000
χ10844-4-4-44-444444-4-4-4-400000000000000002222−22−22−22−222222−22−2222222222−22−2200000000000000000000000000000000000000000000000000000000000000000000
χ10944-4-4-44-444444-4-4-4-40000000000000000−22−2222222222−22−222222−22−22−22−22222200000000000000000000000000000000000000000000000000000000000000000000
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χ1114-4-44-444-4-444-4-444-400000000000000002i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000000000000000000000000000000000
χ1124-4-44-444-4-444-4-444-40000000000000000−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000000000000000000000000000000000
χ1134-4-44-4-444-44-444-4-44000000004-4-4-4-4444000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1144-4-4-444444-4-4-444-4-4000000004-444-44-4-4000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1154-4-4-44-44-44-444-4-444000000000000000022−22−222222−22−2222−222222−22−222222−2200000000000000000000000000000000000000000000000000000000000000000000
χ1164-4-4-44-44-44-444-4-4440000000000000000−222222−22−222222−2222−22−222222−22−222200000000000000000000000000000000000000000000000000000000000000000000

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