Finite Group Databasebeta

← Group #110833

Character table — Group #110833

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111111111111222222222222222222222222222222224444444444444444444444444444444444444444444488888888888888881616161616161616
order12222222444444444444444444444444888888888888888822444444444444444444888888888888888888888888888888888888888822448888
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
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111111111-1-1-1-1-1-1-1-111iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111111111-1-1-1-1-1-1-1-111iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1-1-11111111111iiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1-1-11111111111iiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111111111-1-1-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii
χ1411111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111111111-1-1-1-1-1-1-1-111−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-1-1-11111111111−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii
χ17111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1iiii−i−i−i−iiiii−i−i−i−i1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i11-1-111-1-11-11-1i−ii−i
χ18111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1iiii−i−i−i−iiiii−i−i−i−i1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1−i−iii−i−iii-1-111-1-111-11-11−ii−ii
χ19111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1−i−i−i−iiiii−i−i−i−iiiii1-1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111ii−i−iii−i−i11-1-111-1-1-11-11−ii−ii
χ20111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-1iiii−i−i−i−iiiii−i−i−i−i1-1−i−i−i−iiiii−i−i−i−iiiii1-1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111−i−iii−i−iii-1-111-1-1111-11-1i−ii−i
χ21111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1iiii−i−i−i−iiiii−i−i−i−i1-1−i−iii−i−iii-1-1-1-11111-1-1-1-11111ii−i−iii−i−i-1-111-1-1111-11-1−ii−ii
χ22111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1iiii−i−i−i−iiiii−i−i−i−i1-1−i−iii−i−iii-1-1-1-11111-1-1-1-11111−i−iii−i−iii11-1-111-1-1-11-11i−ii−i
χ23111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−i−i−i−iiiii−i−i−i−iiiii1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1ii−i−iii−i−i-1-111-1-111-11-11i−ii−i
χ24111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-1−i−i−i−iiiii−i−i−i−iiiii1-1−i−i−i−iiiii−i−i−i−iiiii1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−iii−i−iii11-1-111-1-11-11-1−ii−ii
χ25111-1-1-1-11-1-1-1-111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-11iiii−i−i−i−i−i−i−i−iiiii1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii−i−iiiii−i−i1-1-111-1-11
χ26111-1-1-1-11-1-1-1-111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-11iiii−i−i−i−i−i−i−i−iiiii1-111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−iii−i−i−i−iii-111-1-111-1
χ27111-1-1-1-11-1-1-1-111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-11−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii−i−iiiii−i−i-111-1-111-1
χ28111-1-1-1-11-1-1-1-111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-11−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−iii−i−i−i−iii1-1-111-1-11
χ29111-1-1-1-11-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11iiii−i−i−i−i−i−i−i−iiiii1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iiiii−i−i−i−iii1-1-11-111-1
χ30111-1-1-1-11-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11iiii−i−i−i−i−i−i−i−iiiii1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i−i−iiiii−i−i-111-11-1-11
χ31111-1-1-1-11-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11−i−i−i−iiiiiiiii−i−i−i−i1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iiiii−i−i−i−iii-111-11-1-11
χ32111-1-1-1-11-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11−i−i−i−iiiiiiiii−i−i−i−i1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i−i−iiiii−i−i1-1-11-111-1
χ33222222222222222222-2-222-2-2-2-222-2-2222222222222222222-2-20000000000000000-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ34222222222222222222-2-222-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2222222220000000000000000000000000000000000000000
χ352222222222222222-2-222-2-22222-2-222-2-20000000000000000-2-222-2-222-2-222-2-222-2-2-2-2000000000000000000000000000000000000000000000000
χ362222222222222222-2-222-2-22222-2-222-2-20000000000000000-2-2-2-222-2-222-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ372222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022000000000000000022000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ382222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000002200000000000000002200000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-222-2-22i2i2i2i2i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i220000000000000000-2-2−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-222-2-22222-2-2-2-222-2-2−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i2i2i2i2i220000000000000000-2-22i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-22200000000000000002222-2-222-2-2-2-222-2-222-2-2000000000000000000000000000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-222000000000000000022-2-222-2-22222-2-222-2-2-2-2000000000000000000000000000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222220000000000000000-2-20000000000000000220000000022-2-222-2-2-2-222-2-222000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222220000000000000000-2-200000000000000002200000000-2-222-2-22222-2-222-2-2000000000000000000000000
χ45222-2-2-2-222222-2-2-2-222-2-2-2-2222222-2-2-2-22i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i-220000000000000000-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ46222-2-2-2-222222-2-2-2-222-2-2-2-2222222-2-2-2-2−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i-220000000000000000-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ47222-2-2-2-222222-2-2-2-2-2-22222-2-2-2-2-2-222220000000000000000-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i-22000000000000000000000000000000000000000000000000
χ48222-2-2-2-222222-2-2-2-2-2-22222-2-2-2-2-2-222220000000000000000-22−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-22000000000000000000000000000000000000000000000000
χ49222-2-2-2-222222-2-2-2-2-2-2-2-2222222-2-2-2-22200000000000000002-200000000000000002-2000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ50222-2-2-2-222222-2-2-2-2-2-2-2-2222222-2-2-2-22200000000000000002-200000000000000002-200000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ51222-2-2-2-22-2-2-2-2222222-2-2-2-2-2-222-2-222222222-2-2-2-2-2-2-2-222222-20000000000000000-22-2-22222-2-20000000000000000000000000000000000000000
χ52222-2-2-2-22-2-2-2-2222222-2-2-2-2-2-222-2-22222-2-2-2-222222222-2-2-2-22-20000000000000000-2222-2-2-2-2220000000000000000000000000000000000000000
χ53222-2-2-2-22-2-2-2-22222-2-2222222-2-222-2-2-2-200000000000000002-22i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-22000000000000000000000000000000000000000000000000
χ54222-2-2-2-22-2-2-2-22222-2-2222222-2-222-2-2-2-200000000000000002-2−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i-22000000000000000000000000000000000000000000000000
χ55222-2-2-2-22-2-2-2-22222-2-2-2-222-2-2222222-2-20000000000000000-2200000000000000002-20000000022-2-2-2-222-2-22222-2-2000000000000000000000000
χ56222-2-2-2-22-2-2-2-22222-2-2-2-222-2-2222222-2-20000000000000000-2200000000000000002-200000000-2-22222-2-222-2-2-2-222000000000000000000000000
χ5722-222-2-2-22i2i−2i−2i2i−2i2i−2i002-2002i−2i2-2002i−2i001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00002i−2i002i−2i002-2002-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i000000000000000000000000
χ5822-222-2-2-22i2i−2i−2i2i−2i2i−2i002-2002i−2i2-2002i−2i001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0000−2i2i00−2i2i00-2200-22001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i000000000000000000000000
χ5922-222-2-2-22i2i−2i−2i2i−2i2i−2i002-2002i−2i2-2002i−2i00−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00002i−2i002i−2i002-2002-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i000000000000000000000000
χ6022-222-2-2-22i2i−2i−2i2i−2i2i−2i002-2002i−2i2-2002i−2i00−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0000−2i2i00−2i2i00-2200-2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i000000000000000000000000
χ6122-222-2-2-22i2i−2i−2i2i−2i2i−2i00-2200−2i2i-2200−2i2i001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i002-2002-2002i−2i002i−2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i1−i−1+i000000000000000000000000
χ6222-222-2-2-22i2i−2i−2i2i−2i2i−2i00-2200−2i2i-2200−2i2i001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00-2200-2200−2i2i00−2i2i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i000000000000000000000000
χ6322-222-2-2-22i2i−2i−2i2i−2i2i−2i00-2200−2i2i-2200−2i2i00−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i002-2002-2002i−2i002i−2i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i−1+i1−i000000000000000000000000
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χ962-222-22-2-2−2i2i−2i2i−2i2i2i−2i2-2002-20000−2i2i00−2i2i−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ32ζ3−2ζ32ζ300000000000000000000000000000000000000000000−22−22i2−i2i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ972-22-22-22-22i−2i2i−2i−2i2i2i−2i2-200-2200002i−2i00−2i2i2ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ300000000000000000000000000000000000000000000i2−i2−i2i2−222−2−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ982-22-22-22-22i−2i2i−2i−2i2i2i−2i2-200-2200002i−2i00−2i2i2ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ3−2ζ300000000000000000000000000000000000000000000−i2i2i2−i22−2−221−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
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χ1054-444-44-4-44i−4i4i−4i4i−4i−4i4i-4400-440000−4i4i00−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1064-444-44-4-4−4i4i−4i4i−4i4i4i−4i-4400-4400004i−4i004i−4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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χ1114-4-44-4-444-444-4-4-444000000000000000022−22−222222−22−2222−222222−22−222222−2200000000000000000000000000000000000000000000000000000000000000000000
χ1124-4-44-4-444-444-4-4-4440000000000000000−222222−22−222222−2222−22−222222−22−222200000000000000000000000000000000000000000000000000000000000000000000
χ1134-4-4-444-444-4-44-4-444000000000000000022−22−2222−222222−2222−22−2222−222222−2200000000000000000000000000000000000000000000000000000000000000000000
χ1144-4-4-444-444-4-44-4-4440000000000000000−222222−2222−22−2222−222222−2222−22−222200000000000000000000000000000000000000000000000000000000000000000000
χ1154-4-4-444-44-444-444-4-400000000000000002i2−2i2−2i22i2−2i22i22i2−2i2−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000000000000000000000000000000000
χ1164-4-4-444-44-444-444-4-40000000000000000−2i22i22i2−2i22i2−2i2−2i22i22i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000000000000000000000000000000000

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