Finite Group Databasebeta

← Group #13016900

Character table — Group #13016900

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222224444444444555555558888888888888888101010101010101016161616161616162020202020202020202020202020202020202020202020202020202020202020202040404040
order12224444224488885881010102020202044444444448810102020404040404040404044448888202020204040404088888888888888888888888888888888882488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii1111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i1111
χ9111111111111-1-1-1-11-1-111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ10111111111111-1-1-1-11-1-111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ11111111111111-1-1-1-11-1-1111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ12111111111111-1-1-1-11-1-1111111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111
χ13111111111111-1-1-1-11-1-11111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111
χ14111111111111-1-1-1-11-1-11111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ15111111111111-1-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i11-1-1
χ16111111111111-1-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-1
χ171111-1-1-1-1-1-111ii−i−i1i−i111-1-1-1-11111-1-1-1-11-1i−i-1-111iiii−i−i−i−i11-1-1ii−i−i11-1-1ii−i−ii−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−i
χ181111-1-1-1-1-1-111ii−i−i1i−i111-1-1-1-11111-1-1-1-11-1i−i-1-111iiii−i−i−i−i11-1-1ii−i−i11-1-1ii−i−ii−i-1-111−i−iii-1-111−i−iii-1-111−i−iii-1-111−i−iii1-1i−i
χ191111-1-1-1-1-1-111ii−i−i1i−i111-1-1-1-11111-1-1-1-1-11−ii-1-111iiii−i−i−i−i11-1-1ii−i−i-1-111−i−iiii−i11-1-1ii−i−i11-1-1ii−i−i-1-111−i−iii-1-111−i−iii-11−ii
χ201111-1-1-1-1-1-111ii−i−i1i−i111-1-1-1-11111-1-1-1-1-11−ii-1-111iiii−i−i−i−i11-1-1ii−i−i-1-111−i−iiii−i-1-111−i−iii-1-111−i−iii11-1-1ii−i−i11-1-1ii−i−i-11−ii
χ211111-1-1-1-1-1-111ii−i−i1i−i111-1-1-1-1-1-1-1-111111-1i−i-1-111iiii−i−i−i−i-1-111−i−iii11-1-1ii−i−i−iiii−i−i-1-111−i−iii11-1-1ii−i−i-1-111−i−iii11-1-1-11−ii
χ221111-1-1-1-1-1-111ii−i−i1i−i111-1-1-1-1-1-1-1-111111-1i−i-1-111iiii−i−i−i−i-1-111−i−iii11-1-1ii−i−i−ii−i−iii11-1-1ii−i−i-1-111−i−iii11-1-1ii−i−i-1-111-11−ii
χ231111-1-1-1-1-1-111ii−i−i1i−i111-1-1-1-1-1-1-1-11111-11−ii-1-111iiii−i−i−i−i-1-111−i−iii-1-111−i−iii−iiii−i−i-1-111−i−iii11-1-1−i−iii11-1-1ii−i−i-1-1111-1i−i
χ241111-1-1-1-1-1-111ii−i−i1i−i111-1-1-1-1-1-1-1-11111-11−ii-1-111iiii−i−i−i−i-1-111−i−iii-1-111−i−iii−ii−i−iii11-1-1ii−i−i-1-111ii−i−i-1-111−i−iii11-1-11-1i−i
χ251111-1-1-1-1-1-111−i−iii1−ii111-1-1-1-11111-1-1-1-11-1−ii-1-111−i−i−i−iiiii11-1-1−i−iii11-1-1−i−iii−ii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii
χ261111-1-1-1-1-1-111−i−iii1−ii111-1-1-1-11111-1-1-1-11-1−ii-1-111−i−i−i−iiiii11-1-1−i−iii11-1-1−i−iii−ii-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i-1-111ii−i−i1-1−ii
χ271111-1-1-1-1-1-111−i−iii1−ii111-1-1-1-11111-1-1-1-1-11i−i-1-111−i−i−i−iiiii11-1-1−i−iii-1-111ii−i−i−ii11-1-1−i−iii11-1-1−i−iii-1-111ii−i−i-1-111ii−i−i-11i−i
χ281111-1-1-1-1-1-111−i−iii1−ii111-1-1-1-11111-1-1-1-1-11i−i-1-111−i−i−i−iiiii11-1-1−i−iii-1-111ii−i−i−ii-1-111ii−i−i-1-111ii−i−i11-1-1−i−iii11-1-1−i−iii-11i−i
χ291111-1-1-1-1-1-111−i−iii1−ii111-1-1-1-1-1-1-1-111111-1−ii-1-111−i−i−i−iiiii-1-111ii−i−i11-1-1−i−iiii−iii−i−i11-1-1−i−iii-1-111ii−i−i11-1-1−i−iii-1-111-11i−i
χ301111-1-1-1-1-1-111−i−iii1−ii111-1-1-1-1-1-1-1-111111-1−ii-1-111−i−i−i−iiiii-1-111ii−i−i11-1-1−i−iiii−i−i−iii-1-111ii−i−i11-1-1−i−iii-1-111ii−i−i11-1-1-11i−i
χ311111-1-1-1-1-1-111−i−iii1−ii111-1-1-1-1-1-1-1-11111-11i−i-1-111−i−i−i−iiiii-1-111ii−i−i-1-111ii−i−ii−iii−i−i11-1-1−i−iii-1-111−i−iii-1-111ii−i−i11-1-11-1−ii
χ321111-1-1-1-1-1-111−i−iii1−ii111-1-1-1-1-1-1-1-11111-11i−i-1-111−i−i−i−iiiii-1-111ii−i−i-1-111ii−i−ii−i−i−iii-1-111ii−i−i11-1-1ii−i−i11-1-1−i−iii-1-1111-1−ii
χ3322222222-2-2-2-222222-2-22222222222222220000-2-2-2-222-2-222-2-2-2-2-2-2222200000000-2-2000000000000000000000000000000000000
χ3422222222-2-2-2-222222-2-22222222-2-2-2-2-2-2-2-20000-2-2-2-222-2-222-2-22222-2-2-2-20000000022000000000000000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-22222222222222222220000-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-20000000022000000000000000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-20000-2-2-2-2-2-222-2-2222222222200000000-2-2000000000000000000000000000000000000
χ372222-2-2-2-222-2-22i2i−2i−2i2−2i2i222-2-2-2-22222-2-2-2-2000022-2-22i2i−2i−2i−2i−2i2i2i-2-2222i2i−2i−2i00000000−2i2i000000000000000000000000000000000000
χ382222-2-2-2-222-2-22i2i−2i−2i2−2i2i222-2-2-2-2-2-2-2-22222000022-2-22i2i−2i−2i−2i−2i2i2i22-2-2−2i−2i2i2i000000002i−2i000000000000000000000000000000000000
χ392222-2-2-2-222-2-2−2i−2i2i2i22i−2i222-2-2-2-22222-2-2-2-2000022-2-2−2i−2i2i2i2i2i−2i−2i-2-222−2i−2i2i2i000000002i−2i000000000000000000000000000000000000
χ402222-2-2-2-222-2-2−2i−2i2i2i22i−2i222-2-2-2-2-2-2-2-22222000022-2-2−2i−2i2i2i2i2i−2i−2i22-2-22i2i−2i−2i00000000−2i2i000000000000000000000000000000000000
χ4122-2-222-2-22-22-200002002-2-2-2-2222i2i−2i−2i2i2i−2i−2i00002-22-2000000002i−2i2i−2i000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000000000
χ4222-2-222-2-22-22-200002002-2-2-2-2222i2i−2i−2i2i2i−2i−2i00002-22-2000000002i−2i2i−2i0000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000000000
χ4322-2-222-2-22-22-200002002-2-2-2-222−2i−2i2i2i−2i−2i2i2i00002-22-200000000−2i2i−2i2i000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000000000
χ4422-2-222-2-22-22-200002002-2-2-2-222−2i−2i2i2i−2i−2i2i2i00002-22-200000000−2i2i−2i2i0000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000000000
χ4522-2-222-2-2-22-2200002002-2-2-2-2222i2i−2i−2i2i2i−2i−2i0000-22-2200000000−2i2i−2i2i00000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000000000
χ4622-2-222-2-2-22-2200002002-2-2-2-2222i2i−2i−2i2i2i−2i−2i0000-22-2200000000−2i2i−2i2i000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000000000
χ4722-2-222-2-2-22-2200002002-2-2-2-222−2i−2i2i2i−2i−2i2i2i0000-22-22000000002i−2i2i−2i00000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000000000
χ4822-2-222-2-2-22-2200002002-2-2-2-222−2i−2i2i2i−2i−2i2i2i0000-22-22000000002i−2i2i−2i000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000000000
χ4922-2-2-2-2222-2-2200002002-2-222-2-22i2i−2i−2i−2i−2i2i2i00002-2-2200000000−2i2i2i−2i00000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000000000
χ5022-2-2-2-2222-2-2200002002-2-222-2-22i2i−2i−2i−2i−2i2i2i00002-2-2200000000−2i2i2i−2i000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000000000
χ5122-2-2-2-2222-2-2200002002-2-222-2-2−2i−2i2i2i2i2i−2i−2i00002-2-22000000002i−2i−2i2i00000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000000000
χ5222-2-2-2-2222-2-2200002002-2-222-2-2−2i−2i2i2i2i2i−2i−2i00002-2-22000000002i−2i−2i2i000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000000000
χ5322-2-2-2-222-222-200002002-2-222-2-22i2i−2i−2i−2i−2i2i2i0000-222-2000000002i−2i−2i2i000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000000000
χ5422-2-2-2-222-222-200002002-2-222-2-22i2i−2i−2i−2i−2i2i2i0000-222-2000000002i−2i−2i2i0000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000000000
χ5522-2-2-2-222-222-200002002-2-222-2-2−2i−2i2i2i2i2i−2i−2i0000-222-200000000−2i2i2i−2i000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000000000
χ5622-2-2-2-222-222-200002002-2-222-2-2−2i−2i2i2i2i2i−2i−2i0000-222-200000000−2i2i2i−2i0000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.