Finite Group Databasebeta

← Group #13016944

Character table — Group #13016944

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222244444444444444445555555588888888888888101010101010101010101010161616161616161620202020202020202020202020202020202020202020202020202020404040404040
order12224444444458888888810101020202020444444444420202020404040404040404022448888888820202020404040404444444488888888888888888888248888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1iiii−i−i−i−i11111111iiii−i−i−i−i-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i-1-1ii−i−i
χ41111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1−i−i−i−iiiii11111111−i−i−i−iiiii-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii-1-1−i−iii
χ511111111111111111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1
χ611111111111111111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−iii−i−i11−i−iii
χ811111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii−i−iii11ii−i−i
χ91111111111111-1-1-1-11111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ101111111111111-1-1-1-11111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111
χ111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiiiii−i−i11−i−iii
χ121111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i−i−iii11ii−i−i
χ131111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ141111111111111-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1
χ151111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii11111111−i−i−i−iiiiiii−i−i-1-1ii−i−i
χ161111111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i11111111iiii−i−i−i−i−i−iii-1-1−i−iii
χ171111-1-1-1-111-1-11ii−i−iii−i−i111-1-1-1-11111-1-1-1-11-111-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-1ii−i−i11-1-111-1-1ii−i−iii−i−i11-1-111-1-1i−ii−i1-1i−ii−i
χ181111-1-1-1-111-1-11ii−i−iii−i−i111-1-1-1-11111-1-1-1-11-111-1-1iiii−i−i−i−i11-1-1−i−iii−i−iii11-1-1ii−i−i-1-111-1-111ii−i−iii−i−i-1-111-1-111−ii−ii1-1−ii−ii
χ191111-1-1-1-111-1-11ii−i−iii−i−i111-1-1-1-1-1-1-1-111111-111-1-1iiii−i−i−i−i-1-11111-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii−i−iii−i−iiiii−i−i1-1-11-111-1-11
χ201111-1-1-1-111-1-11ii−i−iii−i−i111-1-1-1-1-1-1-1-111111-111-1-1iiii−i−i−i−i-1-111-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii−i−iiiii−i−i−i−iii-111-1-11-111-1
χ211111-1-1-1-111-1-11ii−i−i−i−iii111-1-1-1-11111-1-1-1-1-1111-1-1−i−i−i−iiiii11-1-1ii−i−iii−i−i-1-111ii−i−i-1-111-1-111ii−i−i−i−iii11-1-111-1-1i−ii−i-11−ii−ii
χ221111-1-1-1-111-1-11ii−i−i−i−iii111-1-1-1-11111-1-1-1-1-1111-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii-1-111ii−i−i11-1-111-1-1ii−i−i−i−iii-1-111-1-111−ii−ii-11i−ii−i
χ231111-1-1-1-111-1-11ii−i−i−i−iii111-1-1-1-1-1-1-1-11111-1111-1-1−i−i−i−iiiii-1-11111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i1-1-111-1-111-1
χ241111-1-1-1-111-1-11ii−i−i−i−iii111-1-1-1-1-1-1-1-11111-1111-1-1−i−i−i−iiiii-1-111-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iii-111-11-11-1-11
χ251111-1-1-1-111-1-11−i−iiiii−i−i111-1-1-1-11111-1-1-1-1-1111-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i-1-111−i−iii11-1-111-1-1−i−iiiii−i−i-1-111-1-111i−ii−i-11−ii−ii
χ261111-1-1-1-111-1-11−i−iiiii−i−i111-1-1-1-11111-1-1-1-1-1111-1-1iiii−i−i−i−i11-1-1−i−iii−i−iii-1-111−i−iii-1-111-1-111−i−iiiii−i−i11-1-111-1-1−ii−ii-11i−ii−i
χ271111-1-1-1-111-1-11−i−iiiii−i−i111-1-1-1-1-1-1-1-11111-1111-1-1iiii−i−i−i−i-1-11111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii1-1-111-1-111-1
χ281111-1-1-1-111-1-11−i−iiiii−i−i111-1-1-1-1-1-1-1-11111-1111-1-1iiii−i−i−i−i-1-111-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i-111-11-11-1-11
χ291111-1-1-1-111-1-11−i−iii−i−iii111-1-1-1-11111-1-1-1-11-111-1-1−i−i−i−iiiii11-1-1ii−i−iii−i−i11-1-1−i−iii-1-111-1-111−i−iii−i−iii-1-111-1-111i−ii−i1-1i−ii−i
χ301111-1-1-1-111-1-11−i−iii−i−iii111-1-1-1-11111-1-1-1-11-111-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-1−i−iii11-1-111-1-1−i−iii−i−iii11-1-111-1-1−ii−ii1-1−ii−ii
χ311111-1-1-1-111-1-11−i−iii−i−iii111-1-1-1-1-1-1-1-111111-111-1-1−i−i−i−iiiii-1-11111-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−iii−i−iii−i−i−i−iii1-1-11-111-1-11
χ321111-1-1-1-111-1-11−i−iii−i−iii111-1-1-1-1-1-1-1-111111-111-1-1−i−i−i−iiiii-1-111-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−iii−i−i−i−iiiii−i−i-111-1-11-111-1
χ3322222222-2-2-2-220000000022222222222222200-2-2-2-200000000-2-2-2-22222222200000000000000000000000000000000-2-2-2-2000000
χ3422222222-2-2-2-220000000022222222222222200-2-2-2-200000000-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000002222000000
χ3522222222-2-2-2-22000000002222222-2-2-2-2-2-2-2-200-2-2-2-20000000022222i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000−2i−2i2i2i000000
χ3622222222-2-2-2-22000000002222222-2-2-2-2-2-2-2-200-2-2-2-2000000002222−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000002i2i−2i−2i000000
χ372222-2-2-2-2-2-222200000000222-2-2-2-22222-2-2-2-200-2-22200000000-2-2222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000−2i2i−2i2i000000
χ382222-2-2-2-2-2-222200000000222-2-2-2-22222-2-2-2-200-2-22200000000-2-222−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000002i−2i2i−2i000000
χ392222-2-2-2-2-2-222200000000222-2-2-2-2-2-2-2-2222200-2-2220000000022-2-222-2-2-2-22200000000000000000000000000000000-222-2000000
χ402222-2-2-2-2-2-222200000000222-2-2-2-2-2-2-2-2222200-2-2220000000022-2-2-2-22222-2-2000000000000000000000000000000002-2-22000000
χ4122-2-22i−2i2i−2i0000200001−i−1+i1+i−1−i-22-22i−2i2i−2i2i2i−2i−2i22-2-20000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00002-22i−2i2i−2i2-2000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00001+i−1−i1−i−1+i000000000000000000
χ4222-2-22i−2i2i−2i0000200001−i−1+i1+i−1−i-22-22i−2i2i−2i2i2i−2i−2i22-2-20000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000-22−2i2i−2i2i-2200000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00001+i−1−i1−i−1+i000000000000000000
χ4322-2-22i−2i2i−2i0000200001−i−1+i1+i−1−i-22-22i−2i2i−2i−2i−2i2i2i-2-2220000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00002i−2i-222-2−2i2i00000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000−1−i1+i−1+i1−i000000000000000000
χ4422-2-22i−2i2i−2i0000200001−i−1+i1+i−1−i-22-22i−2i2i−2i−2i−2i2i2i-2-2220000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000−2i2i2-2-222i−2i000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000−1−i1+i−1+i1−i000000000000000000
χ4522-2-22i−2i2i−2i000020000−1+i1−i−1−i1+i-22-22i−2i2i−2i2i2i−2i−2i22-2-2000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00002-22i−2i2i−2i2-200000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000−1−i1+i−1+i1−i000000000000000000
χ4622-2-22i−2i2i−2i000020000−1+i1−i−1−i1+i-22-22i−2i2i−2i2i2i−2i−2i22-2-2000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000-22−2i2i−2i2i-22000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000−1−i1+i−1+i1−i000000000000000000
χ4722-2-22i−2i2i−2i000020000−1+i1−i−1−i1+i-22-22i−2i2i−2i−2i−2i2i2i-2-222000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00002i−2i-222-2−2i2i000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00001+i−1−i1−i−1+i000000000000000000
χ4822-2-22i−2i2i−2i000020000−1+i1−i−1−i1+i-22-22i−2i2i−2i−2i−2i2i2i-2-222000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000−2i2i2-2-222i−2i00000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00001+i−1−i1−i−1+i000000000000000000
χ4922-2-2−2i2i−2i2i0000200001+i−1−i1−i−1+i-22-2−2i2i−2i2i2i2i−2i−2i-2-2220000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00002i−2i2-2-22−2i2i000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000−1+i1−i−1−i1+i000000000000000000
χ5022-2-2−2i2i−2i2i0000200001+i−1−i1−i−1+i-22-2−2i2i−2i2i2i2i−2i−2i-2-2220000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000−2i2i-222-22i−2i00000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000−1+i1−i−1−i1+i000000000000000000
χ5122-2-2−2i2i−2i2i0000200001+i−1−i1−i−1+i-22-2−2i2i−2i2i−2i−2i2i2i22-2-20000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00002-2−2i2i−2i2i2-2000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00001−i−1+i1+i−1−i000000000000000000
χ5222-2-2−2i2i−2i2i0000200001+i−1−i1−i−1+i-22-2−2i2i−2i2i−2i−2i2i2i22-2-20000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000-222i−2i2i−2i-2200000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00001−i−1+i1+i−1−i000000000000000000
χ5322-2-2−2i2i−2i2i000020000−1−i1+i−1+i1−i-22-2−2i2i−2i2i2i2i−2i−2i-2-222000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00002i−2i2-2-22−2i2i00000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00001−i−1+i1+i−1−i000000000000000000
χ5422-2-2−2i2i−2i2i000020000−1−i1+i−1+i1−i-22-2−2i2i−2i2i2i2i−2i−2i-2-222000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000−2i2i-222-22i−2i000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00001−i−1+i1+i−1−i000000000000000000
χ5522-2-2−2i2i−2i2i000020000−1−i1+i−1+i1−i-22-2−2i2i−2i2i−2i−2i2i2i22-2-2000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00002-2−2i2i−2i2i2-200000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000−1+i1−i−1−i1+i000000000000000000
χ5622-2-2−2i2i−2i2i000020000−1−i1+i−1+i1−i-22-2−2i2i−2i2i−2i−2i2i2i22-2-2000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000-222i−2i2i−2i-22000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000−1+i1−i−1−i1+i000000000000000000
χ572-22-22i−2i−2i2i2-22i−2i200000000-2-22−2i2i2i−2i2-22-22i−2i2i−2i002-22i−2i000000002-22i−2i000000000000000000000000000000002-22i−2i2-22i−2i0000000000
χ582-22-22i−2i−2i2i2-22i−2i200000000-2-22−2i2i2i−2i2-22-22i−2i2i−2i002-22i−2i000000002-22i−2i00000000000000000000000000000000-22−2i2i-22−2i2i0000000000
χ592-22-22i−2i−2i2i2-22i−2i200000000-2-22−2i2i2i−2i-22-22−2i2i−2i2i002-22i−2i00000000-22−2i2i000000000000000000000000000000002i−2i-22−2i2i2-20000000000
χ602-22-22i−2i−2i2i2-22i−2i200000000-2-22−2i2i2i−2i-22-22−2i2i−2i2i002-22i−2i00000000-22−2i2i00000000000000000000000000000000−2i2i2-22i−2i-220000000000
χ612-22-22i−2i−2i2i-22−2i2i2−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000-2-22−2i2i2i−2i2-22-22i−2i2i−2i00-22−2i2i00000000-22−2i2i000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000000000000000
χ622-22-22i−2i−2i2i-22−2i2i2−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000-2-22−2i2i2i−2i-22-22−2i2i−2i2i00-22−2i2i000000002-22i−2i000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.