Finite Group Databasebeta

← Group #13026876

Character table — Group #13026876

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1122222444558888888881010101010101010101616161616162020202020202032323232404040404040404040404040808080
order1224488581044241016162020404022444448844080808080448888810202020244444161616161616288
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-1-1-1111111111-1-11-1-1-1-1111111-1-1-1-111-1-1-1-11-1-1
χ3111111111111111-1-11111111111111-11-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1-1-1
χ4111111111111111-1-1111111-1-1-1-1111-11-1-1-1-1-1-11-1-1-1-111-1-111-1-1-1-1-1-11111-111
χ5111111111111-1-11111111111111111-1111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1
χ6111111111111-1-1111111111-1-1-1-1111-111111-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111
χ7111111111111-1-11-1-1111111111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111
χ8111111111111-1-11-1-1111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1-1-111-1-11111-1-111111-1-1
χ91111111111-1-1111111111-1-1ii−i−i-1-1-1111111i−i-1ii−i−i1111-1-1ii−i−i-1-1ii−i−i-1i−i
χ101111111111-1-1111111111-1-1−i−iii-1-1-1111111−ii-1−i−iii1111-1-1−i−iii-1-1−i−iii-1−ii
χ111111111111-1-1111-1-11111-1-1ii−i−i-1-1-1-11-1-1-1-1i−i-1ii−i−i11-1-1-1-1ii−i−i11−i−iii1−ii
χ121111111111-1-1111-1-11111-1-1−i−iii-1-1-1-11-1-1-1-1−ii-1−i−iii11-1-1-1-1−i−iii11ii−i−i1i−i
χ131111111111-1-1-1-11111111-1-1ii−i−i-1-1-1-111111i−i-1ii−i−i-1-1-1-111−i−iii-1-1ii−i−i1−ii
χ141111111111-1-1-1-11111111-1-1−i−iii-1-1-1-111111−ii-1−i−iii-1-1-1-111ii−i−i-1-1−i−iii1i−i
χ151111111111-1-1-1-11-1-11111-1-1ii−i−i-1-1-111-1-1-1-1i−i-1ii−i−i-1-11111−i−iii11−i−iii-1i−i
χ161111111111-1-1-1-11-1-11111-1-1−i−iii-1-1-111-1-1-1-1−ii-1−i−iii-1-11111ii−i−i11ii−i−i-1−ii
χ1722222-2-22-22220020022-2-22222222-2-20-2000022-2-2-2-2-20000000000000000000
χ1822222-2-22-22220020022-2-222-2-2-2-22-2-20-20000-2-2-222220000000000000000000
χ1922222-2-22-22-2-20020022-2-2-2-22i2i−2i−2i-2220-200002i−2i2−2i−2i2i2i0000000000000000000
χ2022222-2-22-22-2-20020022-2-2-2-2−2i−2i2i2i-2220-20000−2i2i22i2i−2i−2i0000000000000000000
χ2122-22-2002022200-22−22-200-222222-2000022−2−2-2-20000000000000002−22−22−2000
χ2222-22-2002022200-22−22-200-22-2-2-2-2-2000022−2−2220000000000000002−2−22−22000
χ2322-22-2002022200-2−222-200-222222-20000−2−222-2-2000000000000000−22−22−22000
χ2422-22-2002022200-2−222-200-22-2-2-2-2-20000−2−22222000000000000000−222−22−2000
χ2522-22-200202-2-200-22−22-2002-22i2i−2i−2i2000022−2−2−2i2i000000000000000−22i2−i2−i2i2000
χ2622-22-200202-2-200-22−22-2002-2−2i−2i2i2i2000022−2−22i−2i000000000000000−22−i2i2i2−i2000
χ2722-22-200202-2-200-2−222-2002-22i2i−2i−2i20000−2−222−2i2i0000000000000002−2−i2i2i2−i2000
χ2822-22-200202-2-200-2−222-2002-2−2i−2i2i2i20000−2−2222i−2i0000000000000002−2i2−i2−i2i2000
χ2922-2-22222-22222-2-200-22222-20000-2220-2000000-200002-200-220000000000000
χ3022-2-22222-2222-22-200-22222-20000-2220-2000000-20000-22002-20000000000000
χ3122-2-22222-22-2-22-2-200-2222-2200002-2-20-2000000200002-2002-20000000000000
χ3222-2-22222-22-2-2-22-200-2222-2200002-2-20-200000020000-2200-220000000000000
χ3322-2-22-2-22222200-200-22-2-22-20000-2-2-202000000200000000002i−2i2i−2i000000000
χ3422-2-22-2-22222200-200-22-2-22-20000-2-2-20200000020000000000−2i2i−2i2i000000000
χ3522-2-22-2-2222-2-200-200-22-2-2-22000022202000000-200000000002-2-22000000000
χ3622-2-22-2-2222-2-200-200-22-2-2-22000022202000000-20000000000-222-2000000000
χ374444444-14-10044-144-1-1-1-10000000004-1-1-1-1-10000000-1-1-1-1000000000000000
χ384444444-14-10044-1-4-4-1-1-1-1000000000-4-111110000000-1-111000000000000000
χ394444444-14-100-4-4-144-1-1-1-1000000000-4-1-1-1-1-100000001111000000000000000
χ404444444-14-100-4-4-1-4-4-1-1-1-10000000004-11111000000011-1-1000000000000000
χ41444-4-4004044400400-4-400-4-4000040000000000000000000000000000000000
χ42444-4-400404-4-400400-4-400440000-40000000000000000000000000000000000
χ4344-4-4444-1-4-1004-41001-1-1-1000000000015−55−50000000-115−5000000000000000
χ4444-4-4444-1-4-1004-41001-1-1-100000000001−55−550000000-11−55000000000000000
χ4544-4-4444-1-4-100-441001-1-1-1000000000015−55−500000001-1−55000000000000000
χ4644-4-4444-1-4-100-441001-1-1-100000000001−55−5500000001-15−5000000000000000
χ474-400022−2240-44i−4i000000022−22002+2i−2−2i2−2i−2+2i02i2−2i2000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000000000000
χ484-400022−2240-44i−4i000000022−2200−2−2i2+2i−2+2i2−2i02i2−2i20000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000000000000
χ494-400022−2240-4−4i4i000000022−22002−2i−2+2i2+2i−2−2i0−2i22i20000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000000000000
χ504-400022−2240-4−4i4i000000022−2200−2+2i2−2i−2−2i2+2i0−2i22i2000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000000000000
χ514-4000−222240-44i−4i0000000−2222002+2i−2−2i2−2i−2+2i0−2i22i20000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000000000000
χ524-4000−222240-44i−4i0000000−222200−2−2i2+2i−2+2i2−2i0−2i22i2000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000000000000
χ534-4000−222240-4−4i4i0000000−2222002−2i−2+2i2+2i−2−2i02i2−2i2000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000000000000
χ544-4000−222240-4−4i4i0000000−222200−2+2i2−2i−2−2i2+2i02i2−2i20000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000000000000
χ5588888-8-8-2-8-20000-200-2-22200000000002000000000000000000000000000000
χ56888-8-800-20-20000-20022000000000000010−10−101000000000000000000000000000
χ57888-8-800-20-20000-200220000000000000−101010−1000000000000000000000000000
χ5888-88-800-20-20000242−42-220000000000000−2−22200000000000000000000000000
χ5988-88-800-20-200002−4242-22000000000000022−2−200000000000000000000000000
χ6088-8-88-8-8-28-200002002-2220000000000-2000000000000000000000000000000
χ6116-1600082−82-404000000000−222200000000000000000000000000000000000000000
χ6216-16000−8282-40400000000022−2200000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.