Finite Group Databasebeta

← Group #13019414

Character table — Group #13019414

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size111122224444444445555888888888888888810101010162020202020202020202020202032323232404040404040404040404040404080
order12224444458888101010444444202020202020404040404040404022444488888888888820202020444444888888884
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11
χ3111111111111111111111-1-1111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1
χ4111111111111111111111-1-1111111111111111111-111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1-1-1
χ511111111111111111-1-1-1-11111111111111111-1-1-1-11-1-1-1-1-1ii−i−iii−i−i1111-1-1ii−i−ii−ii−iii−i−i-1
χ611111111111111111-1-1-1-11111111111111111-1-1-1-11-1-1-1-1-1−i−iii−i−iii1111-1-1−i−iii−ii−ii−i−iii-1
χ711111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iii-1-1-1-111−i−iiii−i−iiii−i−i1
χ811111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i-1-1-1-111ii−i−i−iii−i−i−iii1
χ91111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-11-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1
χ101111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1
χ111111111111-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11
χ121111111111-1-1-1-11111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111111
χ131111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i11-1-1-1-1−i−iiii−ii−i−i−iii1
χ141111111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iii11-1-1-1-1ii−i−i−ii−iiii−i−i1
χ151111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11111ii−i−i−i−iii-1-11111ii−i−ii−i−ii−i−iii-1
χ161111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11111−i−iiiii−i−i-1-11111−i−iii−iii−iii−i−i-1
χ17222222-2-2-22000022222220022-2-2-2-20000000022-2-20-20000222200000000000000-2-20000000
χ18222222-2-2-22000022222220022-2-2-2-20000000022-2-20-20000-2-2-2-200000000000000220000000
χ19222222-2-2-220000222-2-2-2-20022-2-2-2-200000000-2-2220200002i2i−2i−2i00000000000000−2i2i0000000
χ20222222-2-2-220000222-2-2-2-20022-2-2-2-200000000-2-222020000−2i−2i2i2i000000000000002i−2i0000000
χ212222-2-222-220000222222200-2-222-2-200000000-2-2220-2000000002222000000000000-2-200000
χ222222-2-222-220000222222200-2-222-2-200000000-2-2220-200000000-2-2-2-20000000000002200000
χ232222-2-222-220000222-2-2-2-200-2-222-2-20000000022-2-202000000002i2i−2i−2i000000000000−2i2i00000
χ242222-2-222-220000222-2-2-2-200-2-222-2-20000000022-2-20200000000−2i−2i2i2i0000000000002i−2i00000
χ252222-2-2-2-222000022222222-2-2-2-2-22200000000-2-2-2-2020000000000002-2002-20000000000000
χ262222-2-2-2-22200002222222-22-2-2-2-22200000000-2-2-2-202000000000000-2200-220000000000000
χ272222-2-2-2-2220000222-2-2-2-22-2-2-2-2-2220000000022220-20000000000002-200-220000000000000
χ282222-2-2-2-2220000222-2-2-2-2-22-2-2-2-2220000000022220-2000000000000-22002-20000000000000
χ2922-2-22-2000222−2−22-2-222-2-2002-200002222−2−2−2−22-2000022−2−22-22-20000000000000000002−22−20
χ3022-2-22-2000222−2−22-2-222-2-2002-200002222−2−2−2−22-2000022−2−2-22-22000000000000000000−22−220
χ3122-2-22-2000222−2−22-2-2-2-222002-200002222−2−2−2−2-220000−2−2222i−2i−2i2i000000000000000000i2−i2−i2i20
χ3222-2-22-2000222−2−22-2-2-2-222002-200002222−2−2−2−2-220000−2−222−2i2i2i−2i000000000000000000−i2i2i2−i20
χ3322-2-22-20002−2−2222-2-222-2-2002-20000−2−2−2−222222-20000−2−2222-22-2000000000000000000−22−220
χ3422-2-22-20002−2−2222-2-222-2-2002-20000−2−2−2−222222-20000−2−222-22-220000000000000000002−22−20
χ3522-2-22-20002−2−2222-2-2-2-222002-20000−2−2−2−22222-22000022−2−22i−2i−2i2i000000000000000000−i2i2i2−i20
χ3622-2-22-20002−2−2222-2-2-2-222002-20000−2−2−2−22222-22000022−2−2−2i2i2i−2i000000000000000000i2−i2−i2i20
χ372-22-2002-2022−22−2-2-222i−2i2i−2i00002-20022−2−222−2−2002i−2i00i2−i2i2−i20000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000001+i−1−i1−i−1+i000000000
χ382-22-2002-2022−22−2-2-222i−2i2i−2i00002-20022−2−222−2−2002i−2i00i2−i2i2−i200002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000−1−i1+i−1+i1−i000000000
χ392-22-2002-2022−22−2-2-22−2i2i−2i2i00002-20022−2−222−2−200−2i2i00−i2i2−i2i20000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−1+i1−i−1−i1+i000000000
χ402-22-2002-2022−22−2-2-22−2i2i−2i2i00002-20022−2−222−2−200−2i2i00−i2i2−i2i200002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000001−i−1+i1+i−1−i000000000
χ412-22-2002-202−22−22-2-222i−2i2i−2i00002-200−2−222−2−222002i−2i00−i2i2−i2i20000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−1−i1+i−1+i1−i000000000
χ422-22-2002-202−22−22-2-222i−2i2i−2i00002-200−2−222−2−222002i−2i00−i2i2−i2i200002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000001+i−1−i1−i−1+i000000000
χ432-22-2002-202−22−22-2-22−2i2i−2i2i00002-200−2−222−2−22200−2i2i00i2−i2i2−i20000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000001−i−1+i1+i−1−i000000000
χ442-22-2002-202−22−22-2-22−2i2i−2i2i00002-200−2−222−2−22200−2i2i00i2−i2i2−i200002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000−1+i1−i−1−i1+i000000000
χ45444444444-14444-1-1-1000044-1-1-1-1-1-1-1-1-1-1-1-1-1-1000040000000000000-1-1-1-1000000000000000
χ46444444444-14444-1-1-10000-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-400000000000001111000000000000000
χ47444444444-1-4-4-4-4-1-1-1000044-1-1-1-1-1-1111111110000-40000000000000-1-111000000000000000
χ48444444444-1-4-4-4-4-1-1-10000-4-4-1-1-1-1-1-11111111100004000000000000011-1-1000000000000000
χ494444-4-4-4-44-10000-1-1-100004-41111-1-15−55−55−55−5000000000000000000-115−5000000000000000
χ504444-4-4-4-44-10000-1-1-100004-41111-1-1−55−55−55−55000000000000000000-11−55000000000000000
χ514444-4-4-4-44-10000-1-1-10000-441111-1-15−55−55−55−50000000000000000001-1−55000000000000000
χ524444-4-4-4-44-10000-1-1-10000-441111-1-1−55−55−55−550000000000000000001-15−5000000000000000
χ5344-4-4-44000400004-4-444-4-400-44000000000000-4400000000000000000000000000000000000
χ5444-4-4-44000400004-4-4-4-44400-440000000000004-400000000000000000000000000000000000
χ554-44-400-44040000-4-444i−4i4i−4i0000-44000000000000−4i4i000000000000000000000000000000000
χ564-44-400-44040000-4-44−4i4i−4i4i0000-440000000000004i−4i000000000000000000000000000000000
χ574-4-440000042-2-22-44-44i−4i−4i4i0000000022-2-2-2-2220000002i−2i−2i2i000000000000000000000000000
χ584-4-440000042-2-22-44-4−4i4i4i−4i0000000022-2-2-2-222000000−2i2i2i−2i000000000000000000000000000
χ594-4-44000004-222-2-44-44i−4i−4i4i00000000-2-22222-2-2000000−2i2i2i−2i000000000000000000000000000
χ604-4-44000004-222-2-44-4−4i4i4i−4i00000000-2-22222-2-20000002i−2i−2i2i000000000000000000000000000
χ61888888-8-8-8-20000-2-2-2000000-2-22222000000000000000000000000000000000000000000000
χ628888-8-888-8-20000-2-2-200000022-2-222000000000000000000000000000000000000000000000
χ6388-8-88-8000-24242−42−42-222000000-220000−2−2−2−222220000000000000000000000000000000000000
χ6488-8-88-8000-2−42−424242-222000000-2200002222−2−2−2−20000000000000000000000000000000000000
χ6588-8-8-88000-20000-2220000002-2000010−1010−10−1010−10100000000000000000000000000000000000000
χ6688-8-8-88000-20000-2220000002-20000−1010−101010−1010−100000000000000000000000000000000000000
χ678-88-8008-80-242−4242−4222-200000000-2200−2−222−2−2220000000000000000000000000000000000000
χ688-88-8008-80-2−4242−424222-200000000-220022−2−222−2−20000000000000000000000000000000000000
χ698-88-800-880-2000022-2000000002-20010−10−101010−10−10100000000000000000000000000000000000000
χ708-88-800-880-2000022-2000000002-200−101010−10−101010−100000000000000000000000000000000000000
χ718-8-8800000-24-4-442-22000000000025−25−1+5−1−51−51+51−51+5−1+5−1−50000000000000000000000000000000000000
χ728-8-8800000-24-4-442-220000000000−2525−1−5−1+51+51−51+51−5−1−5−1+50000000000000000000000000000000000000
χ738-8-8800000-2-444-42-22000000000025−251−51+5−1+5−1−5−1+5−1−51−51+50000000000000000000000000000000000000
χ748-8-8800000-2-444-42-220000000000−25251+51−5−1−5−1+5−1−5−1+51+51−50000000000000000000000000000000000000

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