Finite Group Databasebeta

← Group #13020768

Character table — Group #13020768

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122224444455558888888810101010161616161616161616162020202020202020203232404040404040404040404040808080
order12224444451010104444888820202020444422040404040404040402888888881010888888888888488
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111-1-111111111-111111-1-1-1-1111111111-1-111-1-11111-1-1-1-1-1-1-1
χ41111111111111111111-1-111111111-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-111
χ511111111111111111-1-11111111111-11-1-1-1-11111111111111-1-1-1-111-1-1-1-11111-1-1-1
χ611111111111111111-1-11111111111-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111
χ711111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1111
χ811111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-1
χ91111111111111-1-1-1-111111111-1-1-1-11111111111-1iiii−i−i−i−i11-1-1-1-1i−ii−iii−i−i-1i−i
χ101111111111111-1-1-1-111111111-1-1-1-11111111111-1−i−i−i−iiiii11-1-1-1-1−ii−ii−i−iii-1−ii
χ111111111111111-1-1-1-111-1-11111-1-1-1-1-111111-1-1-1-1-1iiii−i−i−i−i-1-1-1-111i−ii−i−i−iii1−ii
χ121111111111111-1-1-1-111-1-11111-1-1-1-1-111111-1-1-1-1-1−i−i−i−iiiii-1-1-1-111−ii−iiii−i−i1i−i
χ131111111111111-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-11111-1iiii−i−i−i−i-1-111-1-1−ii−iiii−i−i1−ii
χ141111111111111-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-11111-1−i−i−i−iiiii-1-111-1-1i−ii−i−i−iii1i−i
χ151111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i111111−ii−ii−i−iii-1i−i
χ161111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii111111i−ii−iii−i−i-1−ii
χ1722222-22-2-22222222200002-22-222-2-20-200000000-222-2-222-2-200000000000000000
χ1822222-22-2-22222222200002-22-222-2-20-200000000-2-2-222-2-22200000000000000000
χ1922222-22-2-22222-2-2-2-200002-22-2-2-2220-20000000022i2i−2i−2i−2i−2i2i2i00000000000000000
χ2022222-22-2-22222-2-2-2-200002-22-2-2-2220-2000000002−2i−2i2i2i2i2i−2i−2i00000000000000000
χ212222-22-22-2222222220000-22-22-2-2220-200000000-20000000000000022-2-20000000
χ222222-22-22-2222222220000-22-22-2-2220-200000000-200000000000000-2-2220000000
χ232222-22-22-22222-2-2-2-20000-22-2222-2-20-2000000002000000000000002i−2i−2i2i0000000
χ242222-22-22-22222-2-2-2-20000-22-2222-2-20-200000000200000000000000−2i2i2i−2i0000000
χ252222-2-2-2-22222222222i−2i00-2-2-2-2-2-2-2-2022i2i−2i−2i0000200000000002i−2i0000000000000
χ262222-2-2-2-2222222222−2i2i00-2-2-2-2-2-2-2-202−2i−2i2i2i000020000000000−2i2i0000000000000
χ272222-2-2-2-222222-2-2-2-22i−2i00-2-2-2-22222022i2i−2i−2i0000-20000000000−2i2i0000000000000
χ282222-2-2-2-222222-2-2-2-2−2i2i00-2-2-2-2222202−2i−2i2i2i0000-200000000002i−2i0000000000000
χ2922-2-220-20022-2-22i−2i2i−2i002−2-20202i−2i0000000022−2−2000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000i2−i200001−i−1+i1+i−1−i000
χ3022-2-220-20022-2-22i−2i2i−2i002−2-20202i−2i0000000022−2−20002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000i2−i20000−1+i1−i−1−i1+i000
χ3122-2-220-20022-2-22i−2i2i−2i00−22-20202i−2i00000000−2−222000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000−i2i20000−1+i1−i−1−i1+i000
χ3222-2-220-20022-2-22i−2i2i−2i00−22-20202i−2i00000000−2−2220002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000−i2i200001−i−1+i1+i−1−i000
χ3322-2-220-20022-2-2−2i2i−2i2i002−2-2020−2i2i0000000022−2−2000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000−i2i20000−1−i1+i−1+i1−i000
χ3422-2-220-20022-2-2−2i2i−2i2i002−2-2020−2i2i0000000022−2−20002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000−i2i200001+i−1−i1−i−1+i000
χ3522-2-220-20022-2-2−2i2i−2i2i00−22-2020−2i2i00000000−2−222000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000i2−i200001+i−1−i1−i−1+i000
χ3622-2-220-20022-2-2−2i2i−2i2i00−22-2020−2i2i00000000−2−2220002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000i2−i20000−1−i1+i−1+i1−i000
χ37444444444-1-1-1-100004444-1-1-1-100004-1-1-1-1-1-1-1-1-1000000000-1-1000000000000000
χ38444444444-1-1-1-1000044-4-4-1-1-1-10000-4-1-1-1-1-1111100000000011000000000000000
χ39444444444-1-1-1-10000-4-444-1-1-1-10000-4-11111-1-1-1-100000000011000000000000000
χ40444444444-1-1-1-10000-4-4-4-4-1-1-1-100004-111111111000000000-1-1000000000000000
χ414444-4-4-4-44-1-1-1-100004i−4i00111100000-1−i−iiii5−i5i5−i50000000005−5000000000000000
χ424444-4-4-4-44-1-1-1-100004i−4i00111100000-1−i−iii−i5i5−i5i5000000000−55000000000000000
χ434444-4-4-4-44-1-1-1-10000−4i4i00111100000-1ii−i−ii5−i5i5−i5000000000−55000000000000000
χ444444-4-4-4-44-1-1-1-10000−4i4i00111100000-1ii−i−i−i5i5−i5i50000000005−5000000000000000
χ4544-4-4-4040044-4-44i−4i4i−4i000040-40−4i4i00000000000000000000000000000000000000
χ4644-4-4-4040044-4-4−4i4i−4i4i000040-404i−4i00000000000000000000000000000000000000
χ474-44-4040-404-44-44i−4i−4i4i00000-404004i−4i000000000000000000000000000000000000
χ484-44-4040-404-44-4−4i4i4i−4i00000-40400−4i4i000000000000000000000000000000000000
χ494-44-40-40404-44-44i−4i−4i4i0000040-400−4i4i000000000000000000000000000000000000
χ504-44-40-40404-44-4−4i4i4i−4i0000040-4004i−4i000000000000000000000000000000000000
χ514-4-44000004-4-4444-4-4000000000000000000000002i2−2i2002i2−2i20000000000000000000
χ524-4-44000004-4-4444-4-400000000000000000000000−2i22i200−2i22i20000000000000000000
χ534-4-44000004-4-44-4-4440000000000000000000000022−2200−22220000000000000000000
χ544-4-44000004-4-44-4-44400000000000000000000000−22220022−220000000000000000000
χ5588888-88-8-8-2-2-2-200000000-22-220000020000000000000000000000000000000000
χ568888-88-88-8-2-2-2-2000000002-22-20000020000000000000000000000000000000000
χ5788-8-880-800-2-22200000042−4220-200000000000−2−22200000000000000000000000000
χ5888-8-880-800-2-222000000−424220-20000000000022−2−200000000000000000000000000
χ5988-8-8-80800-2-22200000000-20200000000000i10−i10−i10i1000000000000000000000000000
χ6088-8-8-80800-2-22200000000-20200000000000−i10i10i10−i1000000000000000000000000000
χ618-88-8080-80-22-2200000000020-200000010−1010−10000000000000000000000000000000
χ628-88-8080-80-22-2200000000020-2000000−1010−1010000000000000000000000000000000
χ638-88-80-8080-22-22000000000-202000000i10−i10−i10i10000000000000000000000000000000
χ648-88-80-8080-22-22000000000-202000000−i10i10i10−i10000000000000000000000000000000
χ6516-16-161600000-444-40000000000000000000000000000000000000000000000000000

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