Finite Group Databasebeta

← Group #13019864

Character table — Group #13019864

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111122224444455558888888810101010161616161616161616162020202020202020203232404040404040404040404040808080
order12224444451010104444248820202020224441010202020404040404888888882020444444888888288
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11-1-1
χ31111111111111111111-1-111111111-111111-1-1-1-1111111111-1-111-1-1-1-1-1-11111-1-1-1
χ41111111111111111111-1-111111111-111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111
χ511111111111111111-1-11111111111-1-1-11-1-11111111111111-1-1-1-1111111-1-1-1-1-1-1-1
χ611111111111111111-1-11111111111-1-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111
χ711111111111111111-1-1-1-1111111111-1-11-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1111
χ811111111111111111-1-1-1-1111111111-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-111111-1-1
χ91111111111111-1-1-1-111111111-1-1-1-11111111111-1iiii−i−i−i−i11-1-1ii−i−i-1-1ii−i−i-1i−i
χ101111111111111-1-1-1-111111111-1-1-1-11111111111-1−i−i−i−iiiii11-1-1−i−iii-1-1−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-1-1-1-1−i−iii11ii−i−i1−ii
χ121111111111111-1-1-1-111-1-11111-1-1-1-1-111111-1-1-1-1-1−i−i−i−iiiii-1-1-1-1ii−i−i11−i−iii1i−i
χ131111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-11-1-11111-1iiii−i−i−i−i-1-111ii−i−i-1-1−i−iii1−ii
χ141111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-11-1-11111-1−i−i−i−iiiii-1-111−i−iii-1-1ii−i−i1i−i
χ151111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1iiii−i−i−i−i1111−i−iii11−i−iii-1i−i
χ161111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1−i−i−i−iiiii1111ii−i−i11ii−i−i-1−ii
χ17222222-2-2-222222222000022-2-2-2-222000-2000000-222-2-222-2-200000000000000000
χ18222222-2-2-222222222000022-2-2-2-222000-2000000-2-2-222-2-22200000000000000000
χ19222222-2-2-22222-2-2-2-2000022-2-222-2-2000-200000022i2i−2i−2i−2i−2i2i2i00000000000000000
χ20222222-2-2-22222-2-2-2-2000022-2-222-2-2000-20000002−2i−2i2i2i2i2i−2i−2i00000000000000000
χ212222-2-222-2222222222-200-2-22222-2-2022-2-2-20000-20000000000-220000000000000
χ222222-2-222-222222222-2200-2-22222-2-20-2-2-2220000-200000000002-20000000000000
χ232222-2-222-22222-2-2-2-22-200-2-222-2-222022-2-2-20000200000000002-20000000000000
χ242222-2-222-22222-2-2-2-2-2200-2-222-2-2220-2-2-222000020000000000-220000000000000
χ252222-2-2-2-22222222220000-2-2-2-2-2-2-2-2000200000020000000000000000002i−2i2i−2i000
χ262222-2-2-2-22222222220000-2-2-2-2-2-2-2-200020000002000000000000000000−2i2i−2i2i000
χ272222-2-2-2-222222-2-2-2-20000-2-2-2-222220002000000-20000000000000000002-2-22000
χ282222-2-2-2-222222-2-2-2-20000-2-2-2-222220002000000-2000000000000000000-222-2000
χ2922-2-22-20002-22-22i−2i2i−2i00i2−i22-200002i−2i000000i2i2−i2−i2000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700001+i−1−i1−i−1+i2−20000000
χ3022-2-22-20002-22-22i−2i2i−2i00i2−i22-200002i−2i000000i2i2−i2−i20002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000−1−i1+i−1+i1−i2−20000000
χ3122-2-22-20002-22-22i−2i2i−2i00−i2i22-200002i−2i000000−i2−i2i2i2000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000−1−i1+i−1+i1−i−220000000
χ3222-2-22-20002-22-22i−2i2i−2i00−i2i22-200002i−2i000000−i2−i2i2i20002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700001+i−1−i1−i−1+i−220000000
χ3322-2-22-20002-22-2−2i2i−2i2i00i2−i22-20000−2i2i000000i2i2−i2−i2000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900001−i−1+i1+i−1−i−220000000
χ3422-2-22-20002-22-2−2i2i−2i2i00i2−i22-20000−2i2i000000i2i2−i2−i20002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000−1+i1−i−1−i1+i−220000000
χ3522-2-22-20002-22-2−2i2i−2i2i00−i2i22-20000−2i2i000000−i2−i2i2i2000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000−1+i1−i−1−i1+i2−20000000
χ3622-2-22-20002-22-2−2i2i−2i2i00−i2i22-20000−2i2i000000−i2−i2i2i20002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900001−i−1+i1+i−1−i2−20000000
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
χ39444444444-1-1-1-10000-4-444-1-1-1-10000-411-111-1-1-1-100000000011000000000000000
χ40444444444-1-1-1-10000-4-4-4-4-1-1-1-10000411-1111111000000000-1-1000000000000000
χ414444-4-444-4-1-1-1-100004-40011-1-100000-1-11115−55−50000000005−5000000000000000
χ424444-4-444-4-1-1-1-100004-40011-1-100000-1-1111−55−55000000000−55000000000000000
χ434444-4-444-4-1-1-1-10000-440011-1-100000111-1-15−55−5000000000−55000000000000000
χ444444-4-444-4-1-1-1-10000-440011-1-100000111-1-1−55−550000000005−5000000000000000
χ4544-4-4-440004-44-44i−4i4i−4i0000-440000−4i4i000000000000000000000000000000000000
χ4644-4-4-440004-44-4−4i4i−4i4i0000-4400004i−4i000000000000000000000000000000000000
χ474-44-40000044-4-44i−4i−4i4i000000000000000000000002+2i−2−2i002−2i−2+2i0000000000000000000
χ484-44-40000044-4-44i−4i−4i4i00000000000000000000000−2−2i2+2i00−2+2i2−2i0000000000000000000
χ494-44-40000044-4-4−4i4i4i−4i000000000000000000000002−2i−2+2i002+2i−2−2i0000000000000000000
χ504-44-40000044-4-4−4i4i4i−4i00000000000000000000000−2+2i2−2i00−2−2i2+2i0000000000000000000
χ514-4-44004-404-4-4444-4-40000004-44-400000000000000000000000000000000000000
χ524-4-44004-404-4-44-4-4440000004-4-4400000000000000000000000000000000000000
χ534-4-4400-4404-4-4444-4-4000000-44-4400000000000000000000000000000000000000
χ544-4-4400-4404-4-44-4-444000000-444-400000000000000000000000000000000000000
χ55888888-8-8-8-2-2-2-200000000-2-2220000000200000000000000000000000000000000
χ568888-8-8-8-88-2-2-2-20000000022220000000-200000000000000000000000000000000
χ5788-8-88-8000-22-220000004i2−4i2-22000000000000−i2−i2i2i200000000000000000000000000
χ5888-8-88-8000-22-22000000−4i24i2-22000000000000i2i2−i2−i200000000000000000000000000
χ5988-8-8-88000-22-22000000002-2000000000000i10−i10−i10i1000000000000000000000000000
χ6088-8-8-88000-22-22000000002-2000000000000−i10i10i10−i1000000000000000000000000000
χ618-8-88008-80-222-20000000000-22000000002i5−2i5000000000000000000000000000000
χ628-8-88008-80-222-20000000000-2200000000−2i52i5000000000000000000000000000000
χ638-8-8800-880-222-200000000002-20000025−25000000000000000000000000000000000
χ648-8-8800-880-222-200000000002-200000−2525000000000000000000000000000000000
χ6516-1616-1600000-4-4440000000000000000000000000000000000000000000000000000

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