Finite Group Databasebeta

← Group #13019858

Character table — Group #13019858

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size1111222244444444455558888881010101010101010101010101616161616161616161620202020202020202020202020202020203232404040404040808080
order12224444224445101010444488202020202244888888882101020202040404040444448888888888881010444488488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1
χ3111111111111111111111-1-11111111111111111-111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111
χ511111111111111111-1-1-1-1111111-1-1-1-1iiii−i−i−i−i1111111111-1-1-1-1-1iiiiii−i−i−i−i−i−i11ii−i−i-1-1-1i−i
χ611111111111111111-1-1-1-1111111-1-1-1-1−i−i−i−iiiii1111111111-1-1-1-1-1−i−i−i−i−i−iiiiiii11−i−iii-1-1-1−ii
χ711111111111111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-111111-1-1-1-1-1-1-1-1-1iiiiii−i−i−i−i−i−i-1-1−i−iii111−ii
χ811111111111111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-111111-1-1-1-1-1-1-1-1-1−i−i−i−i−i−iiiiiii-1-1ii−i−i111i−i
χ911111111-1-1-1-1111111111111111111111111111-1-1-11-1-111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1
χ1011111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-111
χ1111111111-1-1-1-1111111111-1-111111111111111111-1-11-1-1-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111
χ1211111111-1-1-1-1111111111-1-111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-11-1-1-1-1-1-11111-1-11111111111-1-11-1-1
χ1311111111-1-1-1-111111-1-1-1-1111111-1-1-1-1iiii−i−i−i−i-1-1-11-1-11111-11111ii−i−i−i−i−i−iiiii-1-1ii−i−i-1-11−ii
χ1411111111-1-1-1-111111-1-1-1-1111111-1-1-1-1−i−i−i−iiiii-1-1-11-1-11111-11111−i−iiiiiii−i−i−i−i-1-1−i−iii-1-11i−i
χ1511111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i1-1-11-1-1-1-1-1-1-11111ii−i−i−i−i−i−iiiii11−i−iii11-1i−i
χ1611111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii1-1-11-1-1-1-1-1-1-11111−i−iiiiiii−i−i−i−i11ii−i−i11-1−ii
χ17222222-2-20000-22222222200-222-2-2-22222222222000-2000000-20000-2-20000-2-2000000000000000
χ18222222-2-20000-22222222200-222-2-2-222-2-2-2-2-2-2-2-2000-2000000-2000022000022000000000000000
χ19222222-2-20000-22222-2-2-2-200-222-222-2-22i2i2i2i−2i−2i−2i−2i000-200000020000−2i−2i00002i2i000000000000000
χ20222222-2-20000-22222-2-2-2-200-222-222-2-2−2i−2i−2i−2i2i2i2i2i000-2000000200002i2i0000−2i−2i000000000000000
χ212222-2-22222-2-2-222222222002-2-2222-2-200000000022-2-2-20000-2-2-22200000000000000000000000
χ222222-2-22222-2-2-22222-2-2-2-2002-2-22-2-22200000000022-2-2-20000222-2-200000000000000000000000
χ232222-2-222-2-222-222222222002-2-2222-2-2000000000-2-2-2220000-222-2-200000000000000000000000
χ242222-2-222-2-222-22222-2-2-2-2002-2-22-2-222000000000-2-2-22200002-2-22200000000000000000000000
χ252222-2-2-2-2000022222222200-2-2-2-2-2-2-2-200000000000200000020000002i2i−2i−2i002i2i−2i−2i00000000000
χ262222-2-2-2-2000022222222200-2-2-2-2-2-2-2-20000000000020000002000000−2i−2i2i2i00−2i−2i2i2i00000000000
χ272222-2-2-2-2000022222-2-2-2-200-2-2-2-22222000000000002000000-200000022-2-200-2-22200000000000
χ282222-2-2-2-2000022222-2-2-2-200-2-2-2-22222000000000002000000-2000000-2-2220022-2-200000000000
χ2922-2-22-200000002-2-222i−2i2i−2i2−202-20002i−2i−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ3900000022−2−200000000000000000001+i−1−i1−i−1+ii2−i2000
χ3022-2-22-200000002-2-222i−2i2i−2i2−202-20002i−2i2ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000022−2−20000000000000000000−1−i1+i−1+i1−ii2−i2000
χ3122-2-22-200000002-2-222i−2i2i−2i−2202-20002i−2i−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−2−2220000000000000000000−1−i1+i−1+i1−i−i2i2000
χ3222-2-22-200000002-2-222i−2i2i−2i−2202-20002i−2i2ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000−2−22200000000000000000001+i−1−i1−i−1+i−i2i2000
χ3322-2-22-200000002-2-22−2i2i−2i2i2−202-2000−2i2i−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ3700000022−2−20000000000000000000−1+i1−i−1−i1+i−i2i2000
χ3422-2-22-200000002-2-22−2i2i−2i2i2−202-2000−2i2i2ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000022−2−200000000000000000001−i−1+i1+i−1−i−i2i2000
χ3522-2-22-200000002-2-22−2i2i−2i2i−2202-2000−2i2i−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−2−22200000000000000000001−i−1+i1+i−1−ii2−i2000
χ3622-2-22-200000002-2-22−2i2i−2i2i−2202-2000−2i2i2ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000−2−2220000000000000000000−1+i1−i−1−i1+ii2−i2000
χ372-2-22002-2002i−2i022-2-222-2-200200-2-2200i2−i2i2−i2i2−i2i2−i200002i−2i000002i−2i00i2−i22−22−2i2−i22−22−200000000000
χ382-2-22002-2002i−2i022-2-222-2-200200-2-2200−i2i2−i2i2−i2i2−i2i200002i−2i000002i−2i00−i2i2−22−22−i2i2−22−2200000000000
χ392-2-22002-2002i−2i022-2-2-2-22200200-22-2002−22−2−22−2200002i−2i00000−2i2i002−2−i2i2−i2i2−22i2−i2i2−i200000000000
χ402-2-22002-2002i−2i022-2-2-2-22200200-22-200−22−222−22−200002i−2i00000−2i2i00−22i2−i2i2−i22−2−i2i2−i2i200000000000
χ412-2-22002-200−2i2i022-2-222-2-200200-2-2200i2−i2i2−i2i2−i2i2−i20000−2i2i00000−2i2i00i2−i2−22−22i2−i2−22−2200000000000
χ422-2-22002-200−2i2i022-2-222-2-200200-2-2200−i2i2−i2i2−i2i2−i2i20000−2i2i00000−2i2i00−i2i22−22−2−i2i22−22−200000000000
χ432-2-22002-200−2i2i022-2-2-2-22200200-22-2002−22−2−22−220000−2i2i000002i−2i002−2i2−i2i2−i2−22−i2i2−i2i200000000000
χ442-2-22002-200−2i2i022-2-2-2-22200200-22-200−22−222−22−20000−2i2i000002i−2i00−22−i2i2−i2i22−2i2−i2i2−i200000000000
χ452-2-2200-222-200022-2-222-2-200-20022-200i2−i2i2−i2i2−i2i2−i202-200000000002-2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i200000000000
χ462-2-2200-222-200022-2-222-2-200-20022-200−i2i2−i2i2−i2i2−i2i202-200000000002-2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i200000000000
χ472-2-2200-222-200022-2-2-2-22200-2002-22002−22−2−22−2202-20000000000-22−222−2−222−2−222−200000000000
χ482-2-2200-222-200022-2-2-2-22200-2002-2200−22−222−22−202-20000000000-222−2−222−2−222−2−2200000000000
χ492-2-2200-22-2200022-2-222-2-200-20022-200i2−i2i2−i2i2−i2i2−i20-220000000000-22−i2i2−i2i2i2−i2−i2i2−i2i2i2−i200000000000
χ502-2-2200-22-2200022-2-222-2-200-20022-200−i2i2−i2i2−i2i2−i2i20-220000000000-22i2−i2i2−i2−i2i2i2−i2i2−i2−i2i200000000000
χ512-2-2200-22-2200022-2-2-2-22200-2002-22002−22−2−22−220-2200000000002-2−22−222−22−22−2−2200000000000
χ522-2-2200-22-2200022-2-2-2-22200-2002-2200−22−222−22−20-2200000000002-22−22−2−22−22−222−200000000000
χ534444444444444-1-1-1-1000044-1-1-1-10000000000004-1-1-1-1-1-1-1-1-100000000000000000-1-1000000000
χ544444444444444-1-1-1-10000-4-4-1-1-1-1000000000000-4-1-1-1-1-111110000000000000000011000000000
χ5544444444-4-4-4-44-1-1-1-1000044-1-1-1-1000000000000-411-111-1-1-1-10000000000000000011000000000
χ5644444444-4-4-4-44-1-1-1-10000-4-4-1-1-1-1000000000000411-111111100000000000000000-1-1000000000
χ574444-4-44444-4-4-4-1-1-1-1000000-111-10000000000000-1-11115−55−5000000000000000005−5000000000
χ584444-4-44444-4-4-4-1-1-1-1000000-111-10000000000000-1-1111−55−5500000000000000000−55000000000
χ594444-4-444-4-444-4-1-1-1-1000000-111-10000000000000111-1-15−55−500000000000000000−55000000000
χ604444-4-444-4-444-4-1-1-1-1000000-111-10000000000000111-1-1−55−55000000000000000005−5000000000
χ6144-4-4-4400000004-4-444i−4i4i−4i000-44000−4i4i0000000000000000000000000000000000000000000000
χ6244-4-4-4400000004-4-44−4i4i−4i4i000-440004i−4i0000000000000000000000000000000000000000000000
χ634-44-40000000004-44-44i−4i−4i4i00000000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i00000000000000000000000000000000000000
χ644-44-40000000004-44-44i−4i−4i4i0000000000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i00000000000000000000000000000000000000
χ654-44-40000000004-44-4−4i4i4i−4i00000000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i00000000000000000000000000000000000000
χ664-44-40000000004-44-4−4i4i4i−4i0000000000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i00000000000000000000000000000000000000
χ67888888-8-80000-8-2-2-2-20000002-2-2200000000000000020000000000000000000000000000000000
χ688888-8-8-8-800008-2-2-2-20000002222000000000000000-20000000000000000000000000000000000
χ6988-8-88-80000000-222-2000042−420-220000000000000000000−2−2220000000000000000000000000000
χ7088-8-88-80000000-222-20000−42420-22000000000000000000022−2−20000000000000000000000000000
χ7188-8-8-880000000-222-200000002-2000000000000000000010−10−10100000000000000000000000000000
χ7288-8-8-880000000-222-200000002-20000000000000000000−101010−100000000000000000000000000000
χ738-8-88008-8008i−8i0-2-222000000-20020000000000000000−2i2i00000000000000000000000000000000
χ748-8-88008-800−8i8i0-2-222000000-200200000000000000002i−2i00000000000000000000000000000000
χ758-8-8800-888-8000-2-222000000200-20000000000000-2200000000000000000000000000000000000
χ768-8-8800-88-88000-2-222000000200-200000000000002-200000000000000000000000000000000000
χ7716-1616-16000000000-44-44000000000000000000000000000000000000000000000000000000000000

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