Finite Group Databasebeta

← Group #13019868

Character table — Group #13019868

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size1111222244444444455558888881010101010101010101010101616161616161616161620202020202020202020202020202020203232404040404040808080
order12224444224445101010444488202020204444888888884101020202040404040244448888888888882020888888288
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1
χ3111111111111111111111-1-11111111111111111-111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ511111111111111111-1-1-1-1111111-1-1-1-1iiii−i−i−i−i1111111111-1-1-1-1-1iiiiii−i−i−i−i−i−i11-1-1ii−i−i-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−iiiiiii11-1-1−i−iii-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-1-111−i−iii1−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-1-111ii−i−i1i−i
χ911111111-1-1-1-1111111111111111111111111111-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1
χ1011111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-1-111
χ1111111111-1-1-1-1111111111-1-111111111111111111-1-1-1-11-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111
χ1211111111-1-1-1-1111111111-1-111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11-1-1-1-1-1-11111-1-1111111-1-111111-1-1
χ1311111111-1-1-1-111111-1-1-1-1111111-1-1-1-1iiii−i−i−i−i-1-1-1-1-111111-11111ii−i−i−i−i−i−iiiii-1-1-1-1ii−i−i1−ii
χ1411111111-1-1-1-111111-1-1-1-1111111-1-1-1-1−i−i−i−iiiii-1-1-1-1-111111-11111−i−iiiiiii−i−i−i−i-1-1-1-1−i−iii1i−i
χ1511111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i1-1-1-1-11-1-1-1-1-11111ii−i−i−i−i−i−iiiii1111−i−iii-1i−i
χ1611111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii1-1-1-1-11-1-1-1-1-11111−i−iiiiiii−i−i−i−i1111ii−i−i-1−ii
χ17222222-2-20000-22222222200-222-2-2-2222222222200000-20000-20000-2-20000-2-2000000000000000
χ18222222-2-20000-22222222200-222-2-2-222-2-2-2-2-2-2-2-200000-20000-2000022000022000000000000000
χ19222222-2-20000-22222-2-2-2-200-222-222-2-22i2i2i2i−2i−2i−2i−2i00000-2000020000−2i−2i00002i2i000000000000000
χ20222222-2-20000-22222-2-2-2-200-222-222-2-2−2i−2i−2i−2i2i2i2i2i00000-20000200002i2i0000−2i−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
χ232222-2-222-2-222-222222222002-2-2222-2-2000000000-2-222-20000-222-2-200000000000000000000000
χ242222-2-222-2-222-22222-2-2-2-2002-2-22-2-222000000000-2-222-200002-2-22200000000000000000000000
χ252222-2-2-2-2000022222222200-2-2-2-2-2-2-2-200000000000002000020000002i2i−2i−2i002i2i−2i−2i00000000000
χ262222-2-2-2-2000022222222200-2-2-2-2-2-2-2-20000000000000200002000000−2i−2i2i2i00−2i−2i2i2i00000000000
χ272222-2-2-2-2000022222-2-2-2-200-2-2-2-22222000000000000020000-200000022-2-200-2-22200000000000
χ282222-2-2-2-2000022222-2-2-2-200-2-2-2-22222000000000000020000-2000000-2-2220022-2-200000000000
χ2922-2-22-200000002-22-22i−2i2i−2ii2−i202-20002i−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+2ζ39000000i2i2−i2−i200000000000000000002−21−i−1+i1+i−1−i000
χ3022-2-22-200000002-22-22i−2i2i−2ii2−i202-20002i−2i2ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000i2i2−i2−i200000000000000000002−2−1+i1−i−1−i1+i000
χ3122-2-22-200000002-22-22i−2i2i−2i−i2i202-20002i−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−i2−i2i2i20000000000000000000−22−1+i1−i−1−i1+i000
χ3222-2-22-200000002-22-22i−2i2i−2i−i2i202-20002i−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−i2−i2i2i20000000000000000000−221−i−1+i1+i−1−i000
χ3322-2-22-200000002-22-2−2i2i−2i2ii2−i202-2000−2i2i−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+2ζ37000000i2i2−i2−i20000000000000000000−221+i−1−i1−i−1+i000
χ3422-2-22-200000002-22-2−2i2i−2i2ii2−i202-2000−2i2i2ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000i2i2−i2−i20000000000000000000−22−1−i1+i−1+i1−i000
χ3522-2-22-200000002-22-2−2i2i−2i2i−i2i202-2000−2i2i−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−i2−i2i2i200000000000000000002−2−1−i1+i−1+i1−i000
χ3622-2-22-200000002-22-2−2i2i−2i2i−i2i202-2000−2i2i2ζ7+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−i2−i2i2i200000000000000000002−21+i−1−i1−i−1+i000
χ372-22-2002-2002i−2i022-2-22i−2i−2i2i00-20022i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0002i−2i0000002-2001−i−1+i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000
χ382-22-2002-2002i−2i022-2-22i−2i−2i2i00-20022i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i0002i−2i0000002-200−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000
χ392-22-2002-2002i−2i022-2-2−2i2i2i−2i00-2002−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0002i−2i000000-22001+i−1−i−1+i1−i−1+i1−i1−i−1+i−1−i1+i−1−i1+i00000000000
χ402-22-2002-2002i−2i022-2-2−2i2i2i−2i00-2002−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0002i−2i000000-2200−1−i1+i1−i−1+i1−i−1+i−1+i1−i1+i−1−i1+i−1−i00000000000
χ412-22-2002-200−2i2i022-2-22i−2i−2i2i00-20022i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i000−2i2i000000-22001−i−1+i−1−i1+i−1−i1+i1+i−1−i−1+i1−i−1+i1−i00000000000
χ422-22-2002-200−2i2i022-2-22i−2i−2i2i00-20022i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i000−2i2i000000-2200−1+i1−i1+i−1−i1+i−1−i−1−i1+i1−i−1+i1−i−1+i00000000000
χ432-22-2002-200−2i2i022-2-2−2i2i2i−2i00-2002−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i000−2i2i0000002-2001+i−1−i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000
χ442-22-2002-200−2i2i022-2-2−2i2i2i−2i00-2002−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000−2i2i0000002-200−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000
χ452-22-200-222-200022-2-22i−2i−2i2i00200-2−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i02-200000000002i−2i−1+i1−i1−i−1+i−1+i1−i−1−i1+i−1−i1+i1+i−1−i00000000000
χ462-22-200-222-200022-2-22i−2i−2i2i00200-2−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i02-200000000002i−2i1−i−1+i−1+i1−i1−i−1+i1+i−1−i1+i−1−i−1−i1+i00000000000
χ472-22-200-222-200022-2-2−2i2i2i−2i00200-22i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i02-20000000000−2i2i−1−i1+i1+i−1−i−1−i1+i−1+i1−i−1+i1−i1−i−1+i00000000000
χ482-22-200-222-200022-2-2−2i2i2i−2i00200-22i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i02-20000000000−2i2i1+i−1−i−1−i1+i1+i−1−i1−i−1+i1−i−1+i−1+i1−i00000000000
χ492-22-200-22-2200022-2-22i−2i−2i2i00200-2−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0-220000000000−2i2i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i00000000000
χ502-22-200-22-2200022-2-22i−2i−2i2i00200-2−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i0-220000000000−2i2i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i00000000000
χ512-22-200-22-2200022-2-2−2i2i2i−2i00200-22i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0-2200000000002i−2i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i00000000000
χ522-22-200-22-2200022-2-2−2i2i2i−2i00200-22i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0-2200000000002i−2i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i00000000000
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
χ5544444444-4-4-4-44-1-1-1-1000044-1-1-1-1000000000000-41111-1-1-1-1-10000000000000000011000000000
χ5644444444-4-4-4-44-1-1-1-10000-4-4-1-1-1-100000000000041111-1111100000000000000000-1-1000000000
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
χ594444-4-444-4-444-4-1-1-1-1000000-111-1000000000000011-1-115−55−500000000000000000−55000000000
χ604444-4-444-4-444-4-1-1-1-1000000-111-1000000000000011-1-11−55−55000000000000000005−5000000000
χ6144-4-4-4400000004-44-44i−4i4i−4i000-44000−4i4i0000000000000000000000000000000000000000000000
χ6244-4-4-4400000004-44-4−4i4i−4i4i000-440004i−4i0000000000000000000000000000000000000000000000
χ634-4-440000000004-4-4444-4-400000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ644-4-440000000004-4-4444-4-40000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ654-4-440000000004-4-44-4-444000000000022−22−2222−222222−2200000000000000000000000000000000000000
χ664-4-440000000004-4-44-4-4440000000000−222222−2222−22−222200000000000000000000000000000000000000
χ67888888-8-80000-8-2-2-2-20000002-2-2200000000000000000200000000000000000000000000000000
χ688888-8-8-8-800008-2-2-2-2000000222200000000000000000-200000000000000000000000000000000
χ6988-8-88-80000000-22-2200004i2−4i20-220000000000000000000−i2−i2i2i20000000000000000000000000000
χ7088-8-88-80000000-22-220000−4i24i20-220000000000000000000i2i2−i2−i20000000000000000000000000000
χ7188-8-8-880000000-22-2200000002-20000000000000000000i10−i10−i10i100000000000000000000000000000
χ7288-8-8-880000000-22-2200000002-20000000000000000000−i10i10i10−i100000000000000000000000000000
χ738-88-8008-8008i−8i0-2-222000000200-2000000000000000−2i2i000000000000000000000000000000000
χ748-88-8008-800−8i8i0-2-222000000200-20000000000000002i−2i000000000000000000000000000000000
χ758-88-800-888-8000-2-222000000-20020000000000000-2200000000000000000000000000000000000
χ768-88-800-88-88000-2-222000000-200200000000000002-200000000000000000000000000000000000
χ7716-16-1616000000000-444-4000000000000000000000000000000000000000000000000000000000000

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