Finite Group Databasebeta

← Group #13017789

Character table — Group #13017789

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111122224444444445555888888888888888810101010161616161616161616202020202020202020202020204040404040404040404040408080
order12224444224445101010444424441010101020202020202020202244101020202020202020224448888888822444444888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-11111111111111111-1-1-1-1111111111-1-1-1-1-1iiii−i−i−i−i-1-1-1-1ii−i−iii−i−ii−i
χ411111111111111111-1-1-1-11111111111111111-1-1-1-1111111111-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−iii−i−iii−ii
χ511111111111-1-111111111-11-1-111111111-1-1-1-11111-1-1111-1-1-1-1-1-111111111111-1-11-1-1-1-1-11111-1-1
χ611111111111-1-111111111-11-1-111111111-1-1-1-11111-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-111
χ711111111111-1-11111-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1iiii−i−i−i−i11-11−i−iiiii−i−i−ii
χ811111111111-1-11111-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1−i−i−i−iiiii11-11ii−i−i−i−iiii−i
χ911111111-1-1111111111111-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-111-1-1111111111-1-1-111111-1-1-1-1-1-1
χ1011111111-1-1111111111111-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111
χ1111111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1iiii−i−i−i−i111-1ii−i−i−i−iii−ii
χ1211111111-1-11111111-1-1-1-11-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1−i−i−i−iiiii111-1−i−iiiii−i−ii−i
χ1311111111-1-11-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-11-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111
χ1411111111-1-11-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-11-1-11111-1-1-1-11-1-1-1-1-1-1-1-111-1-111111111-1-1
χ1511111111-1-11-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-111111111-1iiii−i−i−i−i-1-111−i−iii−i−iiii−i
χ1611111111-1-11-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-111111111-1−i−i−i−iiiii-1-111ii−i−iii−i−i−ii
χ17222222-2-200-22222222222-2000000022-2-22222-2-222-2-2-20000002200-200000000000-20000000000
χ18222222-2-200-2222222-2-2-2-2-2000000022-2-2222222-2-2-2-2-2000000-2-20020000000000020000000000
χ19222222-2-200-2-2-2222222222000000022-2-2-2-2-2-2-2-22222-2000000-2-200-20000000000020000000000
χ20222222-2-200-2-2-22222-2-2-2-22000000022-2-2-2-2-2-222-2-222-20000002200200000000000-20000000000
χ212222-2-22222-200222222220-2002222-2-222000022-2-200-2-2-200000022-20000000000-200000000000
χ222222-2-22222-2002222-2-2-2-20-2002222-2-2220000-2-22200-2-2-2000000-2-220000000000200000000000
χ232222-2-222-2-2-200222222220200-2-2-2-2-2-222000022-2-200-222000000-2-2-20000000000200000000000
χ242222-2-222-2-2-2002222-2-2-2-20200-2-2-2-2-2-2220000-2-22200-2220000002220000000000-200000000000
χ252222-2-2-2-20020022222222002-20000-2-2-2-20000-2-2-2-20020022-2-200002000000002-2000000000000
χ262222-2-2-2-2002002222222200-220000-2-2-2-20000-2-2-2-200200-2-2220000200000000-22000000000000
χ272222-2-2-2-2002002222-2-2-2-2002-20000-2-2-2-2000022220020022-2-20000-200000000-22000000000000
χ282222-2-2-2-2002002222-2-2-2-200-220000-2-2-2-20000222200200-2-2220000-2000000002-2000000000000
χ2922-2-22-2000002i−2i2-22-22i−2i2i−2i000000002-2002i2i−2i−2i002i−2i0000000002-20001+i1+i−1−i−1−i1−i1−i−1+i−1+i00001−i−1+i1+i−1−i000000
χ3022-2-22-2000002i−2i2-22-22i−2i2i−2i000000002-2002i2i−2i−2i002i−2i0000000002-2000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000−1+i1−i−1−i1+i000000
χ3122-2-22-2000002i−2i2-22-2−2i2i−2i2i000000002-2002i2i−2i−2i00−2i2i000000000-220001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000−1−i1+i−1+i1−i000000
χ3222-2-22-2000002i−2i2-22-2−2i2i−2i2i000000002-2002i2i−2i−2i00−2i2i000000000-22000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00001+i−1−i1−i−1+i000000
χ3322-2-22-200000−2i2i2-22-22i−2i2i−2i000000002-200−2i−2i2i2i002i−2i000000000-220001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000−1+i1−i−1−i1+i000000
χ3422-2-22-200000−2i2i2-22-22i−2i2i−2i000000002-200−2i−2i2i2i002i−2i000000000-22000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00001−i−1+i1+i−1−i000000
χ3522-2-22-200000−2i2i2-22-2−2i2i−2i2i000000002-200−2i−2i2i2i00−2i2i0000000002-20001−i1−i−1+i−1+i1+i1+i−1−i−1−i00001+i−1−i1−i−1+i000000
χ3622-2-22-200000−2i2i2-22-2−2i2i−2i2i000000002-200−2i−2i2i2i00−2i2i0000000002-2000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000−1−i1+i−1+i1−i000000
χ372-2-22002-22-20002-2-2222-2-2000022-2-2002-200002-200000000000002-20i2−i2i2−i2i2−i2i2−i200000000i2−i2i2−i200
χ382-2-22002-22-20002-2-2222-2-2000022-2-2002-200002-200000000000002-20−i2i2−i2i2−i2i2−i2i200000000−i2i2−i2i200
χ392-2-22002-22-20002-2-22-2-222000022-2-2002-20000-220000000000000-2202−22−2−22−22000000002−2−2200
χ402-2-22002-22-20002-2-22-2-222000022-2-2002-20000-220000000000000-220−22−222−22−200000000−222−200
χ412-2-22002-2-220002-2-2222-2-20000-2-222002-200002-20000000000000-220i2−i2i2−i2i2−i2i2−i200000000−i2i2−i2i200
χ422-2-22002-2-220002-2-2222-2-20000-2-222002-200002-20000000000000-220−i2i2−i2i2−i2i2−i2i200000000i2−i2i2−i200
χ432-2-22002-2-220002-2-22-2-2220000-2-222002-20000-2200000000000002-202−22−2−22−2200000000−222−200
χ442-2-22002-2-220002-2-22-2-2220000-2-222002-20000-2200000000000002-20−22−222−22−2000000002−2−2200
χ454444444444444-1-1-1-100004444-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1000000000000000000000000000
χ4644444444444-4-4-1-1-1-10000-44-4-4-1-1-1-1-1-1-1-11111000011-1-1-11111000000000000000000000000000
χ4744444444-4-4444-1-1-1-100004-4-4-41111-1-1-1-1-1-1-1-10000-1-1-1111111000000000000000000000000000
χ4844444444-4-44-4-4-1-1-1-10000-4-4441111-1-1-1-11111000011-111-1-1-1-1000000000000000000000000000
χ49444444-4-400-444-1-1-1-10000-40005−55−5-1-111-1-1-1-100001115−55−55−5000000000000000000000000000
χ50444444-4-400-444-1-1-1-10000-4000−55−55-1-111-1-1-1-10000111−55−55−55000000000000000000000000000
χ51444444-4-400-4-4-4-1-1-1-1000040005−55−5-1-11111110000-1-115−5−55−55000000000000000000000000000
χ52444444-4-400-4-4-4-1-1-1-100004000−55−55-1-11111110000-1-11−555−55−5000000000000000000000000000
χ534444-4-44444-400-1-1-1-100000-400-1-1-1-111-1-15−55−500005−51115−5−55000000000000000000000000000
χ544444-4-44444-400-1-1-1-100000-400-1-1-1-111-1-1−55−550000−55111−555−5000000000000000000000000000
χ554444-4-444-4-4-400-1-1-1-100000400111111-1-15−55−500005−51-1-1−555−5000000000000000000000000000
χ564444-4-444-4-4-400-1-1-1-100000400111111-1-1−55−550000−551-1-15−5−55000000000000000000000000000
χ574444-4-4-4-400400-1-1-1-10000004-45−55−511115−55−50000−55-1−55-1-111000000000000000000000000000
χ584444-4-4-4-400400-1-1-1-10000004-4−55−551111−55−5500005−5-15−5-1-111000000000000000000000000000
χ594444-4-4-4-400400-1-1-1-1000000-445−55−51111−55−5500005−5-1−5511-1-1000000000000000000000000000
χ604444-4-4-4-400400-1-1-1-1000000-44−55−5511115−55−50000−55-15−511-1-1000000000000000000000000000
χ6144-4-4-4400000004-44-44i−4i4i−4i00000000-4400000000−4i4i000000000000000000000000000000000000
χ6244-4-4-4400000004-44-4−4i4i−4i4i00000000-44000000004i−4i000000000000000000000000000000000000
χ634-44-400000000044-4-44i−4i−4i4i0000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000
χ644-44-400000000044-4-44i−4i−4i4i00000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000
χ654-44-400000000044-4-4−4i4i4i−4i0000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000
χ664-44-400000000044-4-4−4i4i4i−4i00000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000
χ674-4-4400-44000004-4-4444-4-40000000000-440000-4400000000000000000000000000000000000000
χ684-4-4400-44000004-4-44-4-4440000000000-4400004-400000000000000000000000000000000000000
χ6988-8-88-8000008i−8i-22-22000000000000-2200−2i−2i2i2i0000000000000000000000000000000000000000
χ7088-8-88-800000−8i8i-22-22000000000000-22002i2i−2i−2i0000000000000000000000000000000000000000
χ7188-8-8-880000000-22-220000000000002-2002i5−2i5−2i52i50000000000000000000000000000000000000000
χ7288-8-8-880000000-22-220000000000002-200−2i52i52i5−2i50000000000000000000000000000000000000000
χ738-8-88008-88-8000-222-200000000-2-22200-2200000000000000000000000000000000000000000000
χ748-8-88008-8-88000-222-20000000022-2-200-2200000000000000000000000000000000000000000000
χ758-8-8800-8800000-222-20000000025−25−2525002-200000000000000000000000000000000000000000000
χ768-8-8800-8800000-222-200000000−252525−25002-200000000000000000000000000000000000000000000
χ7716-1616-16000000000-4-444000000000000000000000000000000000000000000000000000000000000

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