Finite Group Databasebeta

← Group #13022449

Character table — Group #13022449

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444455558888888888881010101010101616161616161616161616162020202020202020404040404040404040404040404040404040
order12222244445101010444422244410102020202022224410101010101020202020202088888888244444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-1-11111
χ411111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111111111-1-1-1-1
χ5111111111111111111-1-11-1-11111111111111-1-1-1-111-1-1-1-111111111111-1-1-1-111111-1-1-1-1-1-1-1-1
χ6111111111111111111-1-11-1-11111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111111111
χ7111111111111111111-1-1-111-1111111111111-1-1-1-1-1-11111-1-111111111-111-1-1-1-1-1-1-11111-1-1-1-1
χ8111111111111111111-1-1-111-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-11111
χ911111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111111111iiii−i−i−i−i-1-1-1-1-1-1ii−i−iii−i−iii−i−i
χ1011111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111111111−i−i−i−iiiii-1-1-1-1-1-1−i−iii−i−iii−i−iii
χ1111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i111-1-11−i−iii−i−iiiii−i−i
χ1211111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii111-1-11ii−i−iii−i−i−i−iii
χ1311111111111111-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111iiii−i−i−i−i-11111-1ii−i−i−i−iii−i−iii
χ1411111111111111-1-1-1-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111−i−i−i−iiiii-11111-1−i−iiiii−i−iii−i−i
χ1511111111111111-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i1-1-1111−i−iiiii−i−i−i−iii
χ1611111111111111-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii1-1-1111ii−i−i−i−iiiii−i−i
χ17222222-2-2-2-2222222222-2000022-2-2-2-2-2-2-2-22222-2-200000000000000000002-20000000000000
χ18222222-2-2-2-222222222-22000022-2-2-2-2-2-2-2-222-2-2220000000000000000000-220000000000000
χ19222222-2-2-2-22222-2-2-2-22-2000022-2-2-2-22222-2-222-2-20000000000000000000-220000000000000
χ20222222-2-2-2-22222-2-2-2-2-22000022-2-2-2-22222-2-2-2-22200000000000000000002-20000000000000
χ212222-2-222-2-2222222220002-20-2-222-2-22-22-2-2-200000022-2-2000000000002-2000000000000000
χ222222-2-222-2-222222222000-220-2-222-2-22-22-2-2-2000000-2-22200000000000-22000000000000000
χ232222-2-222-2-22222-2-2-2-20002-20-2-222-2-2-22-222200000022-2-200000000000-22000000000000000
χ242222-2-222-2-22222-2-2-2-2000-220-2-222-2-2-22-2222000000-2-222000000000002-2000000000000000
χ252222-2-2-2-2222222222200200-2-2-2-2-222-22-22-2-20000220000-2-200000000-200002000000000000
χ262222-2-2-2-2222222222200-2002-2-2-2-222-22-22-2-20000-2-20000220000000020000-2000000000000
χ272222-2-2-2-2222222-2-2-2-200200-2-2-2-2-2222-22-2220000220000-2-20000000020000-2000000000000
χ282222-2-2-2-2222222-2-2-2-200-2002-2-2-2-2222-22-2220000-2-200002200000000-200002000000000000
χ292-2-222-22-22-22-2-2222-2-20000002-22-22-222-2-2-220000000000000000000000000000002i−2i2i−2i0000
χ302-2-222-22-22-22-2-2222-2-20000002-22-22-222-2-2-22000000000000000000000000000000−2i2i−2i2i0000
χ312-2-222-22-22-22-2-22-2-2220000002-22-22-2-2-2222-20000000000000000000000000000002-2-220000
χ322-2-222-22-22-22-2-22-2-2220000002-22-22-2-2-2222-2000000000000000000000000000000-222-20000
χ332-2-222-2-22-222-2-2222-2-20000002-2-22-22-2-222-22000000000000000000000000002-22-200000000
χ342-2-222-2-22-222-2-2222-2-20000002-2-22-22-2-222-2200000000000000000000000000-22-2200000000
χ352-2-222-2-22-222-2-22-2-2220000002-2-22-2222-2-22-2000000000000000000000000002i−2i−2i2i00000000
χ362-2-222-2-22-222-2-22-2-2220000002-2-22-2222-2-22-200000000000000000000000000−2i2i2i−2i00000000
χ372-2-22-222-2-222-2-2222-2-2000000-222-2-222-2-222-20000000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ382-2-22-222-2-222-2-2222-2-2000000-222-2-222-2-222-2000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ392-2-22-222-2-222-2-22-2-222000000-222-2-22-222-2-2200000000000022-2-2-2-222000000000000000000
χ402-2-22-222-2-222-2-22-2-222000000-222-2-22-222-2-22000000000000-2-22222-2-2000000000000000000
χ412-2-22-22-222-22-2-2222-2-2000000-22-222-2-222-22-200000000000000000000000000000000002i−2i2i−2i
χ422-2-22-22-222-22-2-2222-2-2000000-22-222-2-222-22-20000000000000000000000000000000000−2i2i−2i2i
χ432-2-22-22-222-22-2-22-2-222000000-22-222-22-2-22-2200000000000000000000000000000000002-2-22
χ442-2-22-22-222-22-2-22-2-222000000-22-222-22-2-22-220000000000000000000000000000000000-222-2
χ454444444444-1-1-1-10000444444-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ464444444444-1-1-1-1000044-4-4-4-4-1-1-1-1-1-1000000-1-1-1-11111111100000000000000000000000000
χ474444444444-1-1-1-10000-4-44-4-44-1-1-1-1-1-10000001111-1-11111-1-100000000000000000000000000
χ484444444444-1-1-1-10000-4-4-444-4-1-1-1-1-1-1000000111111-1-1-1-11100000000000000000000000000
χ49444444-4-4-4-4-1-1-1-100004-40000-1-11111000000-1-1115−55−55−55−500000000000000000000000000
χ50444444-4-4-4-4-1-1-1-100004-40000-1-11111000000-1-111−55−55−55−5500000000000000000000000000
χ51444444-4-4-4-4-1-1-1-10000-440000-1-1111100000011-1-15−5−55−555−500000000000000000000000000
χ52444444-4-4-4-4-1-1-1-10000-440000-1-1111100000011-1-1−555−55−5−5500000000000000000000000000
χ534444-4-444-4-4-1-1-1-100000004-4011-1-1110000005−55−55−5-1-111−5500000000000000000000000000
χ544444-4-444-4-4-1-1-1-100000004-4011-1-111000000−55−55−55-1-1115−500000000000000000000000000
χ554444-4-444-4-4-1-1-1-10000000-44011-1-1110000005−55−5−5511-1-15−500000000000000000000000000
χ564444-4-444-4-4-1-1-1-10000000-44011-1-111000000−55−555−511-1-1−5500000000000000000000000000
χ574444-4-4-4-444-1-1-1-1000000400-41111-1-10000005−5−55-1-15−5−551100000000000000000000000000
χ584444-4-4-4-444-1-1-1-1000000400-41111-1-1000000−555−5-1-1−555−51100000000000000000000000000
χ594444-4-4-4-444-1-1-1-1000000-40041111-1-10000005−5−5511−555−5-1-100000000000000000000000000
χ604444-4-4-4-444-1-1-1-1000000-40041111-1-1000000−555−5115−5−55-1-100000000000000000000000000
χ6144-4-400000044-4-44i−4i4i−4i000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000
χ6244-4-400000044-4-44i−4i4i−4i0000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000
χ6344-4-400000044-4-4−4i4i−4i4i000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000
χ6444-4-400000044-4-4−4i4i−4i4i0000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000
χ654-44-40000004-44-44i−4i−4i4i000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000
χ664-44-40000004-44-44i−4i−4i4i0000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000
χ674-44-40000004-44-4−4i4i4i−4i000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000
χ684-44-40000004-44-4−4i4i4i−4i0000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000
χ698-8-888-88-88-8-222-20000000000-22-22-2200000000000000000000000000000000000000000000
χ708-8-888-8-88-88-222-20000000000-222-22-200000000000000000000000000000000000000000000
χ718-8-88-888-8-88-222-200000000002-2-222-200000000000000000000000000000000000000000000
χ728-8-88-88-888-8-222-200000000002-22-2-2200000000000000000000000000000000000000000000
χ731616-16-16000000-4-444000000000000000000000000000000000000000000000000000000000000
χ7416-1616-16000000-44-44000000000000000000000000000000000000000000000000000000000000

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