Finite Group Databasebeta

← Group #13017476

Character table — Group #13017476

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444455558888888888881010101010101616161616161616161616162020202020202020404040404040404040404040404040404040
order12222244445101010444422444410102020202044444410101010202020202020202088888888444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-11-1-1-111111111111111-1-1-1-1-1-111-1-111111111-1-11-11-1-1-1-1-11111-1-1-1-1
χ41111111111111111111-11-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111
χ5111111111111111111-11-11-1-1111111111111-1-111-1-1-1-1-1-11111111111-1-1-11-11-1-1-1-1-1-1-1-11111
χ6111111111111111111-11-11-1-1111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1111111111-1-1-1-1
χ7111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ8111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
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
χ1111111111111111-1-1-1-11-11-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1iiii−i−i−i−i11-11-11−i−iiiii−i−i−i−iii
χ1211111111111111-1-1-1-11-11-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1−i−i−i−iiiii11-11-11ii−i−i−i−iiiii−i−i
χ1311111111111111-1-1-1-1-11-11-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111iiii−i−i−i−i111-11-1−i−iii−i−iiiii−i−i
χ1411111111111111-1-1-1-1-11-11-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111−i−i−i−iiiii111-11-1ii−i−iii−i−i−i−iii
χ1511111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-11111ii−i−i−i−iii−i−iii
χ1611111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-11111−i−iiiii−i−iii−i−i
χ17222222-2-2-2-22222222200002-222-2-2-2-222-2-2-2-2000022-2-20000000000002-20000000000000000
χ18222222-2-2-2-2222222220000-2222-2-2-2-222-2-2-2-20000-2-222000000000000-220000000000000000
χ19222222-2-2-2-22222-2-2-2-200002-222-2-2-2-2-2-22222000022-2-2000000000000-220000000000000000
χ20222222-2-2-2-22222-2-2-2-20000-2222-2-2-2-2-2-222220000-2-2220000000000002-20000000000000000
χ212222-2-222-2-222222222020-200-2-222-2-2-2-222-2-20022000000-2-20000000000020-2000000000000
χ222222-2-222-2-2222222220-20200-2-222-2-2-2-222-2-200-2-20000002200000000000-202000000000000
χ232222-2-222-2-22222-2-2-2-2020-200-2-222-2-222-2-2220022000000-2-200000000000-202000000000000
χ242222-2-222-2-22222-2-2-2-20-20200-2-222-2-222-2-22200-2-2000000220000000000020-2000000000000
χ252222-2-2-2-2222222222220-2000-2-2-2-222-2-2-2-22222000000-2-200000000000020-20000000000000
χ262222-2-2-2-22222222222-202000-2-2-2-222-2-2-2-222-2-200000022000000000000-2020000000000000
χ272222-2-2-2-2222222-2-2-2-220-2000-2-2-2-2222222-2-222000000-2-2000000000000-2020000000000000
χ282222-2-2-2-2222222-2-2-2-2-202000-2-2-2-2222222-2-2-2-20000002200000000000020-20000000000000
χ2922-2-22-22-22-22-2-222i−2i2i−2i0000002-22-22-22i−2i2i−2i2i−2i0000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39
χ3022-2-22-22-22-22-2-222i−2i2i−2i0000002-22-22-22i−2i2i−2i2i−2i00000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39
χ3122-2-22-22-22-22-2-22−2i2i−2i2i0000002-22-22-2−2i2i−2i2i−2i2i0000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37
χ3222-2-22-22-22-22-2-22−2i2i−2i2i0000002-22-22-2−2i2i−2i2i−2i2i00000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37
χ3322-2-22-2-22-222-2-222i−2i2i−2i0000002-2-22-222i−2i−2i2i−2i2i000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000
χ3422-2-22-2-22-222-2-222i−2i2i−2i0000002-2-22-222i−2i−2i2i−2i2i0000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000
χ3522-2-22-2-22-222-2-22−2i2i−2i2i0000002-2-22-22−2i2i2i−2i2i−2i000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000
χ3622-2-22-2-22-222-2-22−2i2i−2i2i0000002-2-22-22−2i2i2i−2i2i−2i0000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000
χ3722-2-2-222-2-222-2-222i−2i2i−2i000000-222-2-22−2i2i2i−2i−2i2i000000000000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000
χ3822-2-2-222-2-222-2-222i−2i2i−2i000000-222-2-22−2i2i2i−2i−2i2i0000000000002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000
χ3922-2-2-222-2-222-2-22−2i2i−2i2i000000-222-2-222i−2i−2i2i2i−2i000000000000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000
χ4022-2-2-222-2-222-2-22−2i2i−2i2i000000-222-2-222i−2i−2i2i2i−2i0000000000002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000
χ4122-2-2-22-222-22-2-222i−2i2i−2i000000-22-222-2−2i2i−2i2i2i−2i00000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000
χ4222-2-2-22-222-22-2-222i−2i2i−2i000000-22-222-2−2i2i−2i2i2i−2i000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000
χ4322-2-2-22-222-22-2-22−2i2i−2i2i000000-22-222-22i−2i2i−2i−2i2i00000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000
χ4422-2-2-22-222-22-2-22−2i2i−2i2i000000-22-222-22i−2i2i−2i−2i2i000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000
χ454444444444-1-1-1-10000444444-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ464444444444-1-1-1-100004-44-4-4-4-1-1-1-1-1-1000000-1-1111111-1-11100000000000000000000000000
χ474444444444-1-1-1-10000-44-44-4-4-1-1-1-1-1-100000011-1-1111111-1-100000000000000000000000000
χ484444444444-1-1-1-10000-4-4-4-444-1-1-1-1-1-10000001111-1-1-1-1111100000000000000000000000000
χ49444444-4-4-4-4-1-1-1-1000000004-4-1-111110000005−55−5-1-1115−55−500000000000000000000000000
χ50444444-4-4-4-4-1-1-1-1000000004-4-1-11111000000−55−55-1-111−55−5500000000000000000000000000
χ51444444-4-4-4-4-1-1-1-100000000-44-1-111110000005−5−5511-1-15−5−5500000000000000000000000000
χ52444444-4-4-4-4-1-1-1-100000000-44-1-11111000000−555−511-1-1−555−500000000000000000000000000
χ534444-4-444-4-4-1-1-1-10000040-40011-1-1110000005−5-1-15−55−5−551100000000000000000000000000
χ544444-4-444-4-4-1-1-1-10000040-40011-1-111000000−55-1-1−55−555−51100000000000000000000000000
χ554444-4-444-4-4-1-1-1-100000-4040011-1-1110000005−511−55−55−55-1-100000000000000000000000000
χ564444-4-444-4-4-1-1-1-100000-4040011-1-111000000−55115−55−55−5-1-100000000000000000000000000
χ574444-4-4-4-444-1-1-1-1000040-40001111-1-1000000-1-15−55−5−5511−5500000000000000000000000000
χ584444-4-4-4-444-1-1-1-1000040-40001111-1-1000000-1-1−55−555−5115−500000000000000000000000000
χ594444-4-4-4-444-1-1-1-10000-4040001111-1-1000000115−5−555−5-1-1−5500000000000000000000000000
χ604444-4-4-4-444-1-1-1-10000-4040001111-1-100000011−555−5−55-1-15−500000000000000000000000000
χ614-44-400000044-4-444-4-40000000000000000000000000000002-22-22-22-2000000000000000000
χ624-44-400000044-4-444-4-4000000000000000000000000000000-22-22-22-22000000000000000000
χ634-44-400000044-4-4-4-4440000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000
χ644-44-400000044-4-4-4-444000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000
χ654-4-440000004-44-44i−4i−4i4i000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000
χ664-4-440000004-44-44i−4i−4i4i0000000000000000000000000000002ζ7+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+2ζ37000000000000000000
χ674-4-440000004-44-4−4i4i4i−4i000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000
χ684-4-440000004-44-4−4i4i4i−4i0000000000000000000000000000002ζ13+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+2ζ39000000000000000000
χ6988-8-88-88-88-8-222-20000000000-22-22-2200000000000000000000000000000000000000000000
χ7088-8-88-8-88-88-222-20000000000-222-22-200000000000000000000000000000000000000000000
χ7188-8-8-888-8-88-222-200000000002-2-222-200000000000000000000000000000000000000000000
χ7288-8-8-88-888-8-222-200000000002-22-2-2200000000000000000000000000000000000000000000
χ7316-1616-16000000-4-444000000000000000000000000000000000000000000000000000000000000
χ7416-16-1616000000-44-44000000000000000000000000000000000000000000000000000000000000

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