Finite Group Databasebeta

← Group #13022793

Character table — Group #13022793

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444455558888888888881010101010101616161616161616161616162020202020202020404040404040404040404040404040404040
order12442224445102020224444888810101020202022244420202020404040404040404088888888448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ5111111111111111111-1-111-1-1111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ8111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
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
χ1111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-11111−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−iiiii-1-11111ii−i−iii−i−i−i−iii
χ1311111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-111−i−iiiii−i−i−i−iii
χ1411111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-111ii−i−i−i−iiiii−i−i
χ1511111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i1111-1-1ii−i−i−i−iii−i−iii
χ1611111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii1111-1-1−i−iiiii−i−iii−i−i
χ1722222-2-22-2-22222222200002i−2i2-2-22-2-22-2-2-22-2000000002i2i−2i−2i0000000000002i−2i000000000000
χ1822222-2-22-2-2222222220000−2i2i2-2-22-2-22-2-2-22-200000000−2i−2i2i2i000000000000−2i2i000000000000
χ1922222-2-22-2-22222-2-2-2-200002i−2i2-2-22-2-2-2222-22000000002i2i−2i−2i000000000000−2i2i000000000000
χ2022222-2-22-2-22222-2-2-2-20000−2i2i2-2-22-2-2-2222-2200000000−2i−2i2i2i0000000000002i−2i000000000000
χ212222-22-2-2-2222222222000000-22-2-2-22-22-22-2-20000000000000000000000000000002i−2i2i−2i0000
χ222222-22-2-2-2222222222000000-22-2-2-22-22-22-2-2000000000000000000000000000000−2i2i−2i2i0000
χ232222-22-2-2-222222-2-2-2-2000000-22-2-2-222-22-2220000000000000000000000000000002-2-220000
χ242222-22-2-2-222222-2-2-2-2000000-22-2-2-222-22-222000000000000000000000000000000-222-20000
χ252222-2-22-22-222222222000000-2-22-22-2-2-22-2-2200000000000000000000000000000000002-22-2
χ262222-2-22-22-222222222000000-2-22-22-2-2-22-2-220000000000000000000000000000000000-22-22
χ272222-2-22-22-22222-2-2-2-2000000-2-22-22-222-222-200000000000000000000000000000000002i−2i−2i2i
χ282222-2-22-22-22222-2-2-2-2000000-2-22-22-222-222-20000000000000000000000000000000000−2i2i2i−2i
χ2922-2-2222-2-2-222-2-222-2-22-20000222-2-2-2222-2-2-222-2-200000000000000002-20000000000000000
χ3022-2-2222-2-2-222-2-222-2-2-220000222-2-2-2222-2-2-2-2-2220000000000000000-220000000000000000
χ3122-2-2222-2-2-222-2-2-2-2222-20000222-2-2-2-2-2-222222-2-20000000000000000-220000000000000000
χ3222-2-2222-2-2-222-2-2-2-222-220000222-2-2-2-2-2-2222-2-22200000000000000002-20000000000000000
χ3322-2-22-2-2-22222-2-222-2-2002i−2i002-2-2-2222-2-22-2200002i2i−2i−2i000000000000002i−2i00000000000000
χ3422-2-22-2-2-22222-2-222-2-200−2i2i002-2-2-2222-2-22-220000−2i−2i2i2i00000000000000−2i2i00000000000000
χ3522-2-22-2-2-22222-2-2-2-222002i−2i002-2-2-222-222-22-200002i2i−2i−2i00000000000000−2i2i00000000000000
χ3622-2-22-2-2-22222-2-2-2-22200−2i2i002-2-2-222-222-22-20000−2i−2i2i2i000000000000002i−2i00000000000000
χ3722-2-2-22-222-222-2-222-2-2000000-22-222-2-22-2-222000000000000000000000000002i−2i2i−2i00000000
χ3822-2-2-22-222-222-2-222-2-2000000-22-222-2-22-2-22200000000000000000000000000−2i2i−2i2i00000000
χ3922-2-2-22-222-222-2-2-2-222000000-22-222-22-222-2-2000000000000000000000000002-2-2200000000
χ4022-2-2-22-222-222-2-2-2-222000000-22-222-22-222-2-200000000000000000000000000-222-200000000
χ4122-2-2-2-222-2222-2-222-2-2000000-2-222-22-2-2222-20000000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ4222-2-2-2-222-2222-2-222-2-2000000-2-222-22-2-2222-2000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ4322-2-2-2-222-2222-2-2-2-222000000-2-222-2222-2-2-2200000000000022-2-2-2-222000000000000000000
χ4422-2-2-2-222-2222-2-2-2-222000000-2-222-2222-2-2-22000000000000-2-22222-2-2000000000000000000
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
χ474444444444-1-1-1-10000-4-444-4-4-1-1-1-1-1-10000001111-1-1-1-1111100000000000000000000000000
χ484444444444-1-1-1-10000-4-4-4-444-1-1-1-1-1-100000011111111-1-1-1-100000000000000000000000000
χ4944444-4-44-4-4-1-1-1-1000000004i−4i-111-111000000i5−i5i5−i55−55−5−i−iii00000000000000000000000000
χ5044444-4-44-4-4-1-1-1-1000000004i−4i-111-111000000−i5i5−i5i5−55−55−i−iii00000000000000000000000000
χ5144444-4-44-4-4-1-1-1-100000000−4i4i-111-111000000i5−i5i5−i5−55−55ii−i−i00000000000000000000000000
χ5244444-4-44-4-4-1-1-1-100000000−4i4i-111-111000000−i5i5−i5i55−55−5ii−i−i00000000000000000000000000
χ5344-4-4444-4-4-4-1-11100004-40000-1-1-1111000000-1-111i5−i5−i5i5i5−i5i5−i500000000000000000000000000
χ5444-4-4444-4-4-4-1-11100004-40000-1-1-1111000000-1-111−i5i5i5−i5−i5i5−i5i500000000000000000000000000
χ5544-4-4444-4-4-4-1-1110000-440000-1-1-111100000011-1-1i5−i5−i5i5−i5i5−i5i500000000000000000000000000
χ5644-4-4444-4-4-4-1-1110000-440000-1-1-111100000011-1-1−i5i5i5−i5i5−i5i5−i500000000000000000000000000
χ5744-4-44-4-4-444-1-1110000004i−4i00-1111-1-1000000i5−i5−i5i5−i−iii−555−500000000000000000000000000
χ5844-4-44-4-4-444-1-1110000004i−4i00-1111-1-1000000−i5i5i5−i5−i−iii5−5−5500000000000000000000000000
χ5944-4-44-4-4-444-1-111000000−4i4i00-1111-1-1000000i5−i5−i5i5ii−i−i5−5−5500000000000000000000000000
χ6044-4-44-4-4-444-1-111000000−4i4i00-1111-1-1000000−i5i5i5−i5ii−i−i−555−500000000000000000000000000
χ614-44i−4i0000004-44i−4i4-44i−4i000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000
χ624-44i−4i0000004-44i−4i4-44i−4i0000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000
χ634-44i−4i0000004-44i−4i-44−4i4i000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000
χ644-44i−4i0000004-44i−4i-44−4i4i0000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000
χ654-4−4i4i0000004-4−4i4i4-4−4i4i000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000
χ664-4−4i4i0000004-4−4i4i4-4−4i4i0000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000
χ674-4−4i4i0000004-4−4i4i-444i−4i000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000
χ684-4−4i4i0000004-4−4i4i-444i−4i0000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000
χ698888-88-8-8-88-2-2-2-200000000002-2222-200000000000000000000000000000000000000000000
χ708888-8-88-88-8-2-2-2-2000000000022-22-2200000000000000000000000000000000000000000000
χ7188-8-8-88-888-8-2-22200000000002-22-2-2200000000000000000000000000000000000000000000
χ7288-8-8-8-888-88-2-222000000000022-2-22-200000000000000000000000000000000000000000000
χ7316-1616i−16i000000-44−4i4i000000000000000000000000000000000000000000000000000000000000
χ7416-16−16i16i000000-444i−4i000000000000000000000000000000000000000000000000000000000000

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