Finite Group Databasebeta

← Group #13020691

Character table — Group #13020691

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444455558888888888881010101010101616161616161616161616162020202020202020404040404040404040404040404040404040
order12222244445101010444444888810102020202044444420202020404040404040404088888888228888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111
χ5111111111111111111-1-111-1-1111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-111-1-1-1-111-1-1-1-1
χ6111111111111111111-1-111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111
χ7111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ911111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111111111iiii−i−i−i−i-1-1-1-1-1-1i−iii−i−ii−iii−i−i
χ1011111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111111111−i−i−i−iiiii-1-1-1-1-1-1−ii−i−iii−ii−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−iiii−i−i−ii−i−iii
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-1-11111i−i−i−iiii−iii−i−i
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−i11-1-111i−i−i−iiii−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−iiiii11-1-111−iiii−i−i−iiii−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−i1111-1-1−ii−i−iii−iiii−i−i
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−iiiii1111-1-1i−iii−i−ii−i−i−iii
χ17222222-2-2-2-222222222002i−2i0022-2-2-2-222-2-2-2-200002i2i−2i−2i000000000000002i−2i00000000000000
χ18222222-2-2-2-22222222200−2i2i0022-2-2-2-222-2-2-2-20000−2i−2i2i2i00000000000000−2i2i00000000000000
χ19222222-2-2-2-22222-2-2-2-2002i−2i0022-2-2-2-2-2-2222200002i2i−2i−2i00000000000000−2i2i00000000000000
χ20222222-2-2-2-22222-2-2-2-200−2i2i0022-2-2-2-2-2-222220000−2i−2i2i2i000000000000002i−2i00000000000000
χ212222-2-22-22-222222222000000-2-22-22-2-2-222-2-200000000000022-2-222-2-2000000000000000000
χ222222-2-22-22-222222222000000-2-22-22-2-2-222-2-2000000000000-2-222-2-222000000000000000000
χ232222-2-22-22-22222-2-2-2-2000000-2-22-22-222-2-2220000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ242222-2-22-22-22222-2-2-2-2000000-2-22-22-222-2-222000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ252222-2-2-22-2222222222000000-2-2-22-22-2-2-2-22200000000000000000000000000220000-2-20000
χ262222-2-2-22-2222222222000000-2-2-22-22-2-2-2-22200000000000000000000000000-2-20000220000
χ272222-2-2-22-222222-2-2-2-2000000-2-2-22-222222-2-2000000000000000000000000002i−2i0000−2i2i0000
χ282222-2-2-22-222222-2-2-2-2000000-2-2-22-222222-2-200000000000000000000000000−2i2i00002i−2i0000
χ2922-2-22-222-2-22-22-22i−2i2i−2i0000002-2-2-2222i−2i2i−2i2i−2i0000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39
χ3022-2-22-222-2-22-22-22i−2i2i−2i0000002-2-2-2222i−2i2i−2i2i−2i00000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39
χ3122-2-22-222-2-22-22-2−2i2i−2i2i0000002-2-2-222−2i2i−2i2i−2i2i0000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37
χ3222-2-22-222-2-22-22-2−2i2i−2i2i0000002-2-2-222−2i2i−2i2i−2i2i00000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37
χ3322-2-22-2-2-2222-22-22i−2i2i−2i0000002-222-2-22i−2i−2i2i−2i2i0000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000
χ3422-2-22-2-2-2222-22-22i−2i2i−2i0000002-222-2-22i−2i−2i2i−2i2i00000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000
χ3522-2-22-2-2-2222-22-2−2i2i−2i2i0000002-222-2-2−2i2i2i−2i2i−2i0000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000
χ3622-2-22-2-2-2222-22-2−2i2i−2i2i0000002-222-2-2−2i2i2i−2i2i−2i00000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000
χ3722-2-2-222-2-222-22-22i−2i2i−2i00002i−2i-22-222-2−2i2i2i−2i−2i2i000000002i2i−2i−2i0000000000002-2000000000000
χ3822-2-2-222-2-222-22-22i−2i2i−2i0000−2i2i-22-222-2−2i2i2i−2i−2i2i00000000−2i−2i2i2i000000000000-22000000000000
χ3922-2-2-222-2-222-22-2−2i2i−2i2i00002i−2i-22-222-22i−2i−2i2i2i−2i000000002i2i−2i−2i000000000000-22000000000000
χ4022-2-2-222-2-222-22-2−2i2i−2i2i0000−2i2i-22-222-22i−2i−2i2i2i−2i00000000−2i−2i2i2i0000000000002-2000000000000
χ4122-2-2-22-222-22-22-22i−2i2i−2i2i−2i0000-222-2-22−2i2i−2i2i2i−2i2i2i−2i−2i00000000000000002-20000000000000000
χ4222-2-2-22-222-22-22-22i−2i2i−2i−2i2i0000-222-2-22−2i2i−2i2i2i−2i−2i−2i2i2i0000000000000000-220000000000000000
χ4322-2-2-22-222-22-22-2−2i2i−2i2i2i−2i0000-222-2-222i−2i2i−2i−2i2i2i2i−2i−2i0000000000000000-220000000000000000
χ4422-2-2-22-222-22-22-2−2i2i−2i2i−2i2i0000-222-2-222i−2i2i−2i−2i2i−2i−2i2i2i00000000000000002-20000000000000000
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
χ49444444-4-4-4-4-1-1-1-10000004i−4i00-1-111110000005−55−5−i−iiii5−i5i5−i500000000000000000000000000
χ50444444-4-4-4-4-1-1-1-10000004i−4i00-1-11111000000−55−55−i−iii−i5i5−i5i500000000000000000000000000
χ51444444-4-4-4-4-1-1-1-1000000−4i4i00-1-111110000005−55−5ii−i−i−i5i5−i5i500000000000000000000000000
χ52444444-4-4-4-4-1-1-1-1000000−4i4i00-1-11111000000−55−55ii−i−ii5−i5i5−i500000000000000000000000000
χ5344-4-4-444-4-44-11-11000000004i−4i1-11-1-11000000i5−i5−i5i55−55−5−i−iii00000000000000000000000000
χ5444-4-4-444-4-44-11-11000000004i−4i1-11-1-11000000−i5i5i5−i5−55−55−i−iii00000000000000000000000000
χ5544-4-4-444-4-44-11-1100000000−4i4i1-11-1-11000000i5−i5−i5i5−55−55ii−i−i00000000000000000000000000
χ5644-4-4-444-4-44-11-1100000000−4i4i1-11-1-11000000−i5i5i5−i55−55−5ii−i−i00000000000000000000000000
χ5744-4-4-44-444-4-11-1100004i−4i00001-1-111-1000000−i−iiii5−i5−i5i5−555−500000000000000000000000000
χ5844-4-4-44-444-4-11-1100004i−4i00001-1-111-1000000−i−iii−i5i5i5−i55−5−5500000000000000000000000000
χ5944-4-4-44-444-4-11-110000−4i4i00001-1-111-1000000ii−i−ii5−i5−i5i55−5−5500000000000000000000000000
χ6044-4-4-44-444-4-11-110000−4i4i00001-1-111-1000000ii−i−i−i5i5i5−i5−555−500000000000000000000000000
χ614-44-400000044-4-44i−4i−4i4i000000000000000000000000000000002+2i−2−2i002−2i−2+2i000000000000000000
χ624-44-400000044-4-44i−4i−4i4i00000000000000000000000000000000−2−2i2+2i00−2+2i2−2i000000000000000000
χ634-44-400000044-4-4−4i4i4i−4i000000000000000000000000000000002−2i−2+2i002+2i−2−2i000000000000000000
χ644-44-400000044-4-4−4i4i4i−4i00000000000000000000000000000000−2+2i2−2i00−2−2i2+2i000000000000000000
χ654-4-440000004-4-4444-4-40000000000000000000000000000002i2−2i2002i2−2i200000000000000000000
χ664-4-440000004-4-4444-4-4000000000000000000000000000000−2i22i200−2i22i200000000000000000000
χ674-4-440000004-4-44-4-44400000000000000000000000000000022−2200−222200000000000000000000
χ684-4-440000004-4-44-4-444000000000000000000000000000000−22220022−2200000000000000000000
χ698888-8-88-88-8-2-2-2-2000000000022-22-2200000000000000000000000000000000000000000000
χ708888-8-8-88-88-2-2-2-20000000000222-22-200000000000000000000000000000000000000000000
χ7188-8-88-888-8-8-22-220000000000-2222-2-200000000000000000000000000000000000000000000
χ7288-8-88-8-8-888-22-220000000000-22-2-22200000000000000000000000000000000000000000000
χ7316-1616-16000000-4-444000000000000000000000000000000000000000000000000000000000000
χ7416-16-1616000000-444-4000000000000000000000000000000000000000000000000000000000000

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