Finite Group Databasebeta

← Group #13022738

Character table — Group #13022738

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1111222222444455558888888888881010101010101616161616161616161616162020202020202020404040404040404040404040404040404040
order12222244445101010444444448810102020202022224420202020202020204040404088888888444444448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-111111111-111-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-1-1-11111
χ5111111111111111111-1-111-1-111111111111111-1-1-1-111-1-1-1-1111111111-1-111111-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111-1-111-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-111111111
χ7111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111
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-1-1-1-1ii−i−i-1-1ii−i−iii−i−i
χ1011111111111111-1-1-1-1111111111111-1-1-1-1-1-1111111111111−i−i−i−iiiii-1-1-1-1−i−iii-1-1−i−iii−i−iii
χ1111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i1-1-11−i−iii11ii−i−i−i−iii
χ1211111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii1-1-11ii−i−i11−i−iiiii−i−i
χ1311111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1iiii−i−i−i−i-111-1ii−i−i11−i−iii−i−iii
χ1411111111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1−i−i−i−iiiii-111-1−i−iii11ii−i−iii−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−i−iii-1-1−i−iiiii−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−iiiii1111ii−i−i-1-1ii−i−i−i−iii
χ17222222-2-2-2-22222222200000022-2-2-2-2-2-2-2-2220000000000000000000000000000002-22-20000
χ18222222-2-2-2-22222222200000022-2-2-2-2-2-2-2-222000000000000000000000000000000-22-220000
χ19222222-2-2-2-22222-2-2-2-200000022-2-2-2-22222-2-20000000000000000000000000000002i−2i−2i2i0000
χ20222222-2-2-2-22222-2-2-2-200000022-2-2-2-22222-2-2000000000000000000000000000000−2i2i2i−2i0000
χ212222-2-222-2-222222222000000-2-222-2-22-2-22-2-200000000000000000000000000000000002-22-2
χ222222-2-222-2-222222222000000-2-222-2-22-2-22-2-20000000000000000000000000000000000-22-22
χ232222-2-222-2-22222-2-2-2-2000000-2-222-2-2-222-22200000000000000000000000000000000002i−2i−2i2i
χ242222-2-222-2-22222-2-2-2-2000000-2-222-2-2-222-2220000000000000000000000000000000000−2i2i2i−2i
χ252222-2-2-2-22222222222002-200-2-2-2-222-222-2-2-2-2-2000022000000000000-200200000000000000
χ262222-2-2-2-2222222222200-2200-2-2-2-222-222-2-2-2220000-2-2000000000000200-200000000000000
χ272222-2-2-2-2222222-2-2-2-2002-200-2-2-2-2222-2-2222-2-2000022000000000000200-200000000000000
χ282222-2-2-2-2222222-2-2-2-200-2200-2-2-2-2222-2-2222220000-2-2000000000000-200200000000000000
χ2922-2-22-22-22-222-2-222-2-20000002-22-22-222-2-2-2200000000000022-2-222-2-2000000000000000000
χ3022-2-22-22-22-222-2-222-2-20000002-22-22-222-2-2-22000000000000-2-222-2-222000000000000000000
χ3122-2-22-22-22-222-2-2-2-2220000002-22-22-2-2-2222-20000000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ3222-2-22-22-22-222-2-2-2-2220000002-22-22-2-2-2222-2000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ3322-2-22-2-22-2222-2-222-2-22i−2i00002-2-22-22-2-222-22002i2i−2i−2i0000000000000002i−2i000000000000000
χ3422-2-22-2-22-2222-2-222-2-2−2i2i00002-2-22-22-2-222-2200−2i−2i2i2i000000000000000−2i2i000000000000000
χ3522-2-22-2-22-2222-2-2-2-2222i−2i00002-2-22-2222-2-22-2002i2i−2i−2i000000000000000−2i2i000000000000000
χ3622-2-22-2-22-2222-2-2-2-222−2i2i00002-2-22-2222-2-22-200−2i−2i2i2i0000000000000002i−2i000000000000000
χ3722-2-2-222-2-2222-2-222-2-200002-2-222-2-222-22-22-20000000022-2-200000000000000002-200000000
χ3822-2-2-222-2-2222-2-222-2-20000-22-222-2-222-22-22-200000000-2-2220000000000000000-2200000000
χ3922-2-2-222-2-2222-2-2-2-22200002-2-222-2-22-22-22-220000000022-2-20000000000000000-2200000000
χ4022-2-2-222-2-2222-2-2-2-2220000-22-222-2-22-22-22-2200000000-2-22200000000000000002-200000000
χ4122-2-2-22-222-222-2-222-2-2000000-22-222-2-22-222-20000000000000000000000002-22-20000000000
χ4222-2-2-22-222-222-2-222-2-2000000-22-222-2-22-222-2000000000000000000000000-22-220000000000
χ4322-2-2-22-222-222-2-2-2-222000000-22-222-22-22-2-220000000000000000000000002i−2i−2i2i0000000000
χ4422-2-2-22-222-222-2-2-2-222000000-22-222-22-22-2-22000000000000000000000000−2i2i2i−2i0000000000
χ454444444444-1-1-1-10000444444-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000
χ464444444444-1-1-1-1000044-4-4-4-4-1-1-1-1-1-100000011-1-1-1-111111100000000000000000000000000
χ474444444444-1-1-1-10000-4-444-4-4-1-1-1-1-1-1000000-1-11111-1-1111100000000000000000000000000
χ484444444444-1-1-1-10000-4-4-4-444-1-1-1-1-1-100000011111111-1-1-1-100000000000000000000000000
χ494444-4-4-4-444-1-1-1-10000004-4001111-1-1000000115−55−5-1-15−55−500000000000000000000000000
χ504444-4-4-4-444-1-1-1-10000004-4001111-1-100000011−55−55-1-1−55−5500000000000000000000000000
χ514444-4-4-4-444-1-1-1-1000000-44001111-1-1000000-1-15−55−511−55−5500000000000000000000000000
χ524444-4-4-4-444-1-1-1-1000000-44001111-1-1000000-1-1−55−55115−55−500000000000000000000000000
χ5344-4-44-4-44-44-1-11100004i−4i0000-111-11-1000000i5−i5−i−iiii5−i55−5−5500000000000000000000000000
χ5444-4-44-4-44-44-1-11100004i−4i0000-111-11-1000000−i5i5−i−iii−i5i5−555−500000000000000000000000000
χ5544-4-44-4-44-44-1-1110000−4i4i0000-111-11-1000000i5−i5ii−i−ii5−i5−555−500000000000000000000000000
χ5644-4-44-4-44-44-1-1110000−4i4i0000-111-11-1000000−i5i5ii−i−i−i5i55−5−5500000000000000000000000000
χ5744-4-4-444-4-44-1-111000000004-41-1-111-1000000i5−i5−i5i5i5−i5−i5i5-1-11100000000000000000000000000
χ5844-4-4-444-4-44-1-111000000004-41-1-111-1000000−i5i5i5−i5−i5i5i5−i5-1-11100000000000000000000000000
χ5944-4-4-444-4-44-1-11100000000-441-1-111-1000000i5−i5i5−i5−i5i5−i5i511-1-100000000000000000000000000
χ6044-4-4-444-4-44-1-11100000000-441-1-111-1000000−i5i5−i5i5i5−i5i5−i511-1-100000000000000000000000000
χ614-44-40000004-4-444i−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
χ624-44-40000004-4-444i−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
χ634-44-40000004-4-44−4i4i−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
χ644-44-40000004-4-44−4i4i−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
χ654-4-440000004-44-44i−4i−4i4i000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000
χ664-4-440000004-44-44i−4i−4i4i0000000000000000000000000000002ζ13+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
χ674-4-440000004-44-4−4i4i4i−4i000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000
χ684-4-440000004-44-4−4i4i4i−4i0000000000000000000000000000002ζ7+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
χ69888888-8-8-8-8-2-2-2-20000000000-2-2222200000000000000000000000000000000000000000000
χ708888-8-888-8-8-2-2-2-2000000000022-2-22200000000000000000000000000000000000000000000
χ7188-8-88-88-88-8-2-2220000000000-22-22-2200000000000000000000000000000000000000000000
χ7288-8-8-88-888-8-2-22200000000002-22-2-2200000000000000000000000000000000000000000000
χ7316-1616-16000000-444-4000000000000000000000000000000000000000000000000000000000000
χ7416-16-1616000000-44-44000000000000000000000000000000000000000000000000000000000000

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