Finite Group Databasebeta

← Group #10590857

Character table — Group #10590857

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size11112222222222222244444444444444444444444444441818181818181818242424242424242424242424
order12223344666666888836661212121212121212242424242424242424242424242424242244888844441212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-111-1-1
χ611111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-111-1-111
χ711111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111
χ811111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1
χ9222222-2-222222200002222-2-2-2-2-2-2-2-2000000000000000022-2-20000000000000000
χ10222222-2-222222200002222-2-2-2-2-2-2-2-20000000000000000-2-2220000000000000000
χ1122222-12222-1-1-122222-1-1-1-1-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000002200-1-1-1-10000
χ1222222-12222-1-1-122222-1-1-1-1-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000-2-20011110000
χ1322222-12222-1-1-12-2-2-2-2-1-1-1-1-12-1-1-12-1-1-2-2-2-2111111111111000000002-200-1-1110000
χ1422222-12222-1-1-12-2-2-2-2-1-1-1-1-12-1-1-12-1-1-2-2-2-211111111111100000000-220011-1-10000
χ152222-1222-1-1222-12222-1-1-1-12-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000220000-1-1-1-1
χ162222-1222-1-1222-12222-1-1-1-12-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000-2-200001111
χ172222-1222-1-1222-1-2-2-2-2-1-1-1-12-1-1-12-1-1-11111-2-2-2-21111111100000000002-20000-1-111
χ182222-1222-1-1222-1-2-2-2-2-1-1-1-12-1-1-12-1-1-11111-2-2-2-2111111110000000000-22000011-1-1
χ1922-2-222002-22-2-2-222−2−222-2-20000000022−2−222−2−22222−2−2−2−22-20022−2−2000000000000
χ2022-2-222002-22-2-2-222−2−222-2-20000000022−2−222−2−22222−2−2−2−2-2200−2−222000000000000
χ2122-2-222002-22-2-2-2−2−22222-2-200000000−2−222−2−222−2−2−2−222222-200−2−222000000000000
χ2222-2-222002-22-2-2-2−2−22222-2-200000000−2−222−2−222−2−2−2−22222-220022−2−2000000000000
χ232-22-22200-22-2-22-22−22−22-22-2000000002−22−22−22−222−2−222−2−2002i−2i−i2i2−i2i2000000000000
χ242-22-22200-22-2-22-22−22−22-22-2000000002−22−22−22−222−2−222−2−200−2i2ii2−i2i2−i2000000000000
χ252-22-22200-22-2-22-2−22−222-22-200000000−22−22−22−22−2−222−2−222002i−2ii2−i2i2−i2000000000000
χ262-22-22200-22-2-22-2−22−222-22-200000000−22−22−22−22−2−222−2−22200−2i2i−i2i2−i2i2000000000000
χ272-2-22222-2-2-2-22-2200002-2-222222-2-2-2-2000000000000000000002i−2i−2i2i000000000000
χ282-2-22222-2-2-2-22-2200002-2-222222-2-2-2-200000000000000000000−2i2i2i−2i000000000000
χ292-2-2222-22-2-2-22-222-2-222-2-22-2-2-2-222222-2-222-2-2222-2-2-2-22200000000000000000000
χ302-2-2222-22-2-2-22-22-222-22-2-22-2-2-2-22222-222-2-222-2-2-22222-2-200000000000000000000
χ312-2-222-1-22-2-21-1122-2-22-111-11-211-12-1-12-2-22-111-1-1-11111-1-10000000000003−33−30000
χ322-2-222-1-22-2-21-1122-2-22-111-11-211-12-1-12-2-22-111-1-1-11111-1-1000000000000−33−330000
χ332-2-222-1-22-2-21-112-222-2-111-11-211-12-1-1-222-21-1-1111-1-1-1-1110000000000003−3−330000
χ342-2-222-1-22-2-21-112-222-2-111-11-211-12-1-1-222-21-1-1111-1-1-1-111000000000000−333−30000
χ352-2-22-12-2211-22-2-12-2-22-111-1-21112-1-1-1-111-12-2-22-1-11111-1-10000000000000000−i3i3−i3i3
χ362-2-22-12-2211-22-2-12-2-22-111-1-21112-1-1-1-111-12-2-22-1-11111-1-10000000000000000i3−i3i3−i3
χ372-2-22-12-2211-22-2-1-222-2-111-1-21112-1-1-11-1-11-222-211-1-1-1-1110000000000000000−i3i3i3−i3
χ382-2-22-12-2211-22-2-1-222-2-111-1-21112-1-1-11-1-11-222-211-1-1-1-1110000000000000000i3−i3−i3i3
χ3944444-2-4-444-2-2-240000-2-2-2-22-4222-422000000000000000000000000000000000000
χ404444-24-4-4-2-2444-20000-2-2-2-2-4222-4222000000000000000000000000000000000000
χ414444-2-244-2-2-2-2-2-244441111-2-211-2-211-2-2-2-2-2-2-2-21111111100000000000000000000
χ424444-2-244-2-2-2-2-2-2-4-4-4-41111-2-211-2-21122222222-1-1-1-1-1-1-1-100000000000000000000
χ434444-2-2-4-4-2-2-2-2-2-20000111122-1-122-1-1000000003i−3i3i−3i3i−3i3i−3i00000000000000000000
χ444444-2-2-4-4-2-2-2-2-2-20000111122-1-122-1-100000000−3i3i−3i3i−3i3i−3i3i00000000000000000000
χ4544-4-44-2004-4-222-42222−22−22-2-222000000002222−22−22−2−222−2−2−2−2222200000000000000000000
χ4644-4-44-2004-4-222-4−22−222222-2-22200000000−22−22222222−2−22222−2−2−2−200000000000000000000
χ4744-4-4-2400-224-4-422222−22−22-2-22200000000−2−2222222−22−22−2−2−2−2222200000000000000000000
χ4844-4-4-2400-224-4-42−22−222222-2-2220000000022−2−2−22−2222222222−2−2−2−200000000000000000000
χ4944-4-4-2-200-22-22222222−22−2211-1-1003i−3i003i−3i−2−222−2−222−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ2300000000000000000000
χ5044-4-4-2-200-22-22222222−22−2211-1-100−3i3i00−3i3i−2−222−2−222ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ2300000000000000000000
χ5144-4-4-2-200-22-2222−22−22222211-1-1003i−3i003i−3i22−2−222−2−22ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ2300000000000000000000
χ5244-4-4-2-200-22-2222−22−22222211-1-100−3i3i00−3i3i22−2−222−2−2−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ2300000000000000000000
χ534-44-44-200-4422-2-422−2222−22-22-220000000022−2222−22−22−22−2−222−2−22200000000000000000000
χ544-44-44-200-4422-2-4−2222−2222-22-2200000000−2222−22222−22−222−2−222−2−200000000000000000000
χ554-44-4-24002-2-4-44222−2222−22-22-2200000000−22−2222−2222−22−2−222−2−22200000000000000000000
χ564-44-4-24002-2-4-442−2222−2222-22-22000000002−22−2−2222−222222−2−222−2−200000000000000000000
χ574-44-4-2-2002-222-2222−2222−221-11-1003i−3i00−3i3i−22−22−22−22ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ2300000000000000000000
χ584-44-4-2-2002-222-2222−2222−221-11-100−3i3i003i−3i−22−22−22−22−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ2300000000000000000000
χ594-44-4-2-2002-222-22−2222−22221-11-1003i−3i00−3i3i2−22−22−22−2−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−2ζ5−ζ7−2ζ13−ζ2300000000000000000000
χ604-44-4-2-2002-222-22−2222−22221-11-100−3i3i003i−3i2−22−22−22−22ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ23ζ5+2ζ7+ζ13+2ζ2300000000000000000000
χ614-4-444-24-4-4-42-2240000-222-2-24-2-22-422000000000000000000000000000000000000
χ624-4-44-244-422-44-4-20000-222-24-2-2-2-4222000000000000000000000000000000000000
χ634-4-44-2-24-4222-22-200001-1-11-2-21122-1-1000000003i−3i−3i3i−3i3i3i−3i00000000000000000000
χ644-4-44-2-24-4222-22-200001-1-11-2-21122-1-100000000−3i3i3i−3i3i−3i−3i3i00000000000000000000
χ654-4-44-2-2-44222-22-24-4-441-1-1122-1-1-2-211-222-2-222-211-1-1-1-11100000000000000000000
χ664-4-44-2-2-44222-22-2-444-41-1-1122-1-1-2-2112-2-222-2-22-1-11111-1-100000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.