Finite Group Databasebeta

← Group #13169170

Character table — Group #13169170

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order122233366666666633346666666661212444436661212121212121212121212122444661212121212121212121212121212224444446666666121212121212121212121212122412121212121261224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-111-1-1-11111111111-1-1111111-1-1-1-11111-1-1-1-111-1-111111111-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1111111111111111111-1111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111111-1111111-1-1-1-1-11-1-111-1-1-11-1-1
χ4111111111111111111111111111111111-1-11111111111111111-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-11-1-1-1-1-1111-111
χ51111111111111111111111111111111-1-11111111111111111111-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1111-1-1-1-111111-1-1-1-1-1111-1-1-1
χ61111111111111111111111111111111-1-1111111111111111111-1-11-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-11-1-111-1-1-1111
χ71111111111111111111111111111111-1-1-1-111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111111-1-111-1-1-1-111-1-111-1-111-1-1-1-1111-1-1-1-1-111-1-111-1-1-1111-1-111-111-1
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-11-11111-1-11-1-11
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111111-1-11-1-111-1-1-1-11111-1-1-1-1-1-111-11
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-111111111-1-1-11-111111-1-1-1-111-1-1-1-11111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-111111111111-11-1-1-1-1-11111-1-1-1-1-1-11111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1-111-111-1-11111-1-111-1-1-1-1-1-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111-111-1-1-1-111-1-1111-11111-1-11-11-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-111111-1-111-1-111-1111-1-111-11-11
χ17222222-12-1-122222-12-1-122-1-12-1-1-12-1220022-1-1-1-1-1222-1-1-1-1-1-1-1-12022-1-1000000222222-1-10000002200002-1-1-10-1-1-10000-1-1-1-1200000-1-1-1000
χ18222222-12-1-122222-12-1-122-1-12-1-1-12-1220022-1-1-1-1-1222-1-1-1-1-1-1-1-1-202-2110000002222-2-2-1-1000000-2-20000-21110-1110000-1-1-1-1-200000111000
χ19222222-12-1-122222-12-1-122-1-12-1-1-12-12200-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-120-22-1-1000000-2-2-2-22211000000-2-200002-1-1-101-1-100001111-200000111000
χ20222222-12-1-122222-12-1-122-1-12-1-1-12-12200-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-1-20-2-211000000-2-2-2-2-2-211000000220000-2111011100001111200000-1-1-1000
χ21222222-12-1-122222-12-1-1-22-1-12-1-1-12-1-2-20022-1-1-1-11-2-2-21111111120-2-2-1-100000022-2-2-2-2-1-10000002200002-1-1101110000-1-111-200000-1-11000
χ22222222-12-1-122222-12-1-1-22-1-12-1-1-12-1-2-20022-1-1-1-11-2-2-211111111-20-221100000022-2-222-1-1000000-2-20000-211-101-1-10000-1-11120000011-1000
χ23222222-12-1-122222-12-1-1-22-1-12-1-1-12-1-2-200-2-2-1-1-1-11-2-2-211111111202-2-1-1000000-2-222-2-211000000-2-200002-1-110-111000011-1-120000011-1000
χ24222222-12-1-122222-12-1-1-22-1-12-1-1-12-1-2-200-2-2-1-1-1-11-2-2-211111111-202211000000-2-2222211000000220000-211-10-1-1-1000011-1-1-200000-1-11000
χ2522222-12-12222-12-12-1-122-1-12-1-122-1-1-1-12222-1-1-1-122-1-122-1-1-1-1-1-102200022-1-1-1-1-1-1-1-1002222220000-1-1-1-100002200-1-1-1-1-1-1-1-100-1-100000000
χ2622222-12-12222-12-12-1-122-1-12-1-122-1-1-1-122-2-2-1-1-1-122-1-122-1-1-1-1-1-102-200022-1-1-1-1111100-2-2-2-2-2-20000111100002-200-1-1-1-11111001100000000
χ2722222-12-12222-12-12-1-122-1-12-1-122-1-1-1-1-2-222-1-1-1-122-1-122-1-1-1-1-1-10-22000-2-21111-1-1-1-10022-2-2-2-2000011110000-22001111-1-1-1-1001100000000
χ2822222-12-12222-12-12-1-122-1-12-1-122-1-1-1-1-2-2-2-2-1-1-1-122-1-122-1-1-1-1-1-10-2-2000-2-21111111100-2-222220000-1-1-1-10000-2-2001111111100-1-100000000
χ2922222-12-12222-12-12-1-12-2-1-12-1-122-1-1112222-1-1-1-1-2-211-2-21111110-2-200022-1-111-1-1110022-2-222000011110000-2-200-1-111-1-11100-1-100000000
χ3022222-12-12222-12-12-1-12-2-1-12-1-122-1-11122-2-2-1-1-1-1-2-211-2-21111110-2200022-1-11111-1-100-2-222-2-20000-1-1-1-10000-2200-1-11111-1-1001100000000
χ3122222-12-12222-12-12-1-12-2-1-12-1-122-1-111-2-222-1-1-1-1-2-211-2-211111102-2000-2-211-1-1-1-111002222-2-20000-1-1-1-100002-20011-1-1-1-111001100000000
χ3222222-12-12222-12-12-1-12-2-1-12-1-122-1-111-2-2-2-2-1-1-1-1-2-211-2-2111111022000-2-211-1-111-1-100-2-2-2-222000011110000220011-1-111-1-100-1-100000000
χ332222-122222-1-12-122-12-12-12-1-12-1-1-12222200-1-1-1-12-1-1-1-1-122-1-1-1-1220222-1-122220000-1-100000022000000-1-1-12-10-1-1-1-1-1-100000200-1-1000-100
χ342222-122222-1-12-122-12-12-12-1-12-1-1-12222200-1-1-1-12-1-1-1-1-122-1-1-1-1-220-2-2-2-1-12222000011000000-2-2000000111-2-1011-1-1-1-100000-20011000100
χ352222-122222-1-12-122-12-12-12-1-12-1-1-1222-2-200-1-1-1-12-1-1-1-1-122-1-1-1-12-2022211-2-2-2-20000-1-1000000-2-2000000-1-1-1210-1-1111100000-20011000100
χ362222-122222-1-12-122-12-12-12-1-12-1-1-1222-2-200-1-1-1-12-1-1-1-1-122-1-1-1-1-2-20-2-2-211-2-2-2-200001100000022000000111-21011111100000200-1-1000-100
χ372222-122222-1-12-122-12-1-2-12-1-12-1-1-12-2-22200-1-1-1-1-211111-2-211112-20-222-1-122-2-2000011000000-2-2000000-1-1-1-21011-1-1110000020011000-100
χ382222-122222-1-12-122-12-1-2-12-1-12-1-1-12-2-22200-1-1-1-1-211111-2-21111-2-202-2-2-1-122-2-20000-1-100000022000000111210-1-1-1-11100000-200-1-1000100
χ392222-122222-1-12-122-12-1-2-12-1-12-1-1-12-2-2-2-200-1-1-1-1-211111-2-21111220-22211-2-22200001100000022000000-1-1-1-2-101111-1-100000-200-1-1000100
χ402222-122222-1-12-122-12-1-2-12-1-12-1-1-12-2-2-2-200-1-1-1-1-211111-2-21111-2202-2-211-2-2220000-1-1000000-2-20000001112-10-1-111-1-10000020011000-100
χ4122-2-2222-22-2-222-2-2-22220-2-2-2222-2-2-2002i−2i2i−2i2-2-220000000000000000002i−2i2i−2i002i−2i00002i−2i002-200000000000000002i−2i002i−2i00002-200000000
χ4222-2-2222-22-2-222-2-2-22220-2-2-2222-2-2-2002i−2i−2i2i2-2-220000000000000000002i−2i2i−2i00−2i2i0000−2i2i00-2200000000000000002i−2i00−2i2i0000-2200000000
χ4322-2-2222-22-2-222-2-2-22220-2-2-2222-2-2-200−2i2i2i−2i2-2-22000000000000000000−2i2i−2i2i002i−2i00002i−2i00-220000000000000000−2i2i002i−2i0000-2200000000
χ4422-2-2222-22-2-222-2-2-22220-2-2-2222-2-2-200−2i2i−2i2i2-2-22000000000000000000−2i2i−2i2i00−2i2i0000−2i2i002-20000000000000000−2i2i00−2i2i00002-200000000
χ4522-2-22-1212-2-22-1-21-2-1-12011-2-1-12-211−i3i32i−2i2i−2i-111-100−i3i300−i3i3−i3−i3i3i30000002i−2i−ii3−3−ii3−3002i−2i002-20000−i3−i3i3i300000000−ii3−3−ii3−300-1100000000
χ4622-2-22-1212-2-22-1-21-2-1-12011-2-1-12-211−i3i32i−2i−2i2i-111-100−i3i300−i3i3−i3−i3i3i30000002i−2i−ii3−3i−i−3300−2i2i00-220000i3i3−i3−i300000000−ii3−3i−i−33001-100000000
χ4722-2-22-1212-2-22-1-21-2-1-12011-2-1-12-211−i3i3−2i2i2i−2i-111-100−i3i300−i3i3−i3−i3i3i3000000−2i2ii−i−33−ii3−3002i−2i00-220000i3i3−i3−i300000000i−i−33−ii3−3001-100000000
χ4822-2-22-1212-2-22-1-21-2-1-12011-2-1-12-211−i3i3−2i2i−2i2i-111-100−i3i300−i3i3−i3−i3i3i3000000−2i2ii−i−33i−i−3300−2i2i002-20000−i3−i3i3i300000000i−i−33i−i−3300-1100000000
χ4922-2-22-1212-2-22-1-21-2-1-12011-2-1-12-211i3−i32i−2i2i−2i-111-100i3−i300i3−i3i3i3−i3−i30000002i−2i−ii−33−ii−33002i−2i002-20000i3i3−i3−i300000000−ii−33−ii−3300-1100000000
χ5022-2-22-1212-2-22-1-21-2-1-12011-2-1-12-211i3−i32i−2i−2i2i-111-100i3−i300i3−i3i3i3−i3−i30000002i−2i−ii−33i−i3−300−2i2i00-220000−i3−i3i3i300000000−ii−33i−i3−3001-100000000
χ5122-2-22-1212-2-22-1-21-2-1-12011-2-1-12-211i3−i3−2i2i2i−2i-111-100i3−i300i3−i3i3i3−i3−i3000000−2i2ii−i3−3−ii−33002i−2i00-220000−i3−i3i3i300000000i−i3−3−ii−33001-100000000
χ5222-2-22-1212-2-22-1-21-2-1-12011-2-1-12-211i3−i3−2i2i−2i2i-111-100i3−i300i3−i3i3i3−i3−i3000000−2i2ii−i3−3i−i3−300−2i2i002-20000i3i3−i3−i300000000i−i3−3i−i3−300-1100000000
χ532-2-222222-22-2-2-22-2-2222022-2-2-2-22-2-200000022-2-2000000000000000000000000000000002-2002i−2i2i−2i2-22-2000000000000000000002i−2i2i−2i0000
χ542-2-222222-22-2-2-22-2-2222022-2-2-2-22-2-200000022-2-2000000000000000000000000000000002-200−2i2i−2i2i2-22-200000000000000000000−2i2i−2i2i0000
χ552-2-222222-22-2-2-22-2-2222022-2-2-2-22-2-200000022-2-200000000000000000000000000000000-22002i−2i−2i2i-22-22000000000000000000002i−2i−2i2i0000
χ562-2-222222-22-2-2-22-2-2222022-2-2-2-22-2-200000022-2-200000000000000000000000000000000-2200−2i2i2i−2i-22-2200000000000000000000−2i2i2i−2i0000
χ5744444-2-2-2-2-244-24-2-2-21-24-21-2-21-2-2-21-2-200441111-24-2-2-2-2111111004000000000-2-2-2-200-2-200000000000000000-20000001111000000000000
χ5844444-2-2-2-2-244-24-2-2-21-24-21-2-21-2-2-21-2-200-4-41111-24-2-2-2-211111100-400000000022220022000000000000000002000000-1-1-1-1000000000000
χ5944444-2-2-2-2-244-24-2-2-21-2-4-21-2-21-2-2-2122004411112-42222-1-1-1-1-1-100-4000000000-2-22200-2-200000000000000000200000011-1-1000000000000
χ6044444-2-2-2-2-244-24-2-2-21-2-4-21-2-21-2-2-212200-4-411112-42222-1-1-1-1-1-100400000000022-2-2002200000000000000000-2000000-1-111000000000000
χ614444-24-24-2-2-2-24-24-2-2-214-2-21-2-211-2-24400001111-2-2-2-211-2-211114004-2-20000000000-2-200000000000000-211-2001100000000000000000000
χ624444-24-24-2-2-2-24-24-2-2-214-2-21-2-211-2-24400001111-2-2-2-211-2-21111-400-422000000000022000000000000002-1-1200-1-100000000000000000000
χ634444-24-24-2-2-2-24-24-2-2-21-4-2-21-2-211-2-2-4-4000011112222-1-122-1-1-1-1400-4-2-200000000002200000000000000-211200-1-100000000000000000000
χ644444-24-24-2-2-2-24-24-2-2-21-4-2-21-2-211-2-2-4-4000011112222-1-122-1-1-1-1-4004220000000000-2-2000000000000002-1-1-2001100000000000000000000
χ654444-2-24-244-2-2-2-2-241-2-241-2-21-2-2-21-2-2-2440011114-211-2-2-2-21111040000-2-2-2-2-2-2000000000000000000000000-200011110000000000000000
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χ7244-4-44-2-22-22-44-2-422-21-202-12-21-222-1−2i32i300−4i4i1-1-1100−2i32i300i3−i3i3i3−i3−i30000000000002i−2i−2323002i−2i000000000000000000000000−ii3−3000000000000
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χ7444-4-44-2-22-22-44-2-422-21-202-12-21-222-12i3−2i300−4i4i1-1-11002i3−2i300−i3i3−i3−i3i3i30000000000002i−2i23−23002i−2i000000000000000000000000−ii−33000000000000
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χ7744-4-4-2-2424-42-2-222-41-2-20-1221-2-22-12−2i32i34i−4i001-1-1100i3−i300−2i32i3i3i3−i3−i3000000−2i2i−2i2i23−230000000000000000000000000000i−i−330000000000000000
χ7844-4-4-2-2424-42-2-222-41-2-20-1221-2-22-12−2i32i3−4i4i001-1-1100i3−i300−2i32i3i3i3−i3−i30000002i−2i2i−2i−23230000000000000000000000000000−ii3−30000000000000000
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χ814-44-4444-4-4-44-4-4-4444440-4-44-4-4-4-4440000004-44-4000000000000000000000000000000000000000000000000000000000000000000000000
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χ854-44-44-242-4-44-42-4-24-2-24022422-4-4-2-2000000-22-2200000000000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ864-44-4-244-4-4-4-22-4244-24-202-4-22-422-24000000-22-22000000000000000000000000000023−230000000000000000000023−2300000000000000000000
χ874-44-4-244-4-4-4-22-4244-24-202-4-22-422-24000000-22-220000000000000000000000000000−232300000000000000000000−232300000000000000000000
χ884-44-4-24-2-422-22-424-2-2-21022122-1-1-2-20000001-11-100003i−3i003i−3i3i−3i0000−2i32i3000000000023−23000000000000000i3−i3000−3300000000000000000000
χ894-44-4-24-2-422-22-424-2-2-21022122-1-1-2-20000001-11-100003i−3i003i−3i3i−3i00002i3−2i30000000000−2323000000000000000−i3i30003−300000000000000000000
χ904-44-4-24-2-422-22-424-2-2-21022122-1-1-2-20000001-11-10000−3i3i00−3i3i−3i3i0000−2i32i30000000000−2323000000000000000i3−i30003−300000000000000000000
χ914-44-4-24-2-422-22-424-2-2-21022122-1-1-2-20000001-11-10000−3i3i00−3i3i−3i3i00002i3−2i3000000000023−23000000000000000−i3i3000−3300000000000000000000
χ924-4-4444-242-2-4-4-44-424-2-204-22-422-2-42000000-2-222000000000000000000000000000000000000004i−4i00000000000000000000000000−2i2i0000
χ934-4-4444-242-2-4-4-44-424-2-204-22-422-2-42000000-2-22200000000000000000000000000000000000000−4i4i000000000000000000000000002i−2i0000
χ944-4-444-24-2-44-4-4242-4-2-240-2-2-422-4422000000-2-222000000000000000000000000000000004-4000000-22-220000000000000000000000000000
χ954-4-444-24-2-44-4-4242-4-2-240-2-2-422-4422000000-2-22200000000000000000000000000000000-440000002-22-20000000000000000000000000000
χ964-4-44-2444-4422-4-2-4-4-24-20-2422-42-22-4000000-2-2220000000000000000000000000000000000004i−4i00000000000000000000000000−2i2i000000
χ974-4-44-2444-4422-4-2-4-4-24-20-2422-42-22-4000000-2-222000000000000000000000000000000000000−4i4i000000000000000000000000002i−2i000000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-48-4-8-444-484-84-4-42044-2-4-42-2440000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-44-444-4-44442220-2-2-2222-2-2-2−4i34i30000-111-1002i3−2i3002i3−2i3−i3−i3i3i3000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-44-444-4-44442220-2-2-2222-2-2-24i3−4i30000-111-100−2i32i300−2i32i3i3i3−i3−i3000000000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-44448-84-8-4-4-42-404-2-44-244-420000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-484-8-8-4444-482-4-40-24-4-24442-40000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-4444-4444-4-42220-2-22-2-2-2-222000000-11-1100006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-4444-4444-4-42220-2-22-2-2-2-222000000-11-110000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000000000
χ1078-8-888-4-4-44-4-8-84844-42-40-4244-24-44-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-484-444-8-4-84-4-420-4-4-244-224400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-48-4-88444-44-82-4-402-44-244-4-2400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-4-44-4444-444222022-2-2-2-22-2-2000000-1-1110000000033−33−3333000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-44-4444-444222022-2-2-2-22-2-2000000-1-11100000000−333333−33000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).