Finite Group Databasebeta

← Group #13168486

Character table — Group #13168486

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222222444444444444444444444466666688888888888812121212121212121212121212121212121212121212121818181818182424242424242424242424242424363636363636363636363654547272108
order1222333446666666663336666666661212121212121212121244121212123666121212121212121222244666666666612121212121212124444446666666121212121212122441212121212121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-11-11111111111111111111111-1-11-1-111-1-1-11-111-1-1-1-1-111-1-111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-11-1111-1-1111111-1-1111111-1-1-1-1-1-1-111-1-1111-11-1-11111-1-1-1-1-1-1-1-1-1-1-111-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1111111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-11
χ51111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-11111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-11-1-111-1-111-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-11-11-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-11-111-1-111-1-1-1-1-1-1-1-1-111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1111-11-1-111-1-1-111-1-111-1-111-1-11
χ81111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1
χ91111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111111-1-1-1-1-1-1-11-11-1-1-1-11111-1-11-11
χ101111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-1-11-1-111-1-1-1-1-1-1-1-111111111-1-1111-1-111-1-11-11-1-111-11-1-1-11111-1-111-11-1
χ111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-111-1-111-11-111-1-11-1-11111-1-1-1-1111-1-1
χ121111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-1-11111111-11111-1-1-1-111-1-1-111
χ131111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-1
χ141111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-111-1-11-11-1-1111-1-11111-1-1-1-1-1-11-11
χ151111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-111-111-1-111111111-1-1-1-1-1-111-1-111-111-1-111-11-111-1-1-11-1-1-11111-1-1-1-1-111
χ161111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-11111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111-11-1-1-1-11111111-1-1
χ17222222-122-122-122-1222-1-12-1-1-12-12-1-122-1-122-1-1-1-1222222-1-1-1-122-1-1-1-1-1-1202022200-1-1-1-1-1-100-1-1-1-1-1-100000002-100-1-1-10200-1-12200000000000-1-10
χ18222222-122-122-122-1222-1-12-1-1-12-12-1-122-1-122-1-1-1-1222222-1-1-1-122-1-1-1-1-1-120-20-22200-1-1-1-1-1-100-1-1-1-1-1-10000000-21001110-20011-2-200000000000110
χ19222222-122-122-122-1222-1-12-1-1-12-12-1-122-1-122-1-1-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-1-20202-2-2001111110011111100000002-100-1-1-10200-1-1-2-200000000000110
χ20222222-122-122-122-1222-1-12-1-1-12-12-1-122-1-122-1-1-1-1-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-1-20-20-2-2-200111111001111110000000-21001110-200112200000000000-1-10
χ21222222-1-2-2-122-122-1222-1-12-1-1-12-12-1-1-2-211-2-21111222222-1-1-1-1-2-2111111-2020-2-2-20011111100-1-1-1-1-1-100000002-100-1-110-200112-200000000000-110
χ22222222-1-2-2-122-122-1222-1-12-1-1-12-12-1-1-2-211-2-21111222222-1-1-1-1-2-2111111-20-202-2-20011111100-1-1-1-1-1-10000000-210011-10200-1-1-22000000000001-10
χ23222222-1-2-2-122-122-1222-1-12-1-1-12-12-1-1-2-211-2-21111-2-2-2-2-2-2-1-1-1-1-2-21111112020-22200-1-1-1-1-1-10011111100000002-100-1-110-20011-22000000000001-10
χ24222222-1-2-2-122-122-1222-1-12-1-1-12-12-1-1-2-211-2-21111-2-2-2-2-2-2-1-1-1-1-2-211111120-2022200-1-1-1-1-1-1001111110000000-210011-10200-1-12-200000000000-110
χ2522222-122222-122-12-12-12-1-12-1-1-12-12-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-122020-1-1-1-122-1-1-1-1-1-122-1-1-1-1222200200-1-100020-1-100000-1-100-1-10000000
χ2622222-122222-122-12-12-12-1-12-1-1-12-12-12222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122-1-1-1-12-20-20-1-11122-1-1-1-11122-1-1-1-1-2-2-2-200-20011000-2011000001100110000000
χ2722222-122222-122-12-12-12-1-12-1-1-12-12-12222-1-1-1-1-1-1-2-21111-1-1-1-1-1-122-1-1-1-1-2202011-1-1-2-21111-1-1-2-21111-2-2-2-200200-1-100020-1-1000001100110000000
χ2822222-122222-122-12-12-12-1-12-1-1-12-12-12222-1-1-1-1-1-1-2-21111-1-1-1-1-1-122-1-1-1-1-2-20-201111-2-2111111-2-21111222200-20011000-201100000-1-100-1-10000000
χ2922222-12-2-222-122-12-12-12-1-12-1-1-12-12-1-2-2-2-211111122-1-1-1-1-1-1-1-111-2-21111-220-2011-1-1-2-211111122-1-1-1-122-2-200200-1-1000-2011000001100-1-10000000
χ3022222-12-2-222-122-12-12-12-1-12-1-1-12-12-1-2-2-2-211111122-1-1-1-1-1-1-1-111-2-21111-2-20201111-2-21111-1-122-1-1-1-1-2-22200-2001100020-1-100000-1-100110000000
χ3122222-12-2-222-122-12-12-12-1-12-1-1-12-12-1-2-2-2-2111111-2-21111-1-1-1-111-2-21111220-20-1-1-1-122-1-1-1-111-2-21111-2-22200200-1-1000-201100000-1-100110000000
χ3222222-12-2-222-122-12-12-12-1-12-1-1-12-12-1-2-2-2-2111111-2-21111-1-1-1-111-2-211112-2020-1-11122-1-1-1-1-1-1-2-2111122-2-200-2001100020-1-1000001100-1-10000000
χ332222-122222-122-1222-1-1-12-1-122-1-1-1-12-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-102222002200000022000000000022-1-12-1-1-1-12-1-1-1-1-1-100200-1-100-1-100000
χ342222-122222-122-1222-1-1-12-1-122-1-1-1-12-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-102-22-20022000000220000000000-2-2-11-2-1-111-2-11-1-11100-20011001100000
χ352222-122222-122-1222-1-1-12-1-122-1-1-1-12-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-10-22-2200-2-2000000-2-20000000000-2-21-1211-1-121-111-1-100-20011001100000
χ362222-122222-122-1222-1-1-12-1-122-1-1-1-12-1-122222222000000-1-1-1-1-1-1-1-1-1-1-1-10-2-2-2-200-2-2000000-2-200000000002211-21111-211111100200-1-100-1-100000
χ372222-122-2-22-122-1222-1-1-12-1-122-1-1-1-1211-2-2-2-2-2-2-2-2000000-1-1-1-111111111022-2-20022000000-2-20000000000-2-2-1-12-1-1-1-1-2111111002001100-1-100000
χ382222-122-2-22-122-1222-1-1-12-1-122-1-1-1-1211-2-2-2-2-2-2-2-2000000-1-1-1-11111111102-2-220022000000-2-2000000000022-11-2-1-11121-111-1-100-200-1-1001100000
χ392222-122-2-22-122-1222-1-1-12-1-122-1-1-1-1211-2-2-2-2-2-2-2-2000000-1-1-1-1111111110-222-200-2-2000000220000000000221-1211-1-1-2-11-1-11100-200-1-1001100000
χ402222-122-2-22-122-1222-1-1-12-1-122-1-1-1-1211-2-2-2-2-2-2-2-2000000-1-1-1-1111111110-2-22200-2-2000000220000000000-2-211-211112-1-1-1-1-1-1002001100-1-100000
χ4122-2-222200-22-22-2-2-22-2222-2-2-2-222-2-2200000000002-222-2-22-2-2200000000000000000000000002-222-2-200002i−2i00000000000000000002i−2i00002i−2i000
χ4222-2-222200-22-22-2-2-22-2222-2-2-2-222-2-2200000000002-222-2-22-2-2200000000000000000000000002-222-2-20000−2i2i0000000000000000000−2i2i0000−2i2i000
χ4322-2-222200-22-22-2-2-22-2222-2-2-2-222-2-220000000000-22-2-2222-2-220000000000000000000000000-22-2-22200002i−2i00000000000000000002i−2i0000−2i2i000
χ4422-2-222200-22-22-2-2-22-2222-2-2-2-222-2-220000000000-22-2-2222-2-220000000000000000000000000-22-2-2220000−2i2i0000000000000000000−2i2i00002i−2i000
χ452-22-22222i−2i2-2-2-222-2-2-2222222-2-2-2-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i00000022-2-22i−2i2i−2i2i2i−2i−2i000000000000000000000002i−2i2-200000000000000000002-2002i−2i0000000
χ462-22-22222i−2i2-2-2-222-2-2-2222222-2-2-2-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i00000022-2-22i−2i2i−2i2i2i−2i−2i00000000000000000000000−2i2i-220000000000000000000-2200−2i2i0000000
χ472-22-2222−2i2i2-2-2-222-2-2-2222222-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i00000022-2-2−2i2i−2i2i−2i−2i2i2i000000000000000000000002i−2i-220000000000000000000-22002i−2i0000000
χ482-22-2222−2i2i2-2-2-222-2-2-2222222-2-2-2-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i00000022-2-2−2i2i−2i2i−2i−2i2i2i00000000000000000000000−2i2i2-200000000000000000002-200−2i2i0000000
χ492-22-22-122i−2i2-21-22-1-21-2-12-1-12-111-21-212i−2i2i−2i−ii−i−iii003−33−3-1-111−ii2i−2i−i−iii00000−i3i3−i3i300−i3−i3i3i33−3003−33−32i−2i2-200000−i3i3000003−300000-1100−ii0000000
χ502-22-22-122i−2i2-21-22-1-21-2-12-1-12-111-21-212i−2i2i−2i−ii−i−iii003−33−3-1-111−ii2i−2i−i−iii00000−i3i3i3−i300−i3−i3i3i3−33003−33−3−2i2i-2200000i3−i300000−33000001-100i−i0000000
χ512-22-22-122i−2i2-21-22-1-21-2-12-1-12-111-21-212i−2i2i−2i−ii−i−iii00−33−33-1-111−ii2i−2i−i−iii00000i3−i3−i3i300i3i3−i3−i33−300−33−33−2i2i-2200000−i3i3000003−3000001-100i−i0000000
χ522-22-22-122i−2i2-21-22-1-21-2-12-1-12-111-21-212i−2i2i−2i−ii−i−iii00−33−33-1-111−ii2i−2i−i−iii00000i3−i3i3−i300i3i3−i3−i3−3300−33−332i−2i2-200000i3−i300000−3300000-1100−ii0000000
χ532-22-22-12−2i2i2-21-22-1-21-2-12-1-12-111-21-21−2i2i−2i2ii−iii−i−i003−33−3-1-111i−i−2i2iii−i−i00000i3−i3−i3i300i3i3−i3−i3−33003−33−32i−2i-2200000−i3i300000−33000001-100−ii0000000
χ542-22-22-12−2i2i2-21-22-1-21-2-12-1-12-111-21-21−2i2i−2i2ii−iii−i−i003−33−3-1-111i−i−2i2iii−i−i00000i3−i3i3−i300i3i3−i3−i33−3003−33−3−2i2i2-200000i3−i3000003−300000-1100i−i0000000
χ552-22-22-12−2i2i2-21-22-1-21-2-12-1-12-111-21-21−2i2i−2i2ii−iii−i−i00−33−33-1-111i−i−2i2iii−i−i00000−i3i3−i3i300−i3−i3i3i3−3300−33−33−2i2i2-200000−i3i300000−3300000-1100i−i0000000
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χ5744444-2-244-24-2-24-2-2-24-2-21-2-211-2-2-2-2144-2-2-2-2111144-2-2-2-21111-2-2-2-2111140000-2-200-2-2111100-2-21111000000000000000000000000000000000000
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χ814-44-44-2-24i−4i-2-4224-222-4-2-21-2-21-12222-14i−4i−2i2i−2i2iii−i−i0023−2323−2311-1-1−2i2i−2i2iii−i−i00000−2i32i30000i3i3−i3−i30000−33−33000000000000000000000000000000000000
χ824-44-44-2-24i−4i-2-4224-222-4-2-21-2-21-12222-14i−4i−2i2i−2i2iii−i−i00−2323−232311-1-1−2i2i−2i2iii−i−i000002i3−2i30000−i3−i3i3i300003−33−3000000000000000000000000000000000000
χ834-44-44-2-2−4i4i-2-4224-222-4-2-21-2-21-12222-1−4i4i2i−2i2i−2i−i−iii0023−2323−2311-1-12i−2i2i−2i−i−iii000002i3−2i30000−i3−i3i3i30000−33−33000000000000000000000000000000000000
χ844-44-44-2-2−4i4i-2-4224-222-4-2-21-2-21-12222-1−4i4i2i−2i2i−2i−i−iii00−2323−232311-1-12i−2i2i−2i−i−iii00000−2i32i30000i3i3−i3−i300003−33−3000000000000000000000000000000000000
χ854-44-4-2444i−4i42-4-4-24-4-42-2-24-2-24-42222-4−2i2i4i−4i4i−4i4i4i−4i−4i000000-2-222−2i2i−2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000000
χ864-44-4-244−4i4i42-4-4-24-4-42-2-24-2-24-42222-42i−2i−4i4i−4i4i−4i−4i4i4i000000-2-2222i−2i2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000000
χ874-44-4-24-24i−4i-22-42-242-42-21-2-21-222-12-12−2i2i−2i2i4i−4i−2i−2i2i2i00000011-1-1−2i2ii−iii−i−i00000000000000000000000000000000003-3000003i−3i0000000000000000
χ884-44-4-24-24i−4i-22-42-242-42-21-2-21-222-12-12−2i2i−2i2i4i−4i−2i−2i2i2i00000011-1-1−2i2ii−iii−i−i0000000000000000000000000000000000-3300000−3i3i0000000000000000
χ894-44-4-24-2−4i4i-22-42-242-42-21-2-21-222-12-122i−2i2i−2i−4i4i2i2i−2i−2i00000011-1-12i−2i−ii−i−iii00000000000000000000000000000000003-300000−3i3i0000000000000000
χ904-44-4-24-2−4i4i-22-42-242-42-21-2-21-222-12-122i−2i2i−2i−4i4i2i2i−2i−2i00000011-1-12i−2i−ii−i−iii0000000000000000000000000000000000-33000003i−3i0000000000000000
χ914-44-4-2-244i−4i422-4-2-2-4221-2-21-2-22-12-122−2i2i4i−4i−2i2i−2i−2i2i2i00000011-1-1i−i−2i2iii−i−i0000000−2i32i300000023−23000000000000000i3−i300000−33000000000000000000
χ924-44-4-2-244i−4i422-4-2-2-4221-2-21-2-22-12-122−2i2i4i−4i−2i2i−2i−2i2i2i00000011-1-1i−i−2i2iii−i−i00000002i3−2i3000000−2323000000000000000−i3i3000003−3000000000000000000
χ934-44-4-2-24−4i4i422-4-2-2-4221-2-21-2-22-12-1222i−2i−4i4i2i−2i2i2i−2i−2i00000011-1-1−ii2i−2i−i−iii0000000−2i32i3000000−2323000000000000000i3−i3000003−3000000000000000000
χ944-44-4-2-24−4i4i422-4-2-2-4221-2-21-2-22-12-1222i−2i−4i4i2i−2i2i2i−2i−2i00000011-1-1−ii2i−2i−i−iii00000002i3−2i300000023−23000000000000000−i3i300000−33000000000000000000
χ954-4-4444400-4-44-4-4-44-44444-4-4-44-4-444-400000000000000004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ964-4-4444-2002-442-4-4-2-444-2-2-422-2-424-220000000000000000-22-2200000000000000000−2i32i3−2i32i32i3−2i300000000000000000000000000000000000000000000
χ974-4-4444-2002-442-4-4-2-444-2-2-422-2-424-220000000000000000-22-22000000000000000002i3−2i32i3−2i3−2i32i300000000000000000000000000000000000000000000
χ984-4-444-2400-4-4-2-4-42424-24-22-42-22-4-24200000000000023−23−2323-22-2200000000000000000000000000023−23−2323000000000000000000000000000000000000
χ994-4-444-2400-4-4-2-4-42424-24-22-42-22-4-242000000000000−232323−23-22-22000000000000000000000000000−232323−23000000000000000000000000000000000000
χ1004-4-444-2-2002-4-22-42-224-2-2122-1122-2-2-10000003i−3i−3i3i0023−23−23231-11-100003i−3i−3i3i0000000002i3−2i3−i3i3i3−i30000−333−3000000000000000000000000000000000000
χ1014-4-444-2-2002-4-22-42-224-2-2122-1122-2-2-10000003i−3i−3i3i00−232323−231-11-100003i−3i−3i3i000000000−2i32i3i3−i3−i3i300003−3−33000000000000000000000000000000000000
χ1024-4-444-2-2002-4-22-42-224-2-2122-1122-2-2-1000000−3i3i3i−3i0023−23−23231-11-10000−3i3i3i−3i000000000−2i32i3i3−i3−i3i30000−333−3000000000000000000000000000000000000
χ1034-4-444-2-2002-4-22-42-224-2-2122-1122-2-2-1000000−3i3i3i−3i00−232323−231-11-10000−3i3i3i−3i0000000002i3−2i3−i3i3i3−i300003−3−33000000000000000000000000000000000000
χ1044-4-44-24400-424-42-44-4-2-2-2422-4422-2-2-40000000000000000-22-22000000000000000000000000000000000000000000000000000000000000−2i32i300000
χ1054-4-44-24400-424-42-44-4-2-2-2422-4422-2-2-40000000000000000-22-220000000000000000000000000000000000000000000000000000000000002i3−2i300000
χ1068888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-4-42222000000-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000000000
χ1078888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444444-2-2-2-2000000-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000000000
χ10888-8-8-48-4004-4-8-44-8484-42-44-244-424-2-400000000000000002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-4-4800-8-44844-8-442-4-4-24442-4-24-400000000000000002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-4004-44-4444-44222-2-2-2-222-2-220000006-66-6000000-111-10000-33-3300000000000000000000000000000000000000000000000000000000000
χ11188-8-8-4-4-4004-44-4444-44222-2-2-2-222-2-22000000-66-66000000-111-100003-33-300000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-4-48i−8i-4444-4-4444222222-2-2-2-2-2-2−4i4i−4i4i−4i4i2i2i−2i−2i000000-1-1112i−2i2i−2i−i−iii00000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4-4−8i8i-4444-4-4444222222-2-2-2-2-2-24i−4i4i−4i4i−4i−2i−2i2i2i000000-1-111−2i2i−2i2iii−i−i00000000000000000000000000000000000000000000000000000000000
χ1148-8-88-48-40044844-8-4-8-4-42-44-24-44-2-42400000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1158-8-88-4-4800-84-4-84484-42-4-4-244-4-242-4400000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-40044-4444-44-4222-2-2-22-2-222-20000006i−6i−6i6i000000-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-40044-4444-44-4222-2-2-22-2-222-2000000−6i6i6i−6i000000-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000000

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