Finite Group Databasebeta

← Group #13170601

Character table — Group #13170601

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
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order12233344666121233366666612121212121212121212122244366666612121212121212246666668812121212121224242424882424242466666121212121224242424242444448121212122424121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1-11111-1-1111111-1-11111111111-111-1-1-111-1-1111111-1-1-1-11-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11-1-1111-1-111111111-1-111-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111111-1-1111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-111
χ7111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-1-1-1-111
χ8111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ911-1111-1111111111-1-1-1111-1-11-111-1-11111-11-11-1-1-1-1-11-11-111-1-11-11-11-1111-11-11-1-1-111-1-111111111-111-11-1-1-1111-1-1-11-11-1-111-1-1-1-11-11-1
χ1011-1111-1111111111-1-1-1111-1-11-111-1-11111-11-11-1-1-1-1-11-11-111-1-11-11-11-111-111-11-1-1-1-1-111-1-1-1-1-1-111-111-11-1-1-1-1-1-11111-1-11111-1-111-11-11
χ1111-1111-1111111111-1-1-1111-1-11-111-1-11111-11-11-1-1-1-1-11-11-111-1-1-111-11-1-1-11-11-11-11111-1-1111111-11-1-1-111-111111-1-1-1-11-11-1-1-111-1-1-11-11
χ1211-1111-1111111111-1-1-1111-1-11-111-1-11111-11-11-1-1-1-1-11-11-111-1-1-111-11-1-1-1-111-11-111-1-111-1-1-1-1-1-1-11-1-1-111-111-1-1-1111-111-11-1-111111-11-1
χ1311-1111-1111111111-1-1-1111-1-11-111-1-1111-11-111-1-1-1-1-11-11-111-1-11-1-11-11111-1-11-11-1-111-1-1-1-1-1-1-1-11-1111-1-11-1-1111-1-1-1-111-11-1-111111-1-11
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χ2422222-1-2-222-1-2-22-1-122-12-1-1-2-2111111-2-2-22-2-22-12-1-1-1-1-1-2111111002-2-11i3−i300-221-1i3−i300000000000-11i3−i301-1i3−i300000000000i3−i3i3−i3000000
χ2522222-1-2-222-1-2-22-1-122-12-1-1-2-2111111-2-2-2-222-2-12-1-1-1-1-1-211111100-221-1−i3i3002-2-11−i3i3000000000001-1−i3i30-11−i3i300000000000i3−i3i3−i3000000
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χ272222-12222-1222-12-12-12-12-12-12222-1-1-1-1-10000-1-12-1-1-1-1-1-12-1-1-1-122000022220000222222000000-100-1-1-100-1-1-1-1-1-1-1-100220000000-1-100
χ282222-12222-1222-12-12-12-12-12-12222-1-1-1-1-10000-1-12-1-1-1-1-1-12-1-1-1-122000022-2-2000022-2-2-2-2000000-100-1-1-100-1-111111100-2-200000001100
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χ302222-12222-1222-12-12-12-12-12-12222-1-1-1-1-10000-1-12-1-1-1-1-1-12-1-1-1-1-2-20000-2-2-2-20000-2-2-2-2-2-2000000100111001111111100220000000-1-100
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χ38222-122-2-2-12211-1-12-122-1-121-2-2-211-2-2-211-222-2-1-1-12-1-1-11-211111001-1-220000-112-200−33−330033−3−301-1000-11000−330−330000000003−30000
χ3922-22222-2222-2-2222-2-2-222222-22-2-222-2-2-222-2-22-2-2-2-2-222-22-2-2220022220000-2-2-2-2000000000000022000-2-200000000000000000000000
χ4022-22222-2222-2-2222-2-2-222222-22-2-222-2-2-2-2-2222-2-2-2-2-222-22-2-22200-2-2-2-2000022220000000000000-2-20002200000000000000000000000
χ4122-222-12-222-1-2-22-1-1-2-212-1-1221-111-1-1-2-2-222-2-2-1-21111-121-111-1-10022-1-1−i3i300-2-211i3−i300000000000-1-1−i3i3011i3−i300000000000−i3i3i3−i3000000
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χ4322-222-12-222-1-2-22-1-1-2-212-1-1221-111-1-1-2-2-2-2-222-1-21111-121-111-1-100-2-211−i3i30022-1-1i3−i30000000000011−i3i30-1-1i3−i300000000000i3−i3−i3i3000000
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χ4522-222-1-2222-1222-1-1-2-212-1-1-2-2-11-1-1112222-22-2-1-21111-1-2-11-1-1112-22-2-11-1-1002-2-111100000000002-11-1-1-2-11110000002-2000-1-111000000
χ4622-222-1-2222-1222-1-1-2-212-1-1-2-2-11-1-1112222-22-2-1-21111-1-2-11-1-111-222-2-1111002-2-11-1-10000000000-2-11112-11-1-1000000-2200011-1-1000000
χ4722-222-1-2222-1222-1-1-2-212-1-1-2-2-11-1-111222-22-22-1-21111-1-2-11-1-1112-2-221-1-1-100-221-111000000000021-1-1-1-21-111000000-2200011-1-1000000
χ4822-222-1-2222-1222-1-1-2-212-1-1-2-2-11-1-111222-22-22-1-21111-1-2-11-1-111-22-221-11100-221-1-1-10000000000-21-11121-1-1-10000002-2000-1-111000000
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χ874-4044400-4-4-400444000-4-4-4000000000000000400000-400000000000000000000000000022−2222−2222−220000000000000000000000000000000
χ884-4044400-4-4-400444000-4-4-4000000000000000400000-4000000000000000000000000000−2222−2222−22220000000000000000000000000000000
χ894-40-244002-4-423−23-2-2400022-4000023−2300023−230000-200000200023−23000000000000000000000022−222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ70000000000000000000000000000000
χ904-40-244002-4-423−23-2-2400022-4000023−2300023−230000-200000200023−230000000000000000000000−2222−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ70000000000000000000000000000000
χ914-40-244002-4-4−2323-2-2400022-40000−2323000−23230000-2000002000−2323000000000000000000000022−222ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ230000000000000000000000000000000
χ924-40-244002-4-4−2323-2-2400022-40000−2323000−23230000-2000002000−23230000000000000000000000−2222−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ230000000000000000000000000000000
χ93888-4-4-488-4-4-4-4-4222-4-4-4222-4-4-4-42222-4220000-1222-1-1-1222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ94888-4-4-4-8-8-4-4-444222-4-4-42224444-2-2-2-24-2-20000-1222-1-1-1-2-2-21111000000000000000000000000000000000000000000000000000000000
χ9588-8-4-4-48-8-4-4-444222444222-4-44-4-2-2224-2-20000-1-2-2-211-12-2211-1-1000000000000000000000000000000000000000000000000000000000
χ9688-8-4-4-4-88-4-4-4-4-422244422244-4422-2-2-4220000-1-2-2-211-1-22-2-1-111000000000000000000000000000000000000000000000000000000000
χ978-8088-400-8-84008-4-4000-844000000000000000-40000040000000000000000000000000000000000000000000000000000000000000000
χ988-808-4800-84-800-48-40004-84000000000000000-40000040000000000000000000000000000000000000000000000000000000000000000
χ998-808-4-400-84400-4-4200044-20000006i−6i0000000200000-2000006i−6i000000000000000000000000000000000000000000000000000000000
χ1008-808-4-400-84400-4-4200044-2000000−6i6i0000000200000-200000−6i6i000000000000000000000000000000000000000000000000000000000
χ1018-80-48-4004-8443−43-42-40004-240000−232300043−430000200000-2000−232300000000000000000000000000000000000000000000000000000000000
χ1028-80-48-4004-84−4343-42-40004-24000023−23000−43430000200000-200023−2300000000000000000000000000000000000000000000000000000000000
χ1038-80-4-480044-843−432-4-4000-244000043−43000−23230000200000-2000−232300000000000000000000000000000000000000000000000000000000000
χ1048-80-4-480044-8−43432-4-4000-2440000−434300023−230000200000-200023−2300000000000000000000000000000000000000000000000000000000000
χ1058-80-4-4-40044443−43222000-2-2-20000−23236i−6i0−23230000-1000−3i33i310003−3−3i3i000000000000000000000000000000000000000000000000000000000
χ1068-80-4-4-40044443−43222000-2-2-20000−2323−6i6i0−23230000-10003i3−3i310003−33i−3i000000000000000000000000000000000000000000000000000000000
χ1078-80-4-4-400444−4343222000-2-2-2000023−236i−6i023−230000-10003i3−3i31000−33−3i3i000000000000000000000000000000000000000000000000000000000
χ1088-80-4-4-400444−4343222000-2-2-2000023−23−6i6i023−230000-1000−3i33i31000−333i−3i000000000000000000000000000000000000000000000000000000000

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