Finite Group Databasebeta

← Group #13170532

Character table — Group #13170532

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
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order12233344666121233366666666121212121212121212224436666612121212121212122266666666881212121224242424882424242466666666121224242424242422446681212242461222
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11-11-111-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111111111111111-1-111-1-1-1-111111111-1-1-1-1-1-11-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-11-11-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1111111-11-11-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111
χ7111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-11-111-111-1-1-1-111
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
χ911-1111-1111111111-1-1-1-1-1111-1-11-1111111-11-11-1-1-1-111-1-1-111-1-11-11-11-111-1-11-11-11-111-1-11111111-11-111-1-11-1111-1-1-111-1-111-1-1-1-1-11-11-1
χ1011-1111-1111111111-1-1-1-1-1111-1-11-1111111-11-11-1-1-1-111-1-1-111-1-11-11-11-111-1-1-111-11-1-1-111-1-1-1-1-1-11-11-111-1-11-1-1-1-11111-1-11111-1-111-11-11
χ1111-1111-1111111111-1-1-1-1-1111-1-11-1111111-11-11-1-1-1-111-1-1-111-1-1-111-11-1-1-1111-11-11-111-1-1111111-111-1-1-1111-1111-1-1-1-1-111-1-1-111-1-1-11-11
χ1211-1111-1111111111-1-1-1-1-1111-1-11-1111111-11-11-1-1-1-111-1-1-111-1-1-111-11-1-1-111-111-11-1-1-111-1-1-1-1-1-1-111-1-1-1111-1-1-1-1111-111-1-1-1111111-11-1
χ1311-1111-1111111111-1-1-1-1-1111-1-11-111111-11-111-1-1-1-111-1-1-111-1-11-1-11-1111-1-11-1-11-1111-1-1-1-1-1-1-1-11-1-1111-1-1-11111-1-1-1-111-1-1-1111111-1-11
χ1411-1111-1111111111-1-1-1-1-1111-1-11-111111-11-111-1-1-1-111-1-1-111-1-11-1-11-1111-1-1-11-11-11-1-1111111111-1-1111-1-1-11-1-1-1111-1-111-1-1-111-1-1-111-1
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χ1611-1111-1111111111-1-1-1-1-1111-1-11-111111-11-111-1-1-1-111-1-1-111-1-1-11-11-11-1-111-11-11-11-1-111111111-11-11-1-111-11-1-1-111111-1-111-1-1-1-1-11-1-11
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χ2522222-1-2-222-1-2-22-1-122-1-1-12-1-1-2-21111-2-2-2-222-2-12-1-1-1-11-211111100-221-1−i3i3−i3i3002-2-110000000000001-1−i3i3−i3i3-110000000000i3−i30i3−i3000000
χ2622222-1-2-222-1-2-22-1-122-1-1-12-1-1-2-21111-2-2-2-222-2-12-1-1-1-11-211111100-221-1i3−i3i3−i3002-2-110000000000001-1i3−i3i3−i3-110000000000−i3i30−i3i3000000
χ272222-12222-1222-12-12-12-1-1-1-122-12222-1-1-10000-1-12-1-1-1-1-1-12-1-1-1-122000022222200002222000000-1-100-1-1-1-100-1-1-1-1-1-102020000000-1-100
χ282222-12222-1222-12-12-12-1-1-1-122-12222-1-1-10000-1-12-1-1-1-1-1-12-1-1-1-12200002222-2-20000-2-2-2-2000000-1-100-1-1-1-1001111110-20-200000001100
χ292222-12222-1222-12-12-12-1-1-1-122-12222-1-1-10000-1-12-1-1-1-1-1-12-1-1-1-1-2-20000-2-2-2-222000022220000001100111100-1-1-1-1-1-10-20-200000001100
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χ3922-22222-2222-2-2222-2-2-2-2-222222-22-2-2-2-2-222-2-22-2-2-2-22-2222-2-222002222000000-2-2-2-2000000000000220000-2-2000000000000000000000
χ4022-22222-2222-2-2222-2-2-2-2-222222-22-2-2-2-2-2-2-2222-2-2-2-22-2222-2-22200-2-2-2-20000002222000000000000-2-2000022000000000000000000000
χ4122-222-12-222-1-2-22-1-1-2-21112-1-1221-111-2-2-222-2-2-1-2111-112-1-111-1-10022-1-1−i3i3i3−i300-2-211000000000000-1-1−i3i3i3−i3110000000000−i3i30i3−i3000000
χ4222-222-12-222-1-2-22-1-1-2-21112-1-1221-111-2-2-222-2-2-1-2111-112-1-111-1-10022-1-1i3−i3−i3i300-2-211000000000000-1-1i3−i3−i3i3110000000000i3−i30−i3i3000000
χ4322-222-12-222-1-2-22-1-1-2-21112-1-1221-111-2-2-2-2-222-1-2111-112-1-111-1-100-2-211−i3i3i3−i30022-1-100000000000011−i3i3i3−i3-1-10000000000i3−i30−i3i3000000
χ4422-222-12-222-1-2-22-1-1-2-21112-1-1221-111-2-2-2-2-222-1-2111-112-1-111-1-100-2-211i3−i3−i3i30022-1-100000000000011i3−i3−i3i3-1-10000000000−i3i30i3−i3000000
χ4522-222-1-2222-1222-1-1-2-21112-1-1-2-2-11-1-12222-22-2-1-2111-1-1-211-1-1112-22-2-11-1-111002-2-1100000000002-2-11-1-111-1100000020-20-1-1011000000
χ4622-222-1-2222-1222-1-1-2-21112-1-1-2-2-11-1-12222-22-2-1-2111-1-1-211-1-111-222-2-1111-1-1002-2-110000000000-22-1111-1-1-11000000-2020110-1-1000000
χ4722-222-1-2222-1222-1-1-2-21112-1-1-2-2-11-1-1222-22-22-1-2111-1-1-211-1-1112-2-221-1-1-11100-221-100000000002-21-1-1-1111-1000000-2020110-1-1000000
χ4822-222-1-2222-1222-1-1-2-21112-1-1-2-2-11-1-1222-22-22-1-2111-1-1-211-1-111-22-221-111-1-100-221-10000000000-221-111-1-11-100000020-20-1-1011000000
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χ874-4044400-4-4-40044400000-4-4-4000000000000040000-4000000000000000000000000000022−2222−2222−220000000000000000000000000000000
χ884-4044400-4-4-40044400000-4-4-4000000000000040000-40000000000000000000000000000−2222−2222−22220000000000000000000000000000000
χ894-40-244002-4-423−23-2-24000002-42000023−23023−230000-200002000023−23000000000000000000000022−222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ70000000000000000000000000000000
χ904-40-244002-4-423−23-2-24000002-42000023−23023−230000-200002000023−230000000000000000000000−2222−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ70000000000000000000000000000000
χ914-40-244002-4-4−2323-2-24000002-420000−23230−23230000-2000020000−2323000000000000000000000022−222ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ230000000000000000000000000000000
χ924-40-244002-4-4−2323-2-24000002-420000−23230−23230000-2000020000−23230000000000000000000000−2222−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ230000000000000000000000000000000
χ93888-4-4-488-4-4-4-4-4222-4-4-422222-4-4-4-422-4220000-122-1-1-12222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ94888-4-4-4-8-8-4-4-444222-4-4-4222224444-2-24-2-20000-122-1-1-1-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ9588-8-4-4-48-8-4-4-444222444-2-2222-4-44-4-2-24-2-20000-1-2-211-1-222211-1-1000000000000000000000000000000000000000000000000000000000
χ9688-8-4-4-4-88-4-4-4-4-4222444-2-222244-4422-4220000-1-2-211-12-2-2-2-1-111000000000000000000000000000000000000000000000000000000000
χ978-8088-400-8-84008-4-400000-8440000000000000-40000400000000000000000000000000000000000000000000000000000000000000000
χ988-808-4800-84-800-48-40000044-80000000000000-40000400000000000000000000000000000000000000000000000000000000000000000
χ998-808-4-400-84400-4-420006-64-2400000000000002006-6-200000000000000000000000000000000000000000000000000000000000000000
χ1008-808-4-400-84400-4-42000-664-240000000000000200-66-200000000000000000000000000000000000000000000000000000000000000000
χ1018-80-48-4004-8443−43-42-40000044-20000−2323043−43000020000-20000−232300000000000000000000000000000000000000000000000000000000000
χ1028-80-48-4004-84−4343-42-40000044-2000023−230−4343000020000-2000023−2300000000000000000000000000000000000000000000000000000000000
χ1038-80-4-480044-843−432-4-400000-244000043−430−2323000020000-20000−232300000000000000000000000000000000000000000000000000000000000
χ1048-80-4-480044-8−43432-4-400000-2440000−4343023−23000020000-2000023−2300000000000000000000000000000000000000000000000000000000000
χ1058-80-4-4-40044443−432220006-6-2-2-20000−23230−23230000-100-33100003−333−33000000000000000000000000000000000000000000000000000000000
χ1068-80-4-4-40044443−43222000-66-2-2-20000−23230−23230000-1003-3100003−3−3333000000000000000000000000000000000000000000000000000000000
χ1078-80-4-4-400444−43432220006-6-2-2-2000023−23023−230000-100-3310000−33−3333000000000000000000000000000000000000000000000000000000000
χ1088-80-4-4-400444−4343222000-66-2-2-2000023−23023−230000-1003-310000−3333−33000000000000000000000000000000000000000000000000000000000

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