Finite Group Databasebeta

← Group #13170600

Character table — Group #13170600

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11222222222224444444444444444444466668888888888888812121212121212121212121212121212121212121818181818182424242424242424242424242424242436363636363636363636367272108108
order122333446661212333666666661212121212121212122244366666121212121212121244666688121212121212121224242424882424242466121212121212121224242424242422446681212242461244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11-11-111-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1111111111111-1-111-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111111111-11-11-1-1-1-1-1-1-111-1-1
χ6111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111
χ7111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-11-111-111-1-1-1-111
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
χ911-1111-1111111111-1-1-1-1-1111-1-11-1111111-11-11-1-1-1-11-1-11-111-1-11-11-11-11-11-11-111-1-111-1-11111111-11-11-111-1-1111-1-1-111-1-111-1-1-1-1-11-11-1
χ1011-1111-1111111111-1-1-1-1-1111-1-11-1111111-11-11-1-1-1-11-1-11-111-1-11-11-11-1-111-11-111-1-1-1-111-1-1-1-1-1-11-11-11-111-1-1-1-1-11111-1-11111-1-111-11-11
χ1111-1111-1111111111-1-1-1-1-1111-1-11-1111111-11-11-1-1-1-11-1-11-111-1-1-111-11-11-11-11-1-1-11111-1-11111111-1-111-1-1-111111-1-1-1-1-111-1-1-111-1-1-11-11
χ1211-1111-1111111111-1-1-1-1-1111-1-11-1111111-11-11-1-1-1-11-1-11-111-1-1-111-11-1-111-11-1-1-111-1-111-1-1-1-1-1-11-1-111-1-1-111-1-1-1111-111-1-1-1111111-11-1
χ1311-1111-1111111111-1-1-1-1-1111-1-11-111111-11-111-1-1-1-11-1-11-111-1-11-1-11-111-1-11-1111-1-111-1-1-1-1-1-1-1-1-111-1-1111-1-1111-1-1-1-111-1-1-1111111-1-11
χ1411-1111-1111111111-1-1-1-1-1111-1-11-111111-11-111-1-1-1-11-1-11-111-1-11-1-11-11-11-11-1111-1-1-1-111111111-111-1-1111-1-1-1-1-1111-1-111-1-1-111-1-1-111-1
χ1511-1111-1111111111-1-1-1-1-1111-1-11-111111-11-111-1-1-1-11-1-11-111-1-1-11-11-111-1-11-11-1-11111-1-1-1-1-1-1-1-1-11-11-11-1-111111-1-1-11-1-11111-1-111-111-1
χ1611-1111-1111111111-1-1-1-1-1111-1-11-111111-11-111-1-1-1-11-1-11-111-1-1-11-11-11-11-11-11-1-111-1-111111111-11-11-11-1-111-1-1-111111-1-111-1-1-1-1-11-1-11
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χ2422222-1-2-222-1-2-22-1-122-1-1-12-1-1-2-21111-2-2-22-2-22-12-1-1-1-1-21111111002-2-1100-221-1i3−i3i3−i30000000000-11001-1i3−i3i3−i30000000000i3−i30i3−i3000000
χ2522222-1-2-222-1-2-22-1-122-1-1-12-1-1-2-21111-2-2-2-222-2-12-1-1-1-1-2111111100-221-1002-2-11−i3i3−i3i300000000001-100-11−i3i3−i3i30000000000i3−i30i3−i3000000
χ2622222-1-2-222-1-2-22-1-122-1-1-12-1-1-2-21111-2-2-2-222-2-12-1-1-1-1-2111111100-221-1002-2-11i3−i3i3−i300000000001-100-11i3−i3i3−i30000000000−i3i30−i3i3000000
χ272222-12222-1222-1-122-12-1-1-12-12-12222-1-1-10000-1-12-1-1-1-12-1-1-1-1-1-12200002200002222222200000000-1-100-1-1-1-1-1-1-1-1-1-102020000000-1-100
χ282222-12222-1222-1-122-12-1-1-12-12-12222-1-1-10000-1-12-1-1-1-12-1-1-1-1-1-1220000-2-200002222-2-2-2-200000000-1-100-1-1-1-11111110-20-200000001100
χ292222-12222-1222-1-122-12-1-1-12-12-12222-1-1-10000-1-12-1-1-1-12-1-1-1-1-1-1-2-20000220000-2-2-2-222220000000011001111-1-1-1-1-1-10-20-200000001100
χ302222-12222-1222-1-122-12-1-1-12-12-12222-1-1-10000-1-12-1-1-1-12-1-1-1-1-1-1-2-20000-2-20000-2-2-2-2-2-2-2-2000000001100111111111102020000000-1-100
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χ34222-12222-122-1-1-12-1-12222-1-12-1222-1-12-1-1-2-2-2-2-1-1-1-1-1-1-1-122-1-1-1-10011-2-2-2-211-2-20000111122-1-1-1-11100110000-211-211000000200-1-10000
χ35222-122-2-2-12211-12-1-12222-1-121-2-2-211-2112-2-22-1-1-1-1-1-111-2-2111100-112-2001-1-2200003−33−30033−3−3-11001-1000003−303−30000000003−30000
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χ37222-122-2-2-12211-12-1-12222-1-121-2-2-211-211-222-2-1-1-1-1-1-111-2-21111001-1-2200-112-200003−33−300−3−3331-100-11000003−303−3000000000−330000
χ38222-122-2-2-12211-12-1-12222-1-121-2-2-211-211-222-2-1-1-1-1-1-111-2-21111001-1-2200-112-20000−33−330033−3−31-100-1100000−330−330000000003−30000
χ3922-22222-2222-2-2222-2-2-2-2-222222-22-2-2-2-2-222-2-22-2-2-2-2222-22-2-22200222200-2-2-2-2000000000000002200-2-20000000000000000000000000
χ4022-22222-2222-2-2222-2-2-2-2-222222-22-2-2-2-2-2-2-2222-2-2-2-2222-22-2-22200-2-2-2-200222200000000000000-2-200220000000000000000000000000
χ4122-222-12-222-1-2-22-1-1-2-21112-1-1221-111-2-2-222-2-2-1-2111-12-11-111-1-10022-1-100-2-211−i3i3i3−i30000000000-1-10011−i3i3i3−i30000000000−i3i30i3−i3000000
χ4222-222-12-222-1-2-22-1-1-2-21112-1-1221-111-2-2-222-2-2-1-2111-12-11-111-1-10022-1-100-2-211i3−i3−i3i30000000000-1-10011i3−i3−i3i30000000000i3−i30−i3i3000000
χ4322-222-12-222-1-2-22-1-1-2-21112-1-1221-111-2-2-2-2-222-1-2111-12-11-111-1-100-2-2110022-1-1−i3i3i3−i300000000001100-1-1−i3i3i3−i30000000000i3−i30−i3i3000000
χ4422-222-12-222-1-2-22-1-1-2-21112-1-1221-111-2-2-2-2-222-1-2111-12-11-111-1-100-2-2110022-1-1i3−i3−i3i300000000001100-1-1i3−i3−i3i30000000000−i3i30i3−i3000000
χ4522-222-1-2222-1222-1-1-2-21112-1-1-2-2-11-1-12222-22-2-1-2111-1-21-11-1-1112-22-2-11002-2-11-1-1110000000000-112-2-11-1-11100000020-20-1-1011000000
χ4622-222-1-2222-1222-1-1-2-21112-1-1-2-2-11-1-12222-22-2-1-2111-1-21-11-1-111-222-2-11002-2-1111-1-10000000000-11-22-1111-1-1000000-2020110-1-1000000
χ4722-222-1-2222-1222-1-1-2-21112-1-1-2-2-11-1-1222-22-22-1-2111-1-21-11-1-1112-2-221-100-221-1-1-11100000000001-12-21-1-1-111000000-2020110-1-1000000
χ4822-222-1-2222-1222-1-1-2-21112-1-1-2-2-11-1-1222-22-22-1-2111-1-21-11-1-111-22-221-100-221-111-1-100000000001-1-221-111-1-100000020-20-1-1011000000
χ4922-22-12-222-1222-1-12-21-211-12-1-212-222-1-1-10000-11-211-11-2-11-1-1112-200002-2000022-2-222-2-200000000-1100-1-111-1-1-1111020-20000000-1100
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χ5122-22-12-222-1222-1-12-21-211-12-1-212-222-1-1-10000-11-211-11-2-11-1-111-2200002-20000-2-22222-2-2000000001-10011-1-1-1-1-11110-20200000001-100
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χ5422-2-1222-2-12211-12-11-2-2-2-2-1-12-12-2211-21122-2-2-11111-1-1-1-2211-1-100-1-1220011-2-20000−333−300−3−333-1-1001100000−3303−30000000003−30000
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χ5922-2-122-22-122-1-1-12-11-2-2-2-2-1-121-22-2-1-12-1-1-22-22-11111-1112-2-1-111001-1-222-21-1-220000-1-111-2-211111-1001-100002-1-1-211000000200-1-10000
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χ8044-4-24-24-4-24-222-2-212-4222-21-2-242-2-1-1-422-4-44412-1-1-11-212-2-1-11100222200-2-2-2-200000000000000-1-100110000000000000000000000000
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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
χ894-40-244002-4-423−23-24-20000022-4000023−23023−230000-200002000023−23000000000000000000000022−222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ70000000000000000000000000000000
χ904-40-244002-4-423−23-24-20000022-4000023−23023−230000-200002000023−230000000000000000000000−2222−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ70000000000000000000000000000000
χ914-40-244002-4-4−2323-24-20000022-40000−23230−23230000-2000020000−2323000000000000000000000022−222ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ230000000000000000000000000000000
χ924-40-244002-4-4−2323-24-20000022-40000−23230−23230000-2000020000−23230000000000000000000000−2222−2ζ5+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
χ9588-8-4-4-48-8-4-4-444222444-2-2222-4-44-4-2-24-2-20000-1-2-211-122-2211-1-1000000000000000000000000000000000000000000000000000000000
χ9688-8-4-4-4-88-4-4-4-4-4222444-2-222244-4422-4220000-1-2-211-1-2-22-2-1-111000000000000000000000000000000000000000000000000000000000
χ978-8088-400-8-84008-4-400000-8440000000000000-40000400000000000000000000000000000000000000000000000000000000000000000
χ988-808-4800-84-800-4-48000004-840000000000000-40000400000000000000000000000000000000000000000000000000000000000000000
χ998-808-4-400-84400-42-40006-644-200000000000002006-6-200000000000000000000000000000000000000000000000000000000000000000
χ1008-808-4-400-84400-42-4000-6644-20000000000000200-66-200000000000000000000000000000000000000000000000000000000000000000
χ1018-80-48-4004-8443−43-4-42000004-240000−2323043−43000020000-20000−232300000000000000000000000000000000000000000000000000000000000
χ1028-80-48-4004-84−4343-4-42000004-24000023−230−4343000020000-2000023−2300000000000000000000000000000000000000000000000000000000000
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.