Finite Group Databasebeta

← Group #13167814

Character table — Group #13167814

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1122222222244444444444444444444466666666666688888888888888121212121212121212121212121212121212121212121818242424242424242424363636363636363636484872727272108108
order123334666121233366681212121212122424242424242424224466882424242436121212242424242424242424246666681212121212122424242424242424246661212122424242224681224246126661244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-11111111111111111111111-1-11-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-11-11111111111111111111111111-1-111-1-11-1111-1-1111111-1-111-111-1-1-1-11-1-11-1-1-1-1-1111-1-11-1-1
χ4111111111111111111111111111111111-11-11111111111111111111111-1-11-1-111-1-11-1111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-111
χ511111111111111111111111111111111-11-11-1-1-1-1-1-1-1-11111111111111111-111-1-111-11-1-1-111-1-1-1-1-1-1-1-1111111111-111-1-1-1-1-1-111-111-1-1-1
χ611111111111111111111111111111111-11-11-1-1-1-1-1-1-1-111111111111111-1-1-111-1-111-11-1-1-111-1-1-1-1-1-1-1-1-1-11-1-111111-1-11-1-1-1-1-1-1-11-1-1111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-11111111-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111111111-1-11111-1-1
χ911111111111111111-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-11-111111-1111111-1-1-1-1-1-1-1-111111-1-11-1-1-111-1-11-11-1-11-111-1-11-1
χ1011111111111111111-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1111-11-1-1-11-1-111-11
χ1111111111111111111-1111111-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-11-11-1-1111-11-111111-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-11-1111-11-11-1-11
χ1211111111111111111-1111111-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1111-11-111111-1-1-1-1-1-1-1-1-1-1-111-1111-11-11-11-111-11-11-111-1
χ1311111111111111111-1111111-1-1-1-1-1-1-1-1-11-11-1-111111111111-1-1-1-1-1-1-1-1-11-1-111-1-1-11-11-1-1-1-1-1111111-1-1111-1-11-1-1-1-11-11-11-1111-1-11-11-11
χ1411111111111111111-1111111-1-1-1-1-1-1-1-1-11-11-1-111111111111-1-1-1-1-1-1-1-1-1-11-111-1-1-11-11-1-1-1-1-1111111-1-1-1-11111-1-1-11-11-1-11-111-111-11-11-1
χ1511111111111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1111-1-1111-11-1-11-1-1-1111-1
χ1611111111111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11-1-1-1-1-1-11111111111-1-1-111-111111-1-11-11-1-1-1111-1-1-11
χ1722222-2222-2-22222220-2-2-2-2-2-20000000022-2-22200000022-2-2-200000000000222220-2-2-2-2-2-200000000-2200200-20000000-2020000000000
χ1822222-2222-2-22222220-2-2-2-2-2-2000000002-2-222200000022-2-2-2000000000002-2-22202-22-2-2-2000000002-200-2002000000020-20000000000
χ1922222-2222-2-22222220-2-2-2-2-2-200000000-222-2-2-200000022-2-2-200000000000-222-2-20-22-2222000000002-200200-2000000020-20000000000
χ2022222-2222-2-22222220-2-2-2-2-2-200000000-2-222-2-200000022-2-2-200000000000-2-2-2-2-2022222200000000-2200-20020000000-2020000000000
χ212222-12-122222-1-12-1-12-1222-1-122222222020200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-12202-1002-10200022000000002-1-1-12-1-1-1-1022000000-1-10-1-1000
χ222222-12-122222-1-12-1-12-1222-1-122222222020200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-202-1002-1020002200000000-21-11-2-1-1-1-10-2-200000011011000
χ232222-12-122222-1-12-1-12-1222-1-1222222220-20-200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1220-2100-210-2000-2-2000000002-11-1211110-2-2000000-1-1011000
χ242222-12-122222-1-12-1-12-1222-1-1222222220-20-200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20-2100-210-2000-2-200000000-2111-21111022000000110-1-1000
χ252222-12-122222-1-12-1-1-2-1222-1-1-2-2-2-2-2-2-2-2020200000000-1-1-1-1-11111111112-202-100-2-102000-2-2000000002-1-11-2-111102-2000000-110-11000
χ262222-12-122222-1-12-1-1-2-1222-1-1-2-2-2-2-2-2-2-2020200000000-1-1-1-1-1111111111-2202-100-2-102000-2-200000000-21-1-12-11110-220000001-101-1000
χ272222-12-122222-1-12-1-1-2-1222-1-1-2-2-2-2-2-2-2-20-20-200000000-1-1-1-1-11111111112-20-2100210-200022000000002-111-21-1-1-10-22000000-1101-1000
χ282222-12-122222-1-12-1-1-2-1222-1-1-2-2-2-2-2-2-2-20-20-200000000-1-1-1-1-1111111111-220-2100210-20002200000000-211-121-1-1-102-20000001-10-11000
χ29222-12222-122-12-1-12-122-1-1-12222-1-1-1-1-1-12020-1-1222222-1-1-1-1-1222-1-1-1-1-1-122200-1-10020-1-1-100-1-1-1-1-1-100-1202-10000200200000-1-1-100-100
χ30222-12222-122-12-1-12-122-1-1-12222-1-1-1-1-1-12020-1-1222222-1-1-1-1-1222-1-1-1-1-1-1-2-2200-1-10020-1-1-100-1-1-1-1-1-1001-20-210000-200-20000011100100
χ31222-12222-122-12-1-12-122-1-1-12222-1-1-1-1-1-1-20-2011-2-2-2-2-2-2-1-1-1-1-1222-1-1-1-1-1-122-2001100-201110011111100-1202-10000-200-200000-1-1100100
χ32222-12222-122-12-1-12-122-1-1-12222-1-1-1-1-1-1-20-2011-2-2-2-2-2-2-1-1-1-1-1222-1-1-1-1-1-1-2-2-2001100-2011100111111001-20-21000020020000011-100-100
χ33222-12222-122-12-1-12-1-22-1-1-122-2-21111112020-1-1-2-2-2-2-2-2-1-1-1-1-1-2-2-21111112-2200-1-10020-1-1-10011111100-120-210000200-200000-11-100100
χ34222-12222-122-12-1-12-1-22-1-1-122-2-21111112020-1-1-2-2-2-2-2-2-1-1-1-1-1-2-2-2111111-22200-1-10020-1-1-100111111001-202-10000-2002000001-1100-100
χ35222-12222-122-12-1-12-1-22-1-1-122-2-2111111-20-2011222222-1-1-1-1-1-2-2-21111112-2-2001100-2011100-1-1-1-1-1-100-120-210000-200200000-11100-100
χ36222-12222-122-12-1-12-1-22-1-1-122-2-2111111-20-2011222222-1-1-1-1-1-2-2-2111111-22-2001100-2011100-1-1-1-1-1-1001-202-10000200-2000001-1-100100
χ3722-12222-12-1-1-1-12-1-12222-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-12-1-12-1-122-1-1-1-100-1-12-1-122-1-12-1-1-1-122-1-1-1-12200-100-12-1-10000-12-1-1-100000000
χ3822-12222-12-1-1-1-12-1-12222-1-1-1-1-1-122-1-1-1-12-22-22222-1-1-1-1-1-12-1-12-1-122-1-1-1-100-11-2-1-1-2-2-112-1-11122-1-1-1-1-2-2001001-21100001-211100000000
χ3922-12222-12-1-1-1-12-1-12222-1-1-1-1-1-122-1-1-1-1-22-22-2-2-2-21111-1-12-1-12-1-122-1-1-1-1001-1211221-1-211-1-1-2-21111-2-200-100-12-1-100001-211100000000
χ4022-12222-12-1-1-1-12-1-12222-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-21111-1-12-1-12-1-122-1-1-1-10011-211-2-211-21111-2-2111122001001-2110000-12-1-1-100000000
χ4122-12222-12-1-1-1-12-1-12-222-1-1-1-111-2-21111222222-2-21111-1-12-1-1-211-2-2111100-1-12-1-1-22-1-12-1-111-2-211112200-100-1-2110000-1-2-11100000000
χ4222-12222-12-1-1-1-12-1-12-222-1-1-1-111-2-211112-22-222-2-21111-1-12-1-1-211-2-2111100-11-2-1-12-2-112-1-1-1-1-2-21111-2-20010012-1-10000121-1-100000000
χ4322-12222-12-1-1-1-12-1-12-222-1-1-1-111-2-21111-22-22-2-222-1-1-1-1-1-12-1-1-211-2-21111001-1211-221-1-2111122-1-1-1-1-2-200-100-1-2110000121-1-100000000
χ4422-12222-12-1-1-1-12-1-12-222-1-1-1-111-2-21111-2-2-2-2-2-222-1-1-1-1-1-12-1-1-211-2-211110011-2112-211-211-1-122-1-1-1-1220010012-1-10000-1-2-11100000000
χ4522-122-22-1211-1-12-1-120-2-211113−30033−3−322-2-2220033−3−3-1-1-21103−30033−3−300-1-12-1-10-211-2113−30033−3−3-2200-100103−3000010-13−300000000
χ4622-122-22-1211-1-12-1-120-2-211113−30033−3−32-2-22220033−3−3-1-1-21103−30033−3−300-11-2-1-1021-1-211−330033−3−32-200100-10−330000-101−3300000000
χ4722-122-22-1211-1-12-1-120-2-211113−30033−3−3-222-2-2-200−3−333-1-1-21103−30033−3−3001-12110-2-112-1-13−300−3−3332-200-100103−30000-101−3300000000
χ4822-122-22-1211-1-12-1-120-2-211113−30033−3−3-2-222-2-200−3−333-1-1-21103−30033−3−30011-21102-1-12-1-1−3300−3−333-2200100-10−33000010-13−300000000
χ4922-122-22-1211-1-12-1-120-2-21111−3300−3−33322-2-22200−3−333-1-1-2110−3300−3−33300-1-12-1-10-211-211−3300−3−333-2200-10010−33000010-1−3300000000
χ5022-122-22-1211-1-12-1-120-2-21111−3300−3−3332-2-222200−3−333-1-1-2110−3300−3−33300-11-2-1-1021-1-2113−300−3−3332-200100-103−30000-1013−300000000
χ5122-122-22-1211-1-12-1-120-2-21111−3300−3−333-222-2-2-20033−3−3-1-1-2110−3300−3−333001-12110-2-112-1-1−330033−3−32-200-10010−330000-1013−300000000
χ5222-122-22-1211-1-12-1-120-2-21111−3300−3−333-2-222-2-20033−3−3-1-1-2110−3300−3−3330011-21102-1-12-1-13−30033−3−3-2200100-103−3000010-1−3300000000
χ534444-2-4-244-4-44-2-24-2-202-4-4-42200000000040-400000000-2-22220000000000004-200020-4000000000000000-200200000000000000000000
χ544444-2-4-244-4-44-2-24-2-202-4-4-422000000000-40400000000-2-2222000000000000-42000-204000000000000000200-200000000000000000000
χ55444-24-444-2-4-4-24-2-24-20-4222-4-40000000040-40-2-2000000-2-222200000000000400-2-200-40222000000000000000000000000000000000000
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χ59444-2-24-24-244-2-21-2-21-4-2-2-2-2-2-2-4-422222200000000000011111222-1-1-1-1-1-14-40000000000000000000000-2-202200000000000001-1000000
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χ6244-24-24-2-24-2-2-21-2-21-24-24-2-211-2-244-2-2-2-20-40-40000000011-211-211-2-211110002200-4202000220000000000-100-12-1-100000000000000000
χ6344-24-24-2-24-2-2-21-2-21-2-4-24-2-21122-4-4222204040000000011-2112-1-122-1-1-1-1000-2-200-4-20-200022000000000010012-1-100000000000000000
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χ6744-24-2-4-2-2422-21-2-21-202-422-1-1−232300−23−232323040-400000000112-1-103−30033−3−3000-2-2000202000−23230000000000100-103−300000000000000000
χ6844-24-2-4-2-2422-21-2-21-202-422-1-1−232300−23−2323230-40400000000112-1-103−30033−3−300022000-20-200023−230000000000-10010−3300000000000000000
χ6944-2-2444-2-2-2-21-2-21-2-244-211-2-2-2-2-2-211114040-2-244-2-2-2-211-2114-2-2-2-2111100-2001100-20-21100-2-211110000000000000000000000000000
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χ804-44-240-4-4200-24-22-420000000006−66−66−600002i3−2i32i2−2i22i2−2i22i2−2i2-220000006−66−66−6000002i3−2i3000000000−i2i2−i2i2−i2i20000000000000000000000000000
χ814-44-240-4-4200-24-22-42000000000−66−66−660000−2i32i32i2−2i22i2−2i22i2−2i2-22000000−66−66−6600000−2i32i3000000000−i2i2−i2i2−i2i20000000000000000000000000000
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χ834-4-2440-42-423−23-2-2422-400023−2323−2300000000000000−2i22i22ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7-22023−230000000000000000000000000−2i22i22ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ70000000000000000000000000000
χ844-4-2440-42-423−23-2-2422-400023−2323−23000000000000002i2−2i2−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7-22023−2300000000000000000000000002i2−2i2−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ70000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.