Finite Group Databasebeta

← Group #13167821

Character table — Group #13167821

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1122222222244444444444444444444466666666666688888888888888121212121212121212121212121212121212121212121818242424242424242424363636363636363636484872727272108108
order123334666121233366681212121212122424242424242424224488121224242424361212122424242424242424242266666681212121212242424242424242424666661224242424446812242466612121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-11111111111111111111111-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-11-111111111111111111111111111-1-111-11-1-111-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111-11-11111111111111111111111-1-111-1-111-11-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-111-1-111
χ511111111111111111111111111111111-11-11-1-1-1-1-1-1-1-11111111111111111-1-111-1-11-111-1-111-1-1-1-1-1-1-1-11111111111-1-11-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-11-11-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-11-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111111-1-1-1-111
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
χ911111111111111111-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-11-1111111-111111-1-1-1-1-1-1-1-1111-11-111-1-1-111-1-11-11-1-11-11-11-11-1
χ1011111111111111111-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-11111111-111111-1-1-1-1-1-1-1-111-11-1111-1-1-1-1-1111-11-1-1-11-11-11-11
χ1111111111111111111-1111111-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-11-111-1-11111-1-11111-1-1-1-1-1-1-1-11-11-1-1-1111-11-11-11-1111-1-111-1-11
χ1211111111111111111-1111111-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111-1-11111-1-11111-1-1-1-1-1-1-1-1-11-11-1-11111-11-1-11-111-111-1-111-1
χ1311111111111111111-1111111-1-1-1-1-1-1-1-1-11-1111-1-1111111111-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-111-1-1-1-1111111-1-11-11-111-1-1-11-11-1-11-1111-11-1-11-11
χ1411111111111111111-1111111-1-1-1-1-1-1-1-1-11-1111-1-1111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-1-1-1111111-1-1-11-1111-1-1-1-11-11-11-111-11-111-11-1
χ1511111111111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-11-1-1-1-1-111111111111-11-1-1-1111-1-1111-11-1-11-1-11-111-1
χ1611111111111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1-1-11111111111-11-11-1-111111-1-11-11-1-1-111-11-1-11
χ1722222-2222-2-22222220-2-2-2-2-2-20000000022-2-200-2-2000022-2-2-2000000000002222220-2-2-2-2-200000000-2200002-20000000-2020000000000
χ1822222-2222-2-22222220-2-2-2-2-2-2000000002-2-2200-2-2000022-2-2-20000000000022-2-2220-222-2-2000000002-20000-22000000020-20000000000
χ1922222-2222-2-22222220-2-2-2-2-2-200000000-222-20022000022-2-2-200000000000-2-222-2-202-2-222000000002-200002-2000000020-20000000000
χ2022222-2222-2-22222220-2-2-2-2-2-200000000-2-2220022000022-2-2-200000000000-2-2-2-2-2-202222200000000-220000-220000000-2020000000000
χ212222-122-12222-1-1-12-12-1222-1-122222222020200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-122002-100202-100220000000022-1-1-1-1-1-1-1200200000-1-1-1-10000
χ222222-122-12222-1-1-12-12-1222-1-122222222020200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2002-100202-1002200000000-2-211-1-1-1-1-1-200-20000011110000
χ232222-122-12222-1-1-12-12-1222-1-1222222220-20-200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-12200-2100-20-2100-2-20000000022-1-111111-200-200000-1-1110000
χ242222-122-12222-1-1-12-12-1222-1-1222222220-20-200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2100-20-2100-2-200000000-2-2111111120020000011-1-10000
χ252222-122-12222-1-1-12-1-2-1222-1-1-2-2-2-2-2-2-2-2020200000000-1-1-1-1-11111111112-2002-100-202-100-2-2000000002-2-11-1-1111200-200000-11-110000
χ262222-122-12222-1-1-12-1-2-1222-1-1-2-2-2-2-2-2-2-2020200000000-1-1-1-1-1111111111-22002-100-202-100-2-200000000-221-1-1-1111-2002000001-11-10000
χ272222-122-12222-1-1-12-1-2-1222-1-1-2-2-2-2-2-2-2-20-20-200000000-1-1-1-1-11111111112-200-210020-210022000000002-2-1111-1-1-1-200200000-111-10000
χ282222-122-12222-1-1-12-1-2-1222-1-1-2-2-2-2-2-2-2-20-20-200000000-1-1-1-1-1111111111-2200-210020-21002200000000-221-111-1-1-1200-2000001-1-110000
χ29222-12222-122-12-1-1-1222-1-1-12222-1-1-1-1-1-1202022-1-12222-1-1-1-1-1222-1-1-1-1-1-1222-100-1-10200-1-100-1-1-1-1-1-100-1-12200000022000000-1-100-1-100
χ30222-12222-122-12-1-1-1222-1-1-12222-1-1-1-1-1-1202022-1-12222-1-1-1-1-1222-1-1-1-1-1-1-2-22-100-1-10200-1-100-1-1-1-1-1-10011-2-2000000-2-200000011001100
χ31222-12222-122-12-1-1-1222-1-1-12222-1-1-1-1-1-1-20-20-2-211-2-2-2-2-1-1-1-1-1222-1-1-1-1-1-122-2100110-200110011111100-1-122000000-2-2000000-1-1001100
χ32222-12222-122-12-1-1-1222-1-1-12222-1-1-1-1-1-1-20-20-2-211-2-2-2-2-1-1-1-1-1222-1-1-1-1-1-1-2-2-2100110-20011001111110011-2-2000000220000001100-1-100
χ33222-12222-122-12-1-1-12-22-1-1-122-2-21111112020-2-2-1-1-2-2-2-2-1-1-1-1-1-2-2-21111112-22-100-1-10200-1-10011111100-112-20000002-2000000-1100-1100
χ34222-12222-122-12-1-1-12-22-1-1-122-2-21111112020-2-2-1-1-2-2-2-2-1-1-1-1-1-2-2-2111111-222-100-1-10200-1-100111111001-1-22000000-220000001-1001-100
χ35222-12222-122-12-1-1-12-22-1-1-122-2-2111111-20-2022112222-1-1-1-1-1-2-2-21111112-2-2100110-2001100-1-1-1-1-1-100-112-2000000-22000000-11001-100
χ36222-12222-122-12-1-1-12-22-1-1-122-2-2111111-20-2022112222-1-1-1-1-1-2-2-2111111-22-2100110-2001100-1-1-1-1-1-1001-1-220000002-20000001-100-1100
χ3722-1222-122-1-1-1-122-1-1222-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-12-1-12-1-122-1-1-1-100-12-12-1-12-1-12-1-1-1-122-1-1-1-1220000-1-12-1-10000-12-1-1-100000000
χ3822-1222-122-1-1-1-122-1-1222-1-1-1-1-1-122-1-1-1-12-22-22222-1-1-1-1-1-12-1-12-1-122-1-1-1-100-121-2-1-1-2-11-2-1-11122-1-1-1-1-2-2000011-21100001-211100000000
χ3922-1222-122-1-1-1-122-1-1222-1-1-1-1-1-122-1-1-1-1-22-22-2-2-2-21111-1-12-1-12-1-122-1-1-1-1001-2-121121-1211-1-1-2-21111-2-20000-1-12-1-100001-211100000000
χ4022-1222-122-1-1-1-122-1-1222-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-21111-1-12-1-12-1-122-1-1-1-1001-21-211-211-21111-2-2111122000011-2110000-12-1-1-100000000
χ4122-1222-122-1-1-1-122-1-1-222-1-1-1-111-2-211112222-2-2221111-1-12-1-1-211-2-2111100-12-12-1-1-2-1-12-1-111-2-21111220000-1-1-2110000-1-2-11100000000
χ4222-1222-122-1-1-1-122-1-1-222-1-1-1-111-2-211112-22-2-2-2221111-1-12-1-1-211-2-2111100-121-2-1-12-11-2-1-1-1-1-2-21111-2-20000112-1-10000121-1-100000000
χ4322-1222-122-1-1-1-122-1-1-222-1-1-1-111-2-21111-22-2222-2-2-1-1-1-1-1-12-1-1-211-2-21111001-2-1211-21-12111122-1-1-1-1-2-20000-1-1-2110000121-1-100000000
χ4422-1222-122-1-1-1-122-1-1-222-1-1-1-111-2-21111-2-2-2-222-2-2-1-1-1-1-1-12-1-1-211-2-21111001-21-211211-211-1-122-1-1-1-1220000112-1-10000-1-2-11100000000
χ4522-122-2-12211-1-122-1-10-2-211113−30033−3−322-2-200-2-233−3−3-1-1-21103−30033−3−300-12-12-1-1011-2113−30033−3−3-220000-1103−3000010-13−300000000
χ4622-122-2-12211-1-122-1-10-2-211113−30033−3−32-2-2200-2-233−3−3-1-1-21103−30033−3−300-121-2-1-101-1211−330033−3−32-200001-10−330000-101−3300000000
χ4722-122-2-12211-1-122-1-10-2-211113−30033−3−3-222-20022−3−333-1-1-21103−30033−3−3001-2-12110-11-2-1-13−300−3−3332-20000-1103−30000-101−3300000000
χ4822-122-2-12211-1-122-1-10-2-211113−30033−3−3-2-2220022−3−333-1-1-21103−30033−3−3001-21-2110-1-12-1-1−3300−3−333-2200001-10−33000010-13−300000000
χ4922-122-2-12211-1-122-1-10-2-21111−3300−3−33322-2-200-2-2−3−333-1-1-2110−3300−3−33300-12-12-1-1011-211−3300−3−333-220000-110−33000010-1−3300000000
χ5022-122-2-12211-1-122-1-10-2-21111−3300−3−3332-2-2200-2-2−3−333-1-1-2110−3300−3−33300-121-2-1-101-12113−300−3−3332-200001-103−30000-1013−300000000
χ5122-122-2-12211-1-122-1-10-2-21111−3300−3−333-222-2002233−3−3-1-1-2110−3300−3−333001-2-12110-11-2-1-1−330033−3−32-20000-110−330000-1013−300000000
χ5222-122-2-12211-1-122-1-10-2-21111−3300−3−333-2-222002233−3−3-1-1-2110−3300−3−333001-21-2110-1-12-1-13−30033−3−3-2200001-103−3000010-1−3300000000
χ534444-2-44-24-4-44-2-2-24-202-4-4-42200000000040-400000000-2-222200000000000004-20000-420000000000000000-2200000000000000000000
χ544444-2-44-24-4-44-2-2-24-202-4-4-422000000000-40400000000-2-22220000000000000-4200004-200000000000000002-200000000000000000000
χ55444-24-444-2-4-4-24-2-2-240-4222-4-40000000040-4000220000-2-2222000000000004-200-2-20-40022000000000000000000000000000000000000
χ56444-24-444-2-4-4-24-2-2-240-4222-4-400000000-404000-2-20000-2-222200000000000-4200220400-2-2000000000000000000000000000000000000
χ57444-2-244-2-244-2-211-2-24-2-2-2-2-2-244-2-2-2-2-2-200000000000011111-2-2-2111111440000000000000000000000-2-2-2-20000000000000011000000
χ58444-2-244-2-244-2-211-2-24-2-2-2-2-2-244-2-2-2-2-2-200000000000011111-2-2-2111111-4-40000000000000000000000222200000000000000-1-1000000
χ59444-2-244-2-244-2-211-2-2-4-2-2-2-2-2-2-4-422222200000000000011111222-1-1-1-1-1-14-40000000000000000000000-22-22000000000000001-1000000
χ60444-2-244-2-244-2-211-2-2-4-2-2-2-2-2-2-4-422222200000000000011111222-1-1-1-1-1-1-4400000000000000000000002-22-200000000000000-11000000
χ6144-24-24-2-24-2-2-21-2-2-214-24-2-211-2-244-2-2-2-204040000000011-211-211-2-211110000-2-20040-2-200-2-200000000000011-21100000000000000000
χ6244-24-24-2-24-2-2-21-2-2-214-24-2-211-2-244-2-2-2-20-40-40000000011-211-211-2-2111100002200-40220022000000000000-1-12-1-100000000000000000
χ6344-24-24-2-24-2-2-21-2-2-21-4-24-2-21122-4-4222204040000000011-2112-1-122-1-1-1-10000-2-200-40-2-20022000000000000112-1-100000000000000000
χ6444-24-24-2-24-2-2-21-2-2-21-4-24-2-21122-4-422220-40-40000000011-2112-1-122-1-1-1-100002200402200-2-2000000000000-1-1-21100000000000000000
χ6544-24-2-4-2-2422-21-2-2-2102-422-1-123−23002323−23−23040-400000000112-1-10−3300−3−3330000-2-20000220023−230000000000001-10−3300000000000000000
χ6644-24-2-4-2-2422-21-2-2-2102-422-1-123−23002323−23−230-40400000000112-1-10−3300−3−3330000220000-2-200−2323000000000000-1103−300000000000000000
χ6744-24-2-4-2-2422-21-2-2-2102-422-1-1−232300−23−232323040-400000000112-1-103−30033−3−30000-2-200002200−23230000000000001-103−300000000000000000
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χ6944-2-244-24-2-2-21-2-2-21-244-211-2-2-2-2-2-21111404044-2-2-2-2-2-211-2114-2-2-2-2111100-2-200110-2001100-2-211110000000000000000000000000000
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χ7644-2-24-4-24-2221-2-2-21-20-42-1-122−23230033−3−3-404000-2-22323−23−23112-1-10−23230033−3−3002200-1-10-200110000−3−3330000000000000000000000000000
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χ814-44-240-4-4200-24-222-4000000000−i6i6−i6i6−i6i60000−2i22i2−2323−2i22i2−2i22i2-22000000−i6i6−i6i6−i6i6000000000000−232300i2−i2i2−i2i2−i20000000000000000000000000000
χ824-44-240-4-4200-24-222-4000000000−i6i6−i6i6−i6i600002i2−2i223−232i2−2i22i2−2i2-22000000−i6i6−i6i6−i6i600000000000023−2300−i2i2−i2i2−i2i20000000000000000000000000000
χ834-4-24402-4-423−23-2-24-42200023−2323−23000000000000−2i22i2002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7-22023−230000000000000000000000000−2i22i22ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ70000000000000000000000000000
χ844-4-24402-4-423−23-2-24-42200023−2323−230000000000002i2−2i200−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7-22023−2300000000000000000000000002i2−2i2−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ70000000000000000000000000000
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χ1058-8-4-4-4044443−43222-2-2-2000−2323−2323002i6−2i6−4ζ5−4ζ7−2ζ13−2ζ234ζ5+4ζ7+2ζ13+2ζ232ζ5+2ζ7+4ζ13+4ζ23−2ζ5−2ζ7−4ζ13−4ζ23000000000000-1103−3000−i6i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ2300000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.