Finite Group Databasebeta

← Group #13167828

Character table — Group #13167828

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size112222222224444444444444444444446666668888888888888812121212121212121212121212121212121212181818182424242424242424363636363636363648484848545472727272108
order123334666883336661212121212242424242424242424242466121236121212122424242424242424222266681212122424242424242424246666666666224481224246666246612128
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1
χ31111111111111111111111111111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11
χ511111111111111111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111-1-11111-1-11
χ711111111111111111111111111111111-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1111
χ811111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1
χ9111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-11-1111-1111-1-1-1-1-1-1-1-111111-11-11-11-11-11-1-11-1-11-11-1111-11-1-1
χ10111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-11111-1111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11-11-111-11-1111-1-11-1-1-111-11
χ11111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1111-1111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-11-11-1-111-111-111-1-1-11-1-111
χ12111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-11111-1111-1-1-1-1-1-1-1-11111-11-11-11-11-11-11-11-1-1-11-1111-11-11-1
χ13111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-11-1-1-1-11-1-1-11111111111111-11-11-11-1-11-11-11-1-11-11-1-1-1-11-111
χ14111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11-1-1-11-1-1-111111111-1-1-1-11-11-1-11-111-1-111-1111-1-11111-1-11-1
χ15111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-111111111-1-1-1-1-11-111-11-1-111-11-111-111-111-111-1-1
χ16111111111-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-1-1-11-1-1-1111111111111-11-11-11-111-11-1-11-1-1-11-11-1-11-11-11
χ1722222-222200222222-2-2-2-2-200000000002-222-2-222-2-2-2-20000000000002220-2-2-2000000002-2220000000000000-2000000-2200000
χ1822222-222200222222-2-2-2-2-200000000002-222-2-222-2-2-2-20000000000002220-2-2-200000000-22-2-2000000000000020000002-200000
χ1922222-222200222222-2-2-2-2-20000000000-22-2-22222-2-2-2-2000000000000-2-2-20222000000002-2220000000000000-20000002-200000
χ2022222-222200222222-2-2-2-2-20000000000-22-2-22222-2-2-2-2000000000000-2-2-2022200000000-22-2-200000000000002000000-2200000
χ212222-12-12222-12-12-1-1-12-1-1222-1-1-1-1-1-12222-1-122-1-12-1-1-122-1-1-1-1-1-100222-1-12-1-1-122-1-1-1-1-1-10000000022-1-12200000000-1-100-1-1000
χ222222-12-12222-12-12-1-1-12-1-1222-1-1-1-1-1-12222-1-122-1-12-1-1-122-1-1-1-1-1-100-2-22-1-12-1-1-122-1-1-1-1-1-100000000-2-211-2-200000000110011000
χ232222-12-12222-12-12-1-1-12-1-1222-1-1-1-1-1-122-2-211-2-2-1-12-1-1-122-1-1-1-1-1-10022-211-2111-2-21111110000000022-1-1-2-200000000-1-10011000
χ242222-12-12222-12-12-1-1-12-1-1222-1-1-1-1-1-122-2-211-2-2-1-12-1-1-122-1-1-1-1-1-100-2-2-211-2111-2-211111100000000-2-21122000000001100-1-1000
χ252222-12-122-2-2-12-12-1-1-12-1-12-2-2111111-2-222-1-122-1-12-1-1-1-2-2111111002-22-1-1-2-1-1-1-2-2111111000000002-2-112-200000000-1100-11000
χ262222-12-122-2-2-12-12-1-1-12-1-12-2-2111111-2-222-1-122-1-12-1-1-1-2-211111100-222-1-1-2-1-1-1-2-211111100000000-221-1-22000000001-1001-1000
χ272222-12-122-2-2-12-12-1-1-12-1-12-2-2111111-2-2-2-211-2-2-1-12-1-1-1-2-2111111002-2-211211122-1-1-1-1-1-1000000002-2-11-2200000000-11001-1000
χ282222-12-122-2-2-12-12-1-1-12-1-12-2-2111111-2-2-2-211-2-2-1-12-1-1-1-2-211111100-22-211211122-1-1-1-1-1-100000000-221-12-2000000001-100-11000
χ29222-1222-12222-1-1-1-122222-122222222-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200000000000000022-1-122-1-1-1-12200002-1-1-1-1-1-1-10000000
χ30222-1222-12222-1-1-1-122222-122222222-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2000000000000000-2-21122-1-111-2-20000-2111-1-1110000000
χ31222-1222-12222-1-1-1-122222-122222222-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-222000000000000000-2-211-2-211-1-1220000-211111-1-10000000
χ32222-1222-12222-1-1-1-122222-122222222-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000000000022-1-1-2-21111-2-200002-1-1-111110000000
χ33222-1222-12-2-22-1-1-1-122222-1-2-2-2-2-2-2-2-211000000-1-1-1-1-1-1111111112-22-200000000000000022-1-12-2-11-112-20000-2-111-11-110000000
χ34222-1222-12-2-22-1-1-1-122222-1-2-2-2-2-2-2-2-211000000-1-1-1-1-1-1111111112-2-22000000000000000-2-2112-2-111-1-22000021-1-1-111-10000000
χ35222-1222-12-2-22-1-1-1-122222-1-2-2-2-2-2-2-2-211000000-1-1-1-1-1-111111111-222-2000000000000000-2-211-221-1-112-2000021-1-11-1-110000000
χ36222-1222-12-2-22-1-1-1-122222-1-2-2-2-2-2-2-2-211000000-1-1-1-1-1-111111111-22-2200000000000000022-1-1-221-11-1-220000-2-1111-11-10000000
χ3722-122222-122-1-12-12-12-1-1-12-1-122-1-1-1-1222222-1-1-1-1-12-1-1-1-122-1-1-1-12200-1-1-122-1-1-1-122-1-1-1-10000-1-122000000220000-1-1000000-1-10
χ3822-122222-122-1-12-12-12-1-1-12-1-122-1-1-1-1222222-1-1-1-1-12-1-1-1-122-1-1-1-1-2-200-1-1-122-1-1-1-122-1-1-1-1000011-2-2000000-2-2000011000000110
χ3922-122222-122-1-12-12-12-1-1-12-1-122-1-1-1-122-2-2-2-211-1-1-12-1-1-1-122-1-1-1-12200111-2-21111-2-211110000-1-122000000-2-20000-1-1000000110
χ4022-122222-122-1-12-12-12-1-1-12-1-122-1-1-1-122-2-2-2-211-1-1-12-1-1-1-122-1-1-1-1-2-200111-2-21111-2-21111000011-2-200000022000011000000-1-10
χ4122-122222-1-2-2-1-12-12-12-1-1-1211-2-21111-2-22222-1-1-1-1-12-1-111-2-211112-200-1-1-1-22-1-111-2-211110000-112-20000002-20000-11000000-110
χ4222-122222-1-2-2-1-12-12-12-1-1-1211-2-21111-2-22222-1-1-1-1-12-1-111-2-21111-2200-1-1-1-22-1-111-2-2111100001-1-22000000-2200001-10000001-10
χ4322-122222-1-2-2-1-12-12-12-1-1-1211-2-21111-2-2-2-2-2-211-1-1-12-1-111-2-211112-2001112-211-1-122-1-1-1-10000-112-2000000-220000-110000001-10
χ4422-122222-1-2-2-1-12-12-12-1-1-1211-2-21111-2-2-2-2-2-211-1-1-12-1-111-2-21111-22001112-211-1-122-1-1-1-100001-1-220000002-200001-1000000-110
χ454444-2-4-24400-24-24-2-22-422-400000000004-4-2-2-4-4-2-2-42220000000000004-2-20222000000000000000000000000000000000000000
χ464444-2-4-24400-24-24-2-22-422-40000000000-442244-2-2-4222000000000000-4220-2-2-2000000000000000000000000000000000000000
χ47444-24-44-24004-2-2-2-24-4-4-4-420000000000000000-2-222220000000000000000000000000004-4-2-2000000000000020000000000000
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χ49444-2-24-2-2444-2-21-21-2-24-2-2-244-2-2-2-2-2-2-2-200000011-2111-2-2111111004400000000000000000000000-2-2-2-20000000000110000000
χ50444-2-24-2-2444-2-21-21-2-24-2-2-244-2-2-2-2-2-2-2-200000011-2111-2-211111100-4-40000000000000000000000022220000000000-1-10000000
χ51444-2-24-2-24-4-4-2-21-21-2-24-2-2-2-4-42222222200000011-211122-1-1-1-1-1-1004-400000000000000000000000-22-2200000000001-10000000
χ52444-2-24-2-24-4-4-2-21-21-2-24-2-2-2-4-42222222200000011-211122-1-1-1-1-1-100-44000000000000000000000002-22-20000000000-110000000
χ5344-244-444-200-2-24-24-2-4222-400000000004-44422-2-22-422000000000000-2-2-20-422000000000000000000000000000000000000000
χ5444-244-444-200-2-24-24-2-4222-40000000000-44-4-4-2-2-2-22-42200000000000022204-2-2000000000000000000000000000000000000000
χ5544-24-24-24-2441-2-2-2-21-2-2114-2-2-2-211114444-2-2-2-211-2-211-2-2-2-211110000-2114-211-2-2-2-211110000000000000000000000000000000
χ5644-24-24-24-2441-2-2-2-21-2-2114-2-2-2-2111144-4-4222211-2-211-2-2-2-2111100002-1-1-42-1-12222-1-1-1-10000000000000000000000000000000
χ5744-24-24-24-2-4-41-2-2-2-21-2-21142222-1-1-1-1-4-444-2-2-2-211-2-2112222-1-1-1-10000-211-4-2112222-1-1-1-10000000000000000000000000000000
χ5844-24-24-24-2-4-41-2-2-2-21-2-21142222-1-1-1-1-4-4-4-4222211-2-2112222-1-1-1-100002-1-142-1-1-2-2-2-211110000000000000000000000000000000
χ5944-24-2-4-24-2001-2-2-2-2122-1-1-400003i3i−3i−3i004-4-2-2221122-1-100003i3i−3i−3i0000-21102-1-100003i3i−3i−3i0000000000000000000000000000000
χ6044-24-2-4-24-2001-2-2-2-2122-1-1-400003i3i−3i−3i00-4422-2-21122-1-100003i3i−3i−3i00002-1-10-2110000−3i−3i3i3i0000000000000000000000000000000
χ6144-24-2-4-24-2001-2-2-2-2122-1-1-40000−3i−3i3i3i004-4-2-2221122-1-10000−3i−3i3i3i0000-21102-1-10000−3i−3i3i3i0000000000000000000000000000000
χ6244-24-2-4-24-2001-2-2-2-2122-1-1-40000−3i−3i3i3i00-4422-2-21122-1-10000−3i−3i3i3i00002-1-10-21100003i3i−3i−3i0000000000000000000000000000000
χ6344-2-2444-2-244-21-21-2-24-2-2-2-2-2-244-2-2-2-2-2-2000000111-21111-2-2111144000000000000000000000-2-2-2-200000000000011000000000
χ6444-2-2444-2-244-21-21-2-24-2-2-2-2-2-244-2-2-2-2-2-2000000111-21111-2-21111-4-40000000000000000000002222000000000000-1-1000000000
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χ704-444-202-4-422−22-24-2-4220000022−22−22−22−2222−22002i3−2i300-22000022−22−22−22−22000002i3−2i3000000−i6i6−i6i6−i6i60000000000000000000000000000000
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χ744-44-240-42-422−224-2-222-40000022−2222−2222−2222−22−22000000-220000−22−22−22−220000000000000000000002i3−2i300000000000000−i6i600000000000
χ754-44-240-42-4−22224-2-222-400000−2222−2222−2222−22222−2000000-2200002−22−22−22−2000000000000000000000−2i32i300000000000000−i6i600000000000
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χ864-4-24-202-42−22221-2-222-1003i−3i02−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ23−2222002i3−2i323−231-1003i−3i2−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ2300000−i3i300−33−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ130000000000000000000000000000000
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χ884-4-24-202-42−22221-2-222-100−3i3i02−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−2222002i3−2i3−23231-100−3i3i2−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ2300000−i3i3003−36−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000000000000
χ89888-4-4-8-4-4800-4-42-42-44-84440000000000000000224-2-2-20000000000000000000000000000000000000000000000000000000000
χ9088-4-48-88-4-400-42-42-4-4-84444000000000000000022-24-2-20000000000000000000000000000000000000000000000000000000000
χ9188-4-4-48-4-4-488222222-4-422-4-4-4-4-42222-4-4000000-1-122-1-12222-1-1-1-100000000000000000000000000000000000000000000000000
χ9288-4-4-48-4-4-4-8-8222222-4-422-44444-2-2-2-244000000-1-122-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000
χ9388-4-4-4-8-4-4-40022222244-2-2400006i6i−6i−6i00000000-1-1-2-2110000−3i−3i3i3i00000000000000000000000000000000000000000000000000
χ9488-4-4-4-8-4-4-40022222244-2-240000−6i−6i6i6i00000000-1-1-2-21100003i3i−3i−3i00000000000000000000000000000000000000000000000000
χ958-88-4-4044-842−42-4-424-240000042−42−2222−2222−2222−22220000002-20000−22222−22−22−200000000000000000000000000000000000000000000000000
χ968-88-4-4044-8−4242-4-424-2400000−424222−2222−2222−2222−220000002-2000022−22−22−22−2200000000000000000000000000000000000000000000000000
χ978-8-4-480-84442−42-42-4-24400000−222242−42−2222−2222−22220000002-200002−2−22222−22−200000000000000000000000000000000000000000000000000
χ988-8-4-480-844−4242-42-4-2440000022−22−424222−2222−2222−220000002-20000−2222−22−22−2200000000000000000000000000000000000000000000000000
χ998-8-4-4-4044442−42222-2-2-2006i−6i0−2222−2222−4ζ5−2ζ7−4ζ13−2ζ234ζ5+2ζ7+4ζ13+2ζ232ζ5+4ζ7+2ζ13+4ζ23−2ζ5−4ζ7−2ζ13−4ζ23−2222000000-1100−3i3i2−22−22ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ23−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ2300000000000000000000000000000000000000000000000000
χ1008-8-4-4-4044442−42222-2-2-200−6i6i0−2222−22222ζ5+4ζ7+2ζ13+4ζ23−2ζ5−4ζ7−2ζ13−4ζ23−4ζ5−2ζ7−4ζ13−2ζ234ζ5+2ζ7+4ζ13+2ζ23−2222000000-11003i−3i2−22−2−ζ5−2ζ7−ζ13−2ζ23ζ5+2ζ7+ζ13+2ζ232ζ5+ζ7+2ζ13+ζ23−2ζ5−ζ7−2ζ13−ζ2300000000000000000000000000000000000000000000000000
χ1018-8-4-4-40444−4242222-2-2-2006i−6i022−2222−224ζ5+2ζ7+4ζ13+2ζ23−4ζ5−2ζ7−4ζ13−2ζ23−2ζ5−4ζ7−2ζ13−4ζ232ζ5+4ζ7+2ζ13+4ζ2322−22000000-1100−3i3i−22−22−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ23ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ2300000000000000000000000000000000000000000000000000
χ1028-8-4-4-40444−4242222-2-2-200−6i6i022−2222−22−2ζ5−4ζ7−2ζ13−4ζ232ζ5+4ζ7+2ζ13+4ζ234ζ5+2ζ7+4ζ13+2ζ23−4ζ5−2ζ7−4ζ13−2ζ2322−22000000-11003i−3i−22−22ζ5+2ζ7+ζ13+2ζ23−ζ5−2ζ7−ζ13−2ζ23−2ζ5−ζ7−2ζ13−ζ232ζ5+ζ7+2ζ13+ζ2300000000000000000000000000000000000000000000000000

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