Finite Group Databasebeta

← Group #13156641

Character table — Group #13156641

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11112222222222222222224444444444444444444444448888888888121212121212121212121212121212121212121212121212121212121212121212121212242424242424242424363636363636727272727272216
order12223334466666666612121212333666666666121212121212121212121212366612121212121244881212121212121212121212121212121224242424242424242424242424242424412121212121212128824242424246612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11-111-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ511111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-11-1-111-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-11
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-22-2002222-2-2-2-22222-2-2-2-200000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2200-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000
χ11222222-12222222-1-1-1222222-1-122-1-12-1-1-1-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1220022-1-122-1-1-1-1-1-1-1-1-1-100000000000000002-1-122-1-1-1-100000020-1-1000
χ12222222-12222222-1-1-1222222-1-122-1-12-1-1-1-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1220022-1-122-1-1-1-1-1-1-1-1-1-10000000000000000-211-2-21111000000-2011000
χ13222222-12222222-1-1-1222222-1-122-1-12-1-1-1-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-200-2-211-2-2111111111100000000000000002-1-122-1-1-1-1000000-2011000
χ14222222-12222222-1-1-1222222-1-122-1-12-1-1-1-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-200-2-211-2-211111111110000000000000000-211-2-2111100000020-1-1000
χ15222222-1-2-222222-1-1-12-2-2-2-22-1-122-1-12-1-1-1-111-2-2-21111-2-2-2-1-1-1-11111112-20022-1-1-2-211-1-1-1-1111100000000000000000−i3i300−i3−i3i3i300000000−i3i3000
χ16222222-1-2-222222-1-1-12-2-2-2-22-1-122-1-12-1-1-1-111-2-2-21111-2-2-2-1-1-1-11111112-20022-1-1-2-211-1-1-1-1111100000000000000000i3−i300i3i3−i3−i300000000i3−i3000
χ17222222-1-2-222222-1-1-12-2-2-2-22-1-122-1-12-1-1-1-111-2-2-21111-2-2-2-1-1-1-1111111-2200-2-21122-1-11111-1-1-1-100000000000000000−i3i300−i3−i3i3i300000000i3−i3000
χ18222222-1-2-222222-1-1-12-2-2-2-22-1-122-1-12-1-1-1-111-2-2-21111-2-2-2-1-1-1-1111111-2200-2-21122-1-11111-1-1-1-100000000000000000i3−i300i3i3−i3−i300000000−i3i3000
χ1922222-122222-1-1-12222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-12222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000022-1-1-1-10000000
χ2022222-122222-1-1-12222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-122-2-2-1-122-1-122-1-1-1-1-1-1-1-11111-2-2-2-211111111000000000-2-211110000000
χ2122222-122222-1-1-12222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-22211-2-211-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-1000000000-2-211110000000
χ2222222-122222-1-1-12222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-2-2-211-2-211-2-2111111111111-2-2-2-21111111100000000022-1-1-1-10000000
χ2322222-12-2-222-1-1-122221111-12-1-1-122-1-1-1-12-2-2-2111111-211-1-1-1-1-2-211112-200-1-12211-2-2-1-1-1-1111133−3−300003333−3−3−3−30000000000033−3−30000000
χ2422222-12-2-222-1-1-122221111-12-1-1-122-1-1-1-12-2-2-2111111-211-1-1-1-1-2-211112-200-1-12211-2-2-1-1-1-11111−3−3330000−3−3−3−3333300000000000−3−3330000000
χ2522222-12-2-222-1-1-122221111-12-1-1-122-1-1-1-12-2-2-2111111-211-1-1-1-1-2-21111-220011-2-2-1-1221111-1-1-1-133−3−300003333−3−3−3−300000000000−3−3330000000
χ2622222-12-2-222-1-1-122221111-12-1-1-122-1-1-1-12-2-2-2111111-211-1-1-1-1-2-21111-220011-2-2-1-1221111-1-1-1-1−3−3330000−3−3−3−333330000000000033−3−30000000
χ272222-12222-1-1222222-12222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1002200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-10000000200-1-10
χ282222-12222-1-1222222-12222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1002200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-21111110000000-200110
χ292222-12222-1-1222222-12222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-100-2-20000000000000000-2-2-2-2111111111111222-1-1-1-1-1-10000000-200110
χ302222-12222-1-1222222-12222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-100-2-20000000000000000-2-2-2-2111111111111-2-2-21111110000000200-1-10
χ312-2-222222-2-2-22-2-2-2-22222-2-2222-2-2-2-222-2-222-2-2-2-222-2-22222-2-222-222-2-2002-200000000000000002-22-222-2-222-2-222-2-20000000000000000000000
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χ342-2-22222-22-2-22-2-2-2-222-2-222222-2-2-2-222-2-22-22222-2-222-2-2-22-2-22-22-2-222000000000000000000000000000000000000000000000-22-22-220000000
χ352-2-222-122-2-2-2-111-2-222-1-111-12-111-2-2-1-11122-2-211-1-1112-1-1-111-12-2-1-111002-23−3003−30033−3−333−3−3-11-1122-2-2-1-111-1-111000000000003−3−330000000
χ362-2-222-122-2-2-2-111-2-222-1-111-12-111-2-2-1-11122-2-211-1-1112-1-1-111-12-2-1-111002-2−3300−3300−3−333−3−333-11-1122-2-2-1-111-1-11100000000000−333−30000000
χ372-2-222-122-2-2-2-111-2-222-1-111-12-111-2-2-1-11122-2-211-1-1112-1-1-111-12-2-1-11100-223−3003−30033−3−333−3−31-11-1-2-22211-1-111-1-100000000000−333−30000000
χ382-2-222-122-2-2-2-111-2-222-1-111-12-111-2-2-1-11122-2-211-1-1112-1-1-111-12-2-1-11100-22−3300−3300−3−333−3−3331-11-1-2-22211-1-111-1-1000000000003−3−330000000
χ392-2-222-12-22-2-2-111-2-22211-1-1-12-111-2-2-1-1112-222-1-111-1-1-211-111-1-2211-1-100003−300−330033−3−3−3−3333−3−33000033−3−3−3−333000000000-221-11-10000000
χ402-2-222-12-22-2-2-111-2-22211-1-1-12-111-2-2-1-1112-222-1-111-1-1-211-111-1-2211-1-100003−300−330033−3−3−3−333−333−30000−3−33333−3−30000000002-2-11-110000000
χ412-2-222-12-22-2-2-111-2-22211-1-1-12-111-2-2-1-1112-222-1-111-1-1-211-111-1-2211-1-10000−33003−300−3−33333−3−33−3−33000033−3−3−3−3330000000002-2-11-110000000
χ422-2-222-12-22-2-2-111-2-22211-1-1-12-111-2-2-1-1112-222-1-111-1-1-211-111-1-2211-1-10000−33003−300−3−33333−3−3−333−30000−3−33333−3−3000000000-221-11-10000000
χ432-2-22-1222-2112-2-2-2-22-122-2-2-1-121111-12-2-2-12-211122-2-2-1-1-1-111-1-11-1-111002-200000000000000002-22-2-1-111-1-111-1-111000−i3i3−i3i3−i3i30000000000−i3i30
χ442-2-22-1222-2112-2-2-2-22-122-2-2-1-121111-12-2-2-12-211122-2-2-1-1-1-111-1-11-1-111002-200000000000000002-22-2-1-111-1-111-1-111000i3−i3i3−i3i3−i30000000000i3−i30
χ452-2-22-1222-2112-2-2-2-22-122-2-2-1-121111-12-2-2-12-211122-2-2-1-1-1-111-1-11-1-11100-220000000000000000-22-2211-1-111-1-111-1-1000−i3i3−i3i3−i3i30000000000i3−i30
χ462-2-22-1222-2112-2-2-2-22-122-2-2-1-121111-12-2-2-12-211122-2-2-1-1-1-111-1-11-1-11100-220000000000000000-22-2211-1-111-1-111-1-1000i3−i3i3−i3i3−i30000000000−i3i30
χ4744444-2-24444-2-2-2-2-2-24-2-2-2-2-2-21-2-2-2-2-2111-2-2-24-2-211114-2-21111-2-211114400-2-2-2-2-2-2-2-21111111100000000000000000000000000000000000000
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χ4944444-2-2-4-444-2-2-2-2-2-242222-2-21-2-2-2-2-2111-222-422-1-1-1-1-422111122-1-1-1-14-400-2-2-2-222221111-1-1-1-100000000000000000000000000000000000000
χ5044444-2-2-4-444-2-2-2-2-2-242222-2-21-2-2-2-2-2111-222-422-1-1-1-1-422111122-1-1-1-1-44002222-2-2-2-2-1-1-1-1111100000000000000000000000000000000000000
χ514444-244-4-4-2-2444444-2-4-4-4-4-2-24-2-2-2-2-2444-2-4-4222-4-4-4-4222-2-2-2-22222220000000000000000000000000000000000000000000000000000000000
χ524444-24-244-2-2444-2-2-2-24444-21-2-2-211-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-211111111110000000000000000000000000000000000004-2-2-2-211110000000000000
χ534444-24-244-2-2444-2-2-2-24444-21-2-2-211-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111000000000000000000000000000000000000-42222-1-1-1-10000000000000
χ544444-24-2-4-4-2-2444-2-2-2-2-4-4-4-4-21-2-2-211-2-2-2-212222222222221111-1-1-1-1-1-10000000000000000000000000000000000000−2i32i300i3i3−i3−i30000000000000
χ554444-24-2-4-4-2-2444-2-2-2-2-4-4-4-4-21-2-2-211-2-2-2-212222222222221111-1-1-1-1-1-100000000000000000000000000000000000002i3−2i300−i3−i3i3i30000000000000
χ564444-2-2444-2-2-2-2-2444-2-2-2-2-21-2-211-2-21-2-2-2-244-211-2-2-2-2-2111111-2-2111100440000000000000000-2-2-2-2-2-2-2-2111111110000000000000000000000
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χ594444-2-24-4-4-2-2-2-2-2444-222221-2-211-2-21-2-2-2-2-4-42-1-122222-1-1111122-1-1-1-100000000000000000000−23−23232300003333−3−3−3−30000000000000000000000
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χ834-44-44-2-200-4422-22-22-4−232323−23-2-212-22-22-1-11200023−233−3−330−23231-11-1003−3−33000000−232300003−3−33-333-300000000000000000000000000000000000000
χ844-44-4-244002-2-4-44-44-420000-2-242-22-22-4-442000000000000-22-22000000000000000000000000000000i6−i6−i6i6i6−i6−i6i6i6−i6−i6i60000000000000000000000
χ854-44-4-244002-2-4-44-44-420000-2-242-22-22-4-442000000000000-22-22000000000000000000000000000000−i6i6i6−i6−i6i6i6−i6−i6i6i6−i60000000000000000000000
χ864-44-4-2-24002-222-2-44-4223−23−23231-2-2-112-2-122-220003−323−23−23230−331-11-100−333−3000000000000000000000000i6−i6−i6i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ230000000000000000000000
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χ884-44-4-2-24002-222-2-44-42−232323−231-2-2-112-2-122-22000−33−232323−2303−31-11-1003−3−33000000000000000000000000i6−i6−i6i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ230000000000000000000000
χ894-44-4-2-24002-222-2-44-42−232323−231-2-2-112-2-122-22000−33−232323−2303−31-11-1003−3−33000000000000000000000000−i6i6i6−i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ230000000000000000000000
χ904-4-4444-24-4-4-44-4-422-2444-4-44-2-2-4-4224-222-2-22-4-4-4-2-222444-222-2-22-2-2220000000000000000000000000000000000000000000000000000000000
χ914-4-4444-2-44-4-44-4-422-24-4-4444-2-2-4-4224-222-22-244422-2-2-4-4-4-222-22-222-2-20000000000000000000000000000000000000000000000000000000000
χ924-4-444-2-24-4-4-4-22222-24-2-222-2-212222-21-1-1-2-22-42211-1-14-2-21-1-11-2211-1-1000023−230023−2300−3−333−3−33300000000000000000000000000000000000000
χ934-4-444-2-24-4-4-4-22222-24-2-222-2-212222-21-1-1-2-22-42211-1-14-2-21-1-11-2211-1-10000−232300−23230033−3−333−3−300000000000000000000000000000000000000
χ944-4-444-2-2-44-4-4-22222-2422-2-2-2-212222-21-1-1-22-24-2-2-1-111-4221-1-112-2-1-111000023−2300−232300−3−33333−3−300000000000000000000000000000000000000
χ954-4-444-2-2-44-4-4-22222-2422-2-2-2-212222-21-1-1-22-24-2-2-1-111-4221-1-112-2-1-1110000−23230023−230033−3−3−3−33300000000000000000000000000000000000000
χ964-4-44-244-44224-4-4-4-44-2-4-444-2-242222-24-4-4-2-44-2-2-2-4-444222-222-22-222-2-20000000000000000000000000000000000000000000000000000000000
χ974-4-44-24-24-4224-4-422-2-244-4-4-21-222-1-1-2-2221-22222-2-222-2-2-21-1-111-111-1-1000000000000000000000000000000000000000−2i32i3i3−i3i3−i30000000000000
χ984-4-44-24-24-4224-4-422-2-244-4-4-21-222-1-1-2-2221-22222-2-222-2-2-21-1-111-111-1-10000000000000000000000000000000000000002i3−2i3−i3i3−i3i30000000000000
χ994-4-44-24-2-44224-4-422-2-2-4-444-21-222-1-1-2-22212-2-2-2-222-2-22221-1-11-11-1-111000000000000000000000000000000000000000003-3-330000000000000
χ1004-4-44-24-2-44224-4-422-2-2-4-444-21-222-1-1-2-22212-2-2-2-222-2-22221-1-11-11-1-11100000000000000000000000000000000000000000-333-30000000000000
χ1014-4-44-2-244-422-222-4-44-2-2-2221-2-2-1-1221-222-24-42-1-1-2-222-2111-1-11-2211-1-1004-40000000000000000-22-22-2-22211-1-111-1-10000000000000000000000
χ1024-4-44-2-244-422-222-4-44-2-2-2221-2-2-1-1221-222-24-42-1-1-2-222-2111-1-11-2211-1-100-4400000000000000002-22-222-2-2-1-111-1-1110000000000000000000000
χ1034-4-44-2-24-4422-222-4-44-222-2-21-2-2-1-1221-222-2-44-21122-2-22-1-11-1-112-2-1-1110000000000000000000023−23−23230000−3−33333−3−30000000000000000000000
χ1044-4-44-2-24-4422-222-4-44-222-2-21-2-2-1-1221-222-2-44-21122-2-22-1-11-1-112-2-1-11100000000000000000000−232323−23000033−3−3−3−3330000000000000000000000
χ1058888-4-4-488-4-4-4-4-4-4-4-4-4-4-4-4-4222222222222-4-4-4222222-422-1-1-1-122-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ1068888-4-4-4-8-8-4-4-4-4-4-4-4-4-44444222222222222444-2-2-2-2-2-24-2-2-1-1-1-1-2-211110000000000000000000000000000000000000000000000000000000000
χ10788-8-8-48-400-44-88-8-44440000-42-4-442-244-44-200000000000022-2-20000000000000000000000000000000000000000000000000000000000000000
χ10888-8-8-4-4-400-444-44-444443−4343−432222-22-2-2-22-2-2000−2323−2323−23230−2323-1-111003−33−30000000000000000000000000000000000000000000000000000000000
χ10988-8-8-4-4-400-444-44-4444−4343−43432222-22-2-2-22-2-200023−2323−2323−23023−23-1-11100−33−330000000000000000000000000000000000000000000000000000000000
χ1108-88-8-48-4004-4-8-884-4440000-42-44-4-22444-4-20000000000002-22-20000000000000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-4004-444-44-44443−43−4343222-22-22-2-2-22-200023−23−232323−230−2323-11-11003−3−330000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-4-4004-444-44-444−434343−43222-22-22-2-2-22-2000−232323−23−2323023−23-11-1100−333−30000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-48-844-44444-4-4-4-444222-2-2-2-222-2-22-444-2-222-2-2-422-111-12-2-1-1110000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4-8844-44444-4-444-4-4222-2-2-2-222-2-224-4-422-2-2224-2-2-111-1-2211-1-10000000000000000000000000000000000000000000000000000000000

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