Finite Group Databasebeta

← Group #13156643

Character table — Group #13156643

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11112222222222222222224444444444444444444444448888888888121212121212121212121212121212121212121212121212121212121212121212121212242424242424242424363636363636727272727272216
order1222333446666666661212121233366666666612121212121212121212121236661212121212128888242424242424242424242424242424242424242424242424242424242424242441212121212121212441212121244121212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11-111-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ511111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-11-1-111-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11
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
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000000000000002-222-2-20000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000000000000-22-2-2220000000
χ11222222-1222222-1-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000022-1-1-1-10000000
χ12222222-1222222-1-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111000000000-2-211110000000
χ13222222-1222222-1-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2221111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1000000000-2-211110000000
χ14222222-1222222-1-1-122-1-1-1-12-1-122-1-1-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-21111111100000000022-1-1-1-10000000
χ15222222-1-2-22222-1-1-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−333−3−300003333−3−3−3−300003333−3−3−3−30000000002-2-1-1110000000
χ16222222-1-2-22222-1-1-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-21111000033−3−3−3−33300003333−3−3−3−30000−3−3−3−33333000000000-2211-1-10000000
χ17222222-1-2-22222-1-1-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-211110000−3−33333−3−30000−3−3−3−3333300003333−3−3−3−3000000000-2211-1-10000000
χ18222222-1-2-22222-1-1-12211112-1-122-1-1-1-1-1-12-2-21111-2-21111-1-1-1-1-2-211110000−3−333−3−3330000−3−3−3−333330000−3−3−3−333330000000002-2-1-1110000000
χ1922222-122222-1-12222-12222-12-1-1-122-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-10000000200-1-10
χ2022222-122222-1-12222-12222-12-1-1-122-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-1002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-21111110000000-200110
χ2122222-122222-1-12222-12222-12-1-1-122-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-2000000000000111111111111222-1-1-1-1-1-10000000-200110
χ2222222-122222-1-12222-12222-12-1-1-122-1-12-1-12-122-1-12-122-1-1-1-1-1-1-1-1-1-1-1-100-2-20000-2-2-2-2000000000000111111111111-2-2-21111110000000200-1-10
χ232222-12222-1-122222-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-10000000000002-1-122-1-1-1-100000020-1-1000
χ242222-12222-1-122222-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-1000000000000-211-2-21111000000-2011000
χ252222-12222-1-122222-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-200001111111111110000000000002-1-122-1-1-1-1000000-2011000
χ262222-12222-1-122222-122222-1-12-1-1-1-122-12-1-12-1-122-12-1-122-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-20000111111111111000000000000-211-2-2111100000020-1-1000
χ272-2-222222-2-2-2-2-22-2-22222-2-2222-2-2-2-2-2-22222-222-2-2-22-2-2222-2-222-222-2-2002-200002-22-200000000000022-2-222-2-222-2-20000000000000000000000
χ282-2-222222-2-2-2-2-22-2-22222-2-2222-2-2-2-2-2-22222-222-2-2-22-2-2222-2-222-222-2-200-220000-22-22000000000000-2-222-2-222-2-2220000000000000000000000
χ292-2-22222-22-2-2-2-22-2-222-2-222222-2-2-2-2-2-2222-22-2-2222-222-2-22-2-22-22-2-2222-2002-22-2000022-2-222-2-222-2-20000000000000000000000000000000000
χ302-2-22222-22-2-2-2-22-2-222-2-222222-2-2-2-2-2-2222-22-2-2222-222-2-22-2-22-22-2-222-2200-22-220000-2-222-2-222-2-2220000000000000000000000000000000000
χ312-2-2222-12-2-2-2-2-2-11122-1-1112-1-1-2-21111-1-122-2-1-111-2211-1-1-111-12-2-1-111002-23−3−33-11-11000033−3−3−3−33322-2-2-1-111-1-111000000000003−33−30000000
χ322-2-2222-12-2-2-2-2-2-11122-1-1112-1-1-2-21111-1-122-2-1-111-2211-1-1-111-12-2-1-111002-2−333−3-11-110000−3−33333−3−322-2-2-1-111-1-11100000000000−33−330000000
χ332-2-2222-12-2-2-2-2-2-11122-1-1112-1-1-2-21111-1-122-2-1-111-2211-1-1-111-12-2-1-11100-223−3−331-11-1000033−3−3−3−333-2-22211-1-111-1-100000000000−33−330000000
χ342-2-2222-12-2-2-2-2-2-11122-1-1112-1-1-2-21111-1-122-2-1-111-2211-1-1-111-12-2-1-11100-22−333−31-11-10000−3−33333−3−3-2-22211-1-111-1-1000000000003−33−30000000
χ352-2-2222-1-22-2-2-2-2-1112211-1-12-1-1-2-21111-1-12-2211-1-12-2-1-111-111-1-2211-1-12-200-11-113−3−3322-2-2-1-111-1-111000033−3−3−3−33300000000000−333−30000000
χ362-2-2222-1-22-2-2-2-2-1112211-1-12-1-1-2-21111-1-12-2211-1-12-2-1-111-111-1-2211-1-12-200-11-11−333−322-2-2-1-111-1-1110000−3−33333−3−3000000000003−3−330000000
χ372-2-2222-1-22-2-2-2-2-1112211-1-12-1-1-2-21111-1-12-2211-1-12-2-1-111-111-1-2211-1-1-22001-11-13−3−33-2-22211-1-111-1-1000033−3−3−3−333000000000003−3−330000000
χ382-2-2222-1-22-2-2-2-2-1112211-1-12-1-1-2-21111-1-12-2211-1-12-2-1-111-111-1-2211-1-1-22001-11-1−333−3-2-22211-1-111-1-10000−3−33333−3−300000000000−333−30000000
χ392-2-222-122-2-2-2112-2-22-122-2-2-12-111-2-2112-1-1212211-2-1-2-2-1-1-111-1-11-1-111002-200002-22-2000000000000-1-111-1-111-1-111000−i3i3−i3−i3i3i30000000000−i3i30
χ402-2-222-122-2-2-2112-2-22-122-2-2-12-111-2-2112-1-1212211-2-1-2-2-1-1-111-1-11-1-111002-200002-22-2000000000000-1-111-1-111-1-111000i3−i3i3i3−i3−i30000000000i3−i30
χ412-2-222-122-2-2-2112-2-22-122-2-2-12-111-2-2112-1-1212211-2-1-2-2-1-1-111-1-11-1-11100-220000-22-2200000000000011-1-111-1-111-1-1000−i3i3−i3−i3i3i30000000000i3−i30
χ422-2-222-122-2-2-2112-2-22-122-2-2-12-111-2-2112-1-1212211-2-1-2-2-1-1-111-1-11-1-11100-220000-22-2200000000000011-1-111-1-111-1-1000i3−i3i3i3−i3−i30000000000−i3i30
χ432-2-22-122-2211-2-22-2-2-12-2-222-1-121111-2-2-12-1121122-1-2-1-1-2-2-111-11-111-1-12-2002-22-20000-1-111-1-111-1-1110000000000000−i3i300−i3i3−i3i300000000−i3i3000
χ442-2-22-122-2211-2-22-2-2-12-2-222-1-121111-2-2-12-1121122-1-2-1-1-2-2-111-11-111-1-12-2002-22-20000-1-111-1-111-1-1110000000000000i3−i300i3−i3i3−i300000000i3−i3000
χ452-2-22-122-2211-2-22-2-2-12-2-222-1-121111-2-2-12-1121122-1-2-1-1-2-2-111-11-111-1-1-2200-22-22000011-1-111-1-111-1-10000000000000−i3i300−i3i3−i3i300000000i3−i3000
χ462-2-22-122-2211-2-22-2-2-12-2-222-1-121111-2-2-12-1121122-1-2-1-1-2-2-111-11-111-1-1-2200-22-22000011-1-111-1-111-1-10000000000000i3−i300i3−i3i3−i300000000−i3i3000
χ4744444-24-4-444-2-24444-2-4-4-4-4-24-2-2-244-2-24-2-2-42-4-422-42-4-422-2-2-2-22222220000000000000000000000000000000000000000000000000000000000
χ4844444-2-24444-2-2-2-2-24-2-2-2-2-2-2-21-2-2-2-211-21-24-2-2-2114-2-2-2111111-2-2111100440000-2-2-2-2000000000000-2-2-2-2111111110000000000000000000000
χ4944444-2-24444-2-2-2-2-24-2-2-2-2-2-2-21-2-2-2-211-21-24-2-2-2114-2-2-2111111-2-2111100-4-4000022220000000000002222-1-1-1-1-1-1-1-10000000000000000000000
χ5044444-2-2-4-444-2-2-2-2-24-22222-2-21-2-2-2-211-21-2-4222-1-1-4222-1-1111122-1-1-1-1000000002323−23−230000000000000000−3−3−3−333330000000000000000000000
χ5144444-2-2-4-444-2-2-2-2-24-22222-2-21-2-2-2-211-21-2-4222-1-1-4222-1-1111122-1-1-1-100000000−23−23232300000000000000003333−3−3−3−30000000000000000000000
χ524444-244-4-4-2-244444-24-4-4-4-4-2-24-2-2-2-244-24-22-422-4-42-422-4-4-2-2-2-22222220000000000000000000000000000000000000000000000000000000000
χ534444-24-244-2-244-2-2-2-24-2-2-2-2-21-2-2-211-2-21-2-2-2411-2-2-2411-2-21111-2-211114400-2-2-2-20000-2-2-2-2111111110000000000000000000000000000000000
χ544444-24-244-2-244-2-2-2-24-2-2-2-2-21-2-2-211-2-21-2-2-2411-2-2-2411-2-21111-2-21111-4-400222200002222-1-1-1-1-1-1-1-10000000000000000000000000000000000
χ554444-24-2-4-4-2-244-2-2-2-242222-21-2-2-211-2-21-2-22-4-1-1222-4-1-122111122-1-1-1-100002323−23−2300000000−3−3−3−333330000000000000000000000000000000000
χ564444-24-2-4-4-2-244-2-2-2-242222-21-2-2-211-2-21-2-22-4-1-1222-4-1-122111122-1-1-1-10000−23−232323000000003333−3−3−3−30000000000000000000000000000000000
χ574444-2-2444-2-2-2-2444-2-244441-2-211-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-211111111110000000000000000000000000000000000004-2-2-2-211110000000000000
χ584444-2-2444-2-2-2-2444-2-244441-2-211-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111000000000000000000000000000000000000-42222-1-1-1-10000000000000
χ594444-2-24-4-4-2-2-2-2444-2-2-4-4-4-41-2-211-2-2-2-2-2-212222222222221111-1-1-1-1-1-1000000000000000000000000000000000000000003-3-330000000000000
χ604444-2-24-4-4-2-2-2-2444-2-2-4-4-4-41-2-211-2-2-2-2-2-212222222222221111-1-1-1-1-1-100000000000000000000000000000000000000000-333-30000000000000
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χ6444-4-44-24004-4-22-44-4-420000-24-2-224-4-22-422000000000000-2-222000000000000000000000000000000i6−i6i6−i6i6−i6i6−i6i6−i6i6−i60000000000000000000000
χ6544-4-44-24004-4-22-44-4-420000-24-2-224-4-22-422000000000000-2-222000000000000000000000000000000−i6i6−i6i6−i6i6−i6i6−i6i6−i6i60000000000000000000000
χ6644-4-44-2-2004-4-222-22-4223−2323−23-2-21-22-221-12-120023−23−330023−23−3311-1-100−33−33000000000000000000000000i6−i6i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ230000000000000000000000
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χ7444-4-4-24-200-224-42-222-4−2323−2323-21-2-221-1-22-122003−3−2323003−3−232311-1-1003−33−3000000000000i6−i6i6−i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ230000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.