Finite Group Databasebeta

← Group #13170690

Character table — Group #13170690

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
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χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
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χ3111111111111111111111111111-1111-1-111111111-1-1-1-11-111-1-11-1-11-1-1111111111111111111111111111-1111-1-111111111-1-1-1-11-111-1-11-1-11-1-1
χ4111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-11-1-111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-11-1-111
χ511111111111111111111111111-111-1-11111111111-1-1-1-1-11-1-111-11-1-11-111111111111111111111111111-111-1-11111111111-1-1-1-1-11-1-111-11-1-11-1
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χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1
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χ8022-122222-1-1-12-1-1222-1-1-1-1-1-12-1-10220022-1-122-1-1-1-100000-100-1-10200-10-2-21-2-2-2-2-2111-211-2-2-2111111-2110-2-200-2-211-2-2111100000100110-20010
χ8122-122222-1-1-12-1-1222-1-1-1-1-1-12-1-102-2002211-2-2111100000-100-1-10-20010-2-21-2-2-2-2-2111-211-2-2-2111111-2110-2200-2-2-1-122-1-1-1-100000100110200-10
χ8222-122222-1-1-12-1-1222-1-1-1-1-1-12-1-10-2200-2-2-1-122-1-1-1-100000100110-20010-2-21-2-2-2-2-2111-211-2-2-2111111-21102-2002211-2-2111100000-100-1-10200-10
χ8322-122222-1-1-12-1-1222-1-1-1-1-1-12-1-10-2-200-2-211-2-2111100000100110200-10-2-21-2-2-2-2-2111-211-2-2-2111111-2110220022-1-122-1-1-1-100000-100-1-10-20010
χ844444-2-4-2444-2-2-24-2-42-422-2-2-42220000000000000000000000000000000-4-4-4-4242-4-4-4222-424-24-2-2224-2-2-20000000000000000000000000000000
χ85444-2-24-2-24-2-21-2-21-2-24-2-211-2111400-2-200000000000000-201100000000-4-4-422-422-422-122-122-422-1-12-1-1-1-400220000000000000020-1-100000000
χ86444-2-24-2-24-2-21-2-21-2-24-2-211-2111-400220000000000000020-1-100000000-4-4-422-422-422-122-122-422-1-12-1-1-1400-2-200000000000000-201100000000
χ87444-2-2-4-2-24-2-21-2-2122-422112-1-1-1000−2i32i30000000000000000i3−i300000000-4-4-422422-422-122-1-2-24-2-2-1-1-21110002i3−2i30000000000000000−i3i300000000
χ88444-2-2-4-2-24-2-21-2-2122-422112-1-1-10002i3−2i30000000000000000−i3i300000000-4-4-422422-422-122-1-2-24-2-2-1-1-2111000−2i32i30000000000000000i3−i300000000
χ8944-244-444-2-2-24-2-24-4-4222-2-22-4220000000000000000000000000000000-4-42-4-44-4-4222-422-444-2-2-222-24-2-20000000000000000000000000000000
χ9044-24-24-24-2-21-21-2-24-2-21111-2-2110040000-2-2-2-211110000000000000000-4-42-42-42-422-12-122-422-1-1-1-122-1-100-400002222-1-1-1-10000000000000000
χ9144-24-24-24-2-21-21-2-24-2-21111-2-21100-400002222-1-1-1-10000000000000000-4-42-42-42-422-12-122-422-1-1-1-122-1-10040000-2-2-2-211110000000000000000
χ9244-24-2-4-24-2-21-21-2-2-422-1-11122-1-1000000000003i3i−3i−3i0000000000000000-4-42-4242-422-12-1224-2-211-1-1-2-21100000000000−3i−3i3i3i0000000000000000
χ9344-24-2-4-24-2-21-21-2-2-422-1-11122-1-100000000000−3i−3i3i3i0000000000000000-4-42-4242-422-12-1224-2-211-1-1-2-211000000000003i3i−3i−3i0000000000000000
χ9444-2-2444-2-21-2-2-21-2-24-2-2-2111-21104000-2-20000000000000-20011000000-4-422-4-4-422-1222-122-4222-1-1-12-1-10-4000220000000000000200-1-1000000
χ9544-2-2444-2-21-2-2-21-2-24-2-2-2111-2110-4000220000000000000200-1-1000000-4-422-4-4-422-1222-122-4222-1-1-12-1-104000-2-20000000000000-20011000000
χ9644-2-24-44-2-21-2-2-21-22-422211-12-1-100000−2i32i30000000000000000i3−i3000000-4-422-44-422-1222-12-24-2-2-2-1-11-211000002i3−2i30000000000000000−i3i3000000
χ9744-2-24-44-2-21-2-2-21-22-422211-12-1-1000002i3−2i30000000000000000−i3i3000000-4-422-44-422-1222-12-24-2-2-2-1-11-21100000−2i32i30000000000000000i3−i3000000
χ984-44440-4-4-4444-4-4-4000004-400000000000000000000000000000000000-44-4-4-40444-4-4-444400000-4400000000000000000000000000000000000
χ994-444-202-4-44-2-22-4200000-2200000000000006−66−66−60000000000000000-44-4-420-244-422-24-2000002-20000000000000−66−66−660000000000000000
χ1004-444-202-4-44-2-22-4200000-220000000000000−66−66−660000000000000000-44-4-420-244-422-24-2000002-200000000000006−66−66−60000000000000000
χ1014-44-240-42-4-24-2-42200000-22000000000000000000000−2i32i3000000000000-44-42-404-242-424-2-2000002-20000000000000000000002i3−2i3000000000000
χ1024-44-240-42-4-24-2-42200000-220000000000000000000002i3−2i3000000000000-44-42-404-242-424-2-2000002-2000000000000000000000−2i32i3000000000000
χ1034-4-2440-4-42-2-2422-400000-2200000000000i6−i600i6−i6−i6i60000000000000000-442-4-4044-222-4-2-24000002-200000000000−i6i600−i6i6i6−i60000000000000000
χ1044-4-2440-4-42-2-2422-400000-2200000000000−i6i600−i6i6i6−i60000000000000000-442-4-4044-222-4-2-24000002-200000000000i6−i600i6−i6−i6i60000000000000000
χ1054-4-24-202-42-21-2-1220003i−3i1-1003i−3i0000000i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000-442-420-24-22-121-2-2000−3i3i-1100−3i3i0000000−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000
χ1064-4-24-202-42-21-2-1220003i−3i1-1003i−3i0000000−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000-442-420-24-22-121-2-2000−3i3i-1100−3i3i0000000i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000
χ1074-4-24-202-42-21-2-122000−3i3i1-100−3i3i0000000i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000-442-420-24-22-121-2-20003i−3i-11003i−3i0000000−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000
χ1084-4-24-202-42-21-2-122000−3i3i1-100−3i3i0000000−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000-442-420-24-22-121-2-20003i−3i-11003i−3i0000000i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000
χ10988-4-4-48-4-4-4222222-4-4-422-1-122-1-10000000000000000000000000000000-8-8444-8444-2-2-2-2-2-2444-2-211-2-2110000000000000000000000000000000
χ11088-4-4-4-8-4-4-4222222444-2-2-1-1-2-2110000000000000000000000000000000-8-84448444-2-2-2-2-2-2-4-4-4221122-1-10000000000000000000000000000000
χ1118-88-4-4044-8-4-4244-2000002-200000000000000000000000000000000000-88-8440-4-4844-2-4-4200000-2200000000000000000000000000000000000
χ1128-8-4-480-8442-4-44-24000002-200000000000000000000000000000000000-8844-808-4-4-244-42-400000-2200000000000000000000000000000000000
χ1138-8-4-4-40444222-2-2-20006i−6i-1100−3i3i0000000000000000000000000000000-884440-4-4-4-2-2-2222000−6i6i1-1003i−3i0000000000000000000000000000000
χ1148-8-4-4-40444222-2-2-2000−6i6i-11003i−3i0000000000000000000000000000000-884440-4-4-4-2-2-22220006i−6i1-100−3i3i0000000000000000000000000000000

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