Finite Group Databasebeta

← Group #13170665

Character table — Group #13170665

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
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order123334666333666121212121236121212122466812122424242424242424241212666121212226668226664666666666121212121266121212122466812122424242424242424241212666121212226668
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
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χ3111111111111111111111111111-1111-1-111111111-1-1-1-1111-1-1-11-1-1-11-1111111111111111111111111111-1111-1-111111111-1-1-1-1111-1-1-11-1-1-11-1
χ4111111111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-11-11111111111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-11-11
χ511111111111111111111111111-11-1-111111111111-1-1-1-1-1-1-1111-11-11-1-111111111111111111111111111-11-1-111111111111-1-1-1-1-1-1-1111-11-11-1-1
χ611111111111111111111111111-11-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111111111111111111111111111-11-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111
χ711111111111111111111111111-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-11-1-1111111111111111111111111111-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-11-1-11
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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χ7822-122222-1-12-12-1-1-12222-1-1-1-1-1-1-22110-1-100000000-2-211-2112-1-1001000-2-21-2-2-2-2-211-21-2111-2-2-2-21111112-2-1-10110000000022-1-12-1-1-21100-1000
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χ8122-122-222-1-12-12-1-11-2-2-2-2-1-1111100−i3i30i3−i300000000-22-1-10−i3i30i3−i3001000-2-21-2-22-2-211-21-211-1222211-1-1-1-100i3−i30−i3i3000000002-2110i3−i30−i3i300-1000
χ8222-122-222-1-12-12-1-11-2-2-2-2-1-1111100i3−i30−i3i300000000-22-1-10i3−i30−i3i3001000-2-21-2-22-2-211-21-211-1222211-1-1-1-100−i3i30i3−i3000000002-2110−i3i30i3−i300-1000
χ8322-122-222-1-12-12-1-11-2-2-2-2-1-1111100i3−i30i3−i3000000002-2110i3−i30i3−i300-1000-2-21-2-22-2-211-21-211-1222211-1-1-1-100−i3i30−i3i300000000-22-1-10−i3i30−i3i3001000
χ844444-2-4-2444-2-2-2-24-42-422-2-22-4220000000000000000000000000000000-4-4-4-4242-4-4-42222-44-24-2-222-24-2-20000000000000000000000000000000
χ85444-24-44-24-2-24-24-2-4-4222-2-2-42220000000000000000000000000000000-4-4-42-44-42-422-42-4244-2-2-2224-2-2-20000000000000000000000000000000
χ86444-2-24-2-24-21-21-2-24-2-21111-2-2110000400-2-2-2-211110000000000000000-4-4-422-422-42-12-122-422-1-1-1-122-1-10000-4002222-1-1-1-10000000000000000
χ87444-2-24-2-24-21-21-2-24-2-21111-2-2110000-4002222-1-1-1-10000000000000000-4-4-422-422-42-12-122-422-1-1-1-122-1-10000400-2-2-2-211110000000000000000
χ88444-2-2-4-2-24-21-21-2-2-422-1-11122-1-1000000000003i3i−3i−3i0000000000000000-4-4-422422-42-12-1224-2-211-1-1-2-21100000000000−3i−3i3i3i0000000000000000
χ89444-2-2-4-2-24-21-21-2-2-422-1-11122-1-100000000000−3i−3i3i3i0000000000000000-4-4-422422-42-12-1224-2-211-1-1-2-211000000000003i3i−3i−3i0000000000000000
χ9044-24-24-24-2-2-21-21-2-2-24-2-2111-21140-2-2000000000000000-211000000000-4-42-42-42-4222-12-1222-422-1-1-12-1-1-40220000000000000002-1-1000000000
χ9144-24-24-24-2-2-21-21-2-2-24-2-2111-211-40220000000000000002-1-1000000000-4-42-42-42-4222-12-1222-422-1-1-12-1-140-2-2000000000000000-211000000000
χ9244-24-2-4-24-2-2-21-21-222-42211-12-1-100−2i32i30000000000000000i3−i3000000000-4-42-4242-4222-12-12-2-24-2-2-1-11-211002i3−2i30000000000000000−i3i3000000000
χ9344-24-2-4-24-2-2-21-21-222-42211-12-1-1002i3−2i30000000000000000−i3i3000000000-4-42-4242-4222-12-12-2-24-2-2-1-11-21100−2i32i30000000000000000i3−i3000000000
χ9444-2-2444-2-21-2-2-2-21-24-2-2-211-211104000-2-2000000000000000-211000000-4-422-4-4-422-12222-12-4222-1-12-1-1-10-4000220000000000000002-1-1000000
χ9544-2-2444-2-21-2-2-2-21-24-2-2-211-21110-4000220000000000000002-1-1000000-4-422-4-4-422-12222-12-4222-1-12-1-1-104000-2-2000000000000000-211000000
χ9644-2-24-44-2-21-2-2-2-212-4222112-1-1-100000−2i32i30000000000000000i3−i3000000-4-422-44-422-12222-1-24-2-2-2-1-1-2111000002i3−2i30000000000000000−i3i3000000
χ9744-2-24-44-2-21-2-2-2-212-4222112-1-1-1000002i3−2i30000000000000000−i3i3000000-4-422-44-422-12222-1-24-2-2-2-1-1-211100000−2i32i30000000000000000i3−i3000000
χ984-44440-4-4-4444-4-4-4000004-400000000000000000000000000000000000-44-4-4-40444-4-4-444400000-4400000000000000000000000000000000000
χ994-444-202-4-44-2-222-400000-220000000000000i6−i6i6−i6i6−i60000000000000000-44-4-420-244-422-2-24000002-20000000000000−i6i6−i6i6−i6i60000000000000000
χ1004-444-202-4-44-2-222-400000-220000000000000−i6i6−i6i6−i6i60000000000000000-44-4-420-244-422-2-24000002-20000000000000i6−i6i6−i6i6−i60000000000000000
χ1014-44-240-42-4-2-242-4200000-22000000000006−6006−6−660000000000000000-44-42-404-2422-4-24-2000002-200000000000−6600−666−60000000000000000
χ1024-44-240-42-4-2-242-4200000-2200000000000−6600−666−60000000000000000-44-42-404-2422-4-24-2000002-2000000000006−6006−6−660000000000000000
χ1034-44-2-2022-4-21-2-1220003i−3i1-1003i−3i00000006−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000000000-44-4220-2-242-121-2-2000−3i3i-1100−3i3i0000000−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000000000000
χ1044-44-2-2022-4-21-2-1220003i−3i1-1003i−3i0000000−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000000000000-44-4220-2-242-121-2-2000−3i3i-1100−3i3i00000006−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000000000
χ1054-44-2-2022-4-21-2-122000−3i3i1-100−3i3i00000006−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000000000000-44-4220-2-242-121-2-20003i−3i-11003i−3i0000000−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ130000000000000000
χ1064-44-2-2022-4-21-2-122000−3i3i1-100−3i3i0000000−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ130000000000000000-44-4220-2-242-121-2-20003i−3i-11003i−3i00000006−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000000000000
χ1074-4-2440-4-42-24-2-42200000-2200000000000000000000023−23000000000000-442-4-4044-22-424-2-2000002-2000000000000000000000−2323000000000000
χ1084-4-2440-4-42-24-2-42200000-22000000000000000000000−2323000000000000-442-4-4044-22-424-2-2000002-200000000000000000000023−23000000000000
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
χ1118-8-48-404-84-4-424-24000002-200000000000000000000000000000000000-884-840-48-444-2-42-400000-2200000000000000000000000000000000000
χ1128-8-4-480-8442-4-444-2000002-200000000000000000000000000000000000-8844-808-4-4-244-4-4200000-2200000000000000000000000000000000000
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.