Finite Group Databasebeta

← Group #13170660

Character table — Group #13170660

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
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χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
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χ3111111111111111111111111111-111-1-1111111111-1-1-1-11-111-1-1-11-1-11-1111111111111111111111111111-111-1-1111111111-1-1-1-11-111-1-1-11-1-11-1
χ4111111111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-1-11-11111111111111111111111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-1-11-11
χ511111111111111111111111111-11-1-111111111111-1-1-1-1-11-1-1111-1-11-1-111111111111111111111111111-11-1-111111111111-1-1-1-1-11-1-1111-1-11-1-1
χ611111111111111111111111111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-11111111111111111111111111111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-111
χ711111111111111111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11-1-1111111111111111111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11-1-11
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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χ2422-122222-1-1-12-1-1222-1-1-1-1-1-12-1-1202200-211-2-211110000-10-1-1000-2001022-122222-1-1-12-1-1222-1-1-1-1-1-12-1-1202200-211-2-211110000-10-1-1000-20010
χ2522-122222-1-1-12-1-1222-1-1-1-1-1-12-1-1-20-2-2002-1-122-1-1-1-100001011000-2001022-122222-1-1-12-1-1222-1-1-1-1-1-12-1-1-20-2-2002-1-122-1-1-1-100001011000-20010
χ2622-122222-1-1-12-1-1222-1-1-1-1-1-12-1-1-20-2-200-211-2-2111100001011000200-1022-122222-1-1-12-1-1222-1-1-1-1-1-12-1-1-20-2-200-211-2-2111100001011000200-10
χ274444-2-4-244-24-2-24-2-42-422-2-2-422200000000000000000000000000000004444-2-4-244-24-2-24-2-42-422-2-2-42220000000000000000000000000000000
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χ414-44440-4-4-4444-4-4-4000004-4000000000000000000000000000000000004-44440-4-4-4444-4-4-4000004-400000000000000000000000000000000000
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χ58111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ5911111111111111111111111111111111-1-1-1-1-1-1-1-1-11111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1111
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χ78222-12-22-122-1-12-1-11-2-2-2-2-1-1111100i3−i3−i3i3000000000-221100i3−i3−i3i300-1000-2-2-21-22-21-2-211-211-1222211-1-1-1-100−i3i3i3−i30000000002-2-1-100−i3i3i3−i3001000
χ79222-12-22-122-1-12-1-11-2-2-2-2-1-1111100i3−i3i3−i30000000002-2-1-100i3−i3i3−i3001000-2-2-21-22-21-2-211-211-1222211-1-1-1-100−i3i3−i3i3000000000-221100−i3i3−i3i300-1000
χ8022-122222-1-1-12-1-1222-1-1-1-1-1-12-1-12022002-1-122-1-1-1-10000-10-1-1000200-10-2-21-2-2-2-2-2111-211-2-2-2111111-211-20-2-200-211-2-2111100001011000-20010
χ8122-122222-1-1-12-1-1222-1-1-1-1-1-12-1-1202200-211-2-211110000-10-1-1000-20010-2-21-2-2-2-2-2111-211-2-2-2111111-211-20-2-2002-1-122-1-1-1-100001011000200-10
χ8222-122222-1-1-12-1-1222-1-1-1-1-1-12-1-1-20-2-2002-1-122-1-1-1-100001011000-20010-2-21-2-2-2-2-2111-211-2-2-2111111-211202200-211-2-211110000-10-1-1000200-10
χ8322-122222-1-1-12-1-1222-1-1-1-1-1-12-1-1-20-2-200-211-2-2111100001011000200-10-2-21-2-2-2-2-2111-211-2-2-2111111-2112022002-1-122-1-1-1-10000-10-1-1000-20010
χ844444-2-4-244-24-2-24-2-42-422-2-2-42220000000000000000000000000000000-4-4-4-4242-4-42-422-424-24-2-2224-2-2-20000000000000000000000000000000
χ85444-2-24-2-24-2-21-2-21-2-24-2-211-21110400-2-200000000000000-20011000000-4-4-422-422-422-122-122-422-1-12-1-1-10-4002200000000000000200-1-1000000
χ86444-2-24-2-24-2-21-2-21-2-24-2-211-21110-4002200000000000000200-1-1000000-4-4-422-422-422-122-122-422-1-12-1-1-10400-2-200000000000000-20011000000
χ87444-2-2-4-2-24-2-21-2-2122-422112-1-1-10000−2i32i300000000000000000i3−i3000000-4-4-422422-422-122-1-2-24-2-2-1-1-211100002i3−2i300000000000000000−i3i3000000
χ88444-2-2-4-2-24-2-21-2-2122-422112-1-1-100002i3−2i300000000000000000−i3i3000000-4-4-422422-422-122-1-2-24-2-2-1-1-21110000−2i32i300000000000000000i3−i3000000
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
χ9044-24-24-24-21-2-21-2-24-2-21111-2-2110000004-2-2-2-211110000000000000000-4-42-42-42-42-122-122-422-1-1-1-122-1-1000000-42222-1-1-1-10000000000000000
χ9144-24-24-24-21-2-21-2-24-2-21111-2-211000000-42222-1-1-1-10000000000000000-4-42-42-42-42-122-122-422-1-1-1-122-1-10000004-2-2-2-211110000000000000000
χ9244-24-2-4-24-21-2-21-2-2-422-1-11122-1-1000000000003i3i−3i−3i0000000000000000-4-42-4242-42-122-1224-2-211-1-1-2-21100000000000−3i−3i3i3i0000000000000000
χ9344-24-2-4-24-21-2-21-2-2-422-1-11122-1-100000000000−3i−3i3i3i0000000000000000-4-42-4242-42-122-1224-2-211-1-1-2-211000000000003i3i−3i−3i0000000000000000
χ9444-2-2444-2-2-21-2-21-2-24-2-2-2111-21140-2-2000000000000000-201100000000-4-422-4-4-4222-122-122-4222-1-1-12-1-1-402200000000000000020-1-100000000
χ9544-2-2444-2-2-21-2-21-2-24-2-2-2111-211-402200000000000000020-1-100000000-4-422-4-4-4222-122-122-4222-1-1-12-1-140-2-2000000000000000-201100000000
χ9644-2-24-44-2-2-21-2-21-22-422211-12-1-100−2i32i300000000000000000i3−i300000000-4-422-44-4222-122-12-24-2-2-2-1-11-211002i3−2i300000000000000000−i3i300000000
χ9744-2-24-44-2-2-21-2-21-22-422211-12-1-1002i3−2i300000000000000000−i3i300000000-4-422-44-4222-122-12-24-2-2-2-1-11-21100−2i32i300000000000000000i3−i300000000
χ984-44440-4-4-4444-4-4-4000004-400000000000000000000000000000000000-44-4-4-40444-4-4-444400000-4400000000000000000000000000000000000
χ994-444-202-4-4-24-22-4200000-220000000000000i6−i6i6−i6i6−i60000000000000000-44-4-420-2442-42-24-2000002-20000000000000−i6i6−i6i6−i6i60000000000000000
χ1004-444-202-4-4-24-22-4200000-220000000000000−i6i6−i6i6−i6i60000000000000000-44-4-420-2442-42-24-2000002-20000000000000i6−i6i6−i6i6−i60000000000000000
χ1014-44-240-42-44-2-2-42200000-22000000000000000000000−2i32i3000000000000-44-42-404-24-4224-2-2000002-20000000000000000000002i3−2i3000000000000
χ1024-44-240-42-44-2-2-42200000-220000000000000000000002i3−2i3000000000000-44-42-404-24-4224-2-2000002-2000000000000000000000−2i32i3000000000000
χ1034-4-2440-4-42-2-2422-400000-22000000000006−6006−6−660000000000000000-442-4-4044-222-4-2-24000002-200000000000−6600−666−60000000000000000
χ1044-4-2440-4-42-2-2422-400000-2200000000000−6600−666−60000000000000000-442-4-4044-222-4-2-24000002-2000000000006−6006−6−660000000000000000
χ1054-4-24-202-421-2-2-1220003i−3i1-1003i−3i00000006−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000000000-442-420-24-2-1221-2-2000−3i3i-1100−3i3i0000000−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000000000000
χ1064-4-24-202-421-2-2-1220003i−3i1-1003i−3i0000000−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000000000000-442-420-24-2-1221-2-2000−3i3i-1100−3i3i00000006−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000000000
χ1074-4-24-202-421-2-2-122000−3i3i1-100−3i3i00000006−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000000000000-442-420-24-2-1221-2-20003i−3i-11003i−3i0000000−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ130000000000000000
χ1084-4-24-202-421-2-2-122000−3i3i1-100−3i3i0000000−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ130000000000000000-442-420-24-2-1221-2-20003i−3i-11003i−3i00000006−6−i6i6ζ7−ζ23−ζ7+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
χ1128-8-4-480-844-42-44-24000002-200000000000000000000000000000000000-8844-808-4-44-24-42-400000-2200000000000000000000000000000000000
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.