Finite Group Databasebeta

← Group #13170604

Character table — Group #13170604

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
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order1233346663336661212121212883612121212442424242424242424881212121212121212224424244121222666466666666612121212128866121212124424242424242424248812121212121212122244242441212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
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χ31111111111111111111111111111-1111111111-1-1-11-11-1-111-1-1-11-1-1-1-111111111111111111111111111111-1111111111-1-1-11-11-1-111-1-1-11-1-1-1-11
χ41111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-111-1-1111-1-11111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-111-1-1111-1-1
χ511111111111111111111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-111111111111111111111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1
χ611111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-11-1-11-1111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-11-1-11-11
χ711111111111111111111-1-1111111-11-1-1-1-1-1-1-1-1-1-1-11-11-1-111111-1-1-111-111111111111111111111-1-1111111-11-1-1-1-1-1-1-1-1-1-1-11-11-1-111111-1-1-111-1
χ811111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-111
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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
χ5911111111111111111111111111111-111111111-1-11-11-111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-11-11-1-11111-11111-11
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χ86444-2-244-2-2-2-211-2-2-2-21144411-2-21100-2-2-2-211110000000000000000000-4-4-422-4-42222-1-12222-1-1-4-4-4-1-122-1-1002222-1-1-1-10000000000000000000
χ87444-2-244-2-2-2-211-2-2-2-2114-4-411-2-211002222-1-1-1-10000000000000000000-4-4-422-4-42222-1-12222-1-1-444-1-122-1-100-2-2-2-211110000000000000000000
χ88444-2-2-44-2-2-2-211-2-222-1-1-4001122-1-10000003i−3i3i−3i0000000000000000000-4-4-4224-42222-1-122-2-211400-1-1-2-211000000−3i3i−3i3i0000000000000000000
χ89444-2-2-44-2-2-2-211-2-222-1-1-4001122-1-1000000−3i3i−3i3i0000000000000000000-4-4-4224-42222-1-122-2-211400-1-1-2-2110000003i−3i3i−3i0000000000000000000
χ9044-244-4-244-2-244-2-2-4-4-4-4200-2-2222200000000000000000000000000000-4-42-4-442-4-422-4-4224444-20022-2-2-2-200000000000000000000000000000
χ9144-24-24-24-2-21-2-2-214-2-2-2-20011-21110400000000000-20-20011000000000-4-42-42-42-422-1222-1-4222200-1-12-1-1-10-40000000000020200-1-1000000000
χ9244-24-24-24-2-21-2-2-214-2-2-2-20011-21110-40000000000020200-1-1000000000-4-42-42-42-422-1222-1-4222200-1-12-1-1-10400000000000-20-20011000000000
χ9344-24-2-4-24-2-21-2-2-21-4222200112-1-1-10000000000000000003-3000000000-4-42-4242-422-1222-14-2-2-2-200-1-1-2111000000000000000000-33000000000
χ9444-24-2-4-24-2-21-2-2-21-4222200112-1-1-1000000000000000000-33000000000-4-42-4242-422-1222-14-2-2-2-200-1-1-21110000000000000000003-3000000000
χ9544-2-244-2-241-2-2-21-2-24-2-2-200111-211400000000000-20-201100000000000-4-422-4-422-4-1222-122-422200-1-1-12-1-1-4000000000002020-1-100000000000
χ9644-2-244-2-241-2-2-21-2-24-2-2-200111-211-4000000000002020-1-100000000000-4-422-4-422-4-1222-122-422200-1-1-12-1-1400000000000-20-201100000000000
χ9744-2-24-4-2-241-2-2-21-22-42220011-12-1-100000000000000003-300000000000-4-422-4422-4-1222-12-24-2-2-200-1-11-2110000000000000000-3300000000000
χ9844-2-24-4-2-241-2-2-21-22-42220011-12-1-10000000000000000-3300000000000-4-422-4422-4-1222-12-24-2-2-200-1-11-21100000000000000003-300000000000
χ994-444-20-4-424-2-22-420000022−22-2200000022−22−22−2−2220000000000000000000-44-4-42044-2-422-24-200000−22222-2000000−22222−222−2−20000000000000000000
χ1004-444-20-4-424-2-22-4200000−2222-22000000−22222−222−2−20000000000000000000-44-4-42044-2-422-24-20000022−222-200000022−22−22−2−2220000000000000000000
χ1014-44-240-42-4-24-222-40000022−22-22000000−2222−22−2−2220000000000000000000-44-42-404-242-42-2-2400000−22222-20000002−2−222222−2−20000000000000000000
χ1024-44-240-42-4-24-222-400000−2222-220000002−2−222222−2−20000000000000000000-44-42-404-242-42-2-240000022−222-2000000−2222−22−2−2220000000000000000000
χ1034-44-2-20-422-2-21-122003i−3i022−221-1003i−3i00−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ30000000000000000000-44-42204-2-222-11-2-200−3i3i0−2222-1100−3i3i002−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ30000000000000000000
χ1044-44-2-20-422-2-21-122003i−3i0−22221-1003i−3i002−22−2−2ζ−ζ3ζ+2ζ32ζ+ζ3−ζ−2ζ30000000000000000000-44-42204-2-222-11-2-200−3i3i022−22-1100−3i3i00−22−222ζ+ζ3−ζ−2ζ3−2ζ−ζ3ζ+2ζ30000000000000000000
χ1054-44-2-20-422-2-21-12200−3i3i022−221-100−3i3i00−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ30000000000000000000-44-42204-2-222-11-2-2003i−3i0−2222-11003i−3i002−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ30000000000000000000
χ1064-44-2-20-422-2-21-12200−3i3i0−22221-100−3i3i002−22−2ζ+2ζ3−2ζ−ζ3−ζ−2ζ32ζ+ζ30000000000000000000-44-42204-2-222-11-2-2003i−3i022−22-11003i−3i00−22−22−ζ−2ζ32ζ+ζ3ζ+2ζ3−2ζ−ζ30000000000000000000
χ1074-4-24402-4-4-2-24-4220000000-220000000000000022−22000000000000−22000-442-4-40-24422-44-2-200000002-200000000000000−22220000000000002−2000
χ1084-4-24402-4-4-2-24-4220000000-2200000000000000−22220000000000002−2000-442-4-40-24422-44-2-200000002-20000000000000022−22000000000000−22000
χ10988-4-4-48-4-4-4222222-4-422-400-1-122-1-100000000000000000000000000000-8-8444-8444-2-2-2-2-2-244-2-240011-2-21100000000000000000000000000000
χ11088-4-4-4-8-4-4-422222244-2-2400-1-1-2-21100000000000000000000000000000-8-84448444-2-2-2-2-2-2-4-422-4001122-1-100000000000000000000000000000
χ1118-8-48-404-84-42-444-200000002-2000000000000000000000000000000000-884-840-48-44-24-4-420000000-22000000000000000000000000000000000
χ1128-8-4-48044-82-4-44-2400000002-2000000000000000000000000000000000-8844-80-4-48-244-42-40000000-22000000000000000000000000000000000
χ1138-8-4-4-40444222-2-2-2006i−6i000-1100−3i3i00000000000000000000000000000-884440-4-4-4-2-2-222200−6i6i0001-1003i−3i00000000000000000000000000000
χ1148-8-4-4-40444222-2-2-200−6i6i000-11003i−3i00000000000000000000000000000-884440-4-4-4-2-2-2222006i−6i0001-100−3i3i00000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.