Finite Group Databasebeta

← Group #13170667

Character table — Group #13170667

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
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χ511111111111111111111111111-11111111111-1-111-1-1111-1-1-1-1-1-11-111111111111111111111111111-11111111111-1-111-1-1111-1-1-1-1-1-11-1
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χ8944-2-244-24-2-21-2-21-24-2-2-2-2111-211-400000000002200-1-100000000000-4-422-4-42-422-122-12-42222-1-1-12-1-140000000000-2-2001100000000000
χ9044-2-24-4-24-2-21-2-21-2-4222211-12-1-10000000000000003-300000000000-4-422-442-422-122-124-2-2-2-2-1-11-211000000000000000-3300000000000
χ9144-2-24-4-24-2-21-2-21-2-4222211-12-1-1000000000000000-3300000000000-4-422-442-422-122-124-2-2-2-2-1-11-2110000000000000003-300000000000
χ924-44440-4-4-4444-4-4-4000004-400000000000000000000000000000000-44-4-4-40444-4-4-444400000-4400000000000000000000000000000000
χ934-444-20-42-4-24-22-4200000-22000000000i6−i6i6−i6i6−i600000000000000000-44-4-4204-242-42-24-2000002-2000000000−i6i6−i6i6−i6i600000000000000000
χ944-444-20-42-4-24-22-4200000-22000000000−i6i6−i6i6−i6i600000000000000000-44-4-4204-242-42-24-2000002-2000000000i6−i6i6−i6i6−i600000000000000000
χ954-44-2402-4-44-2-2-42200000-2200000000000000000000000000i6−i60000-44-42-40-244-4224-2-2000002-200000000000000000000000000−i6i60000
χ964-44-2402-4-44-2-2-42200000-2200000000000000000000000000−i6i60000-44-42-40-244-4224-2-2000002-200000000000000000000000000i6−i60000
χ974-4-2440-4-42-2-2422-400000-2200000006−6006−6−6600000000000000000-442-4-4044-222-4-2-24000002-20000000−6600−666−600000000000000000
χ984-4-2440-4-42-2-2422-400000-220000000−6600−666−600000000000000000-442-4-4044-222-4-2-24000002-200000006−6006−6−6600000000000000000
χ994-4-24-20-4221-2-2-122003i−3i01-1003i−3i0006−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ2300000000000000000-442-4204-2-2-1221-2-200−3i3i0-1100−3i3i000−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ2300000000000000000
χ1004-4-24-20-4221-2-2-122003i−3i01-1003i−3i000−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ2300000000000000000-442-4204-2-2-1221-2-200−3i3i0-1100−3i3i0006−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ2300000000000000000
χ1014-4-24-20-4221-2-2-12200−3i3i01-100−3i3i0006−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ1300000000000000000-442-4204-2-2-1221-2-2003i−3i0-11003i−3i000−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300000000000000000
χ1024-4-24-20-4221-2-2-12200−3i3i01-100−3i3i000−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300000000000000000-442-4204-2-2-1221-2-2003i−3i0-11003i−3i0006−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ1300000000000000000
χ10388-4-4-48-4-4-4222222-4-422-4-1-122-1-10000000000000000000000000000-8-8444-8444-2-2-2-2-2-244-2-2411-2-2110000000000000000000000000000
χ10488-4-4-4-8-4-4-422222244-2-24-1-1-2-2110000000000000000000000000000-8-84448444-2-2-2-2-2-2-4-422-41122-1-10000000000000000000000000000
χ1058-88-4-4044-8-4-4244-2000002-200000000000000000000000000000000-88-8440-4-4844-2-4-4200000-2200000000000000000000000000000000
χ1068-8-4-4804-84-42-44-24000002-200000000000000000000000000000000-8844-80-48-44-24-42-400000-2200000000000000000000000000000000
χ1078-8-4-4-40444222-2-2-2006i−6i0-1100−3i3i0000000000000000000000000000-884440-4-4-4-2-2-222200−6i6i01-1003i−3i0000000000000000000000000000
χ1088-8-4-4-40444222-2-2-200−6i6i0-11003i−3i0000000000000000000000000000-884440-4-4-4-2-2-2222006i−6i01-100−3i3i0000000000000000000000000000

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