Finite Group Databasebeta

← Group #13156411

Character table — Group #13156411

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
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χ31111111111111111111111111111111111111111111111111111111111111111111111-1-11-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-11-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-1-1-111-1-1
χ51111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
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χ904-4-44-2-240024222-4-4-2-21-2-2-11-22-2-122200003i−3i00−3i3i1-11-10000−3i3i3i−3i006−6−66i6−i6−i6i6−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ1300000000000000000000000000000000000
χ914-4-44-2-240024222-4-4-2-21-2-2-11-22-2-122200003i−3i00−3i3i1-11-10000−3i3i3i−3i00−666−6−i6i6i6−i6ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ1300000000000000000000000000000000000
χ924-4-44-2-240024222-4-4-2-21-2-2-11-22-2-12220000−3i3i003i−3i1-11-100003i−3i−3i3i006−6−66−i6i6i6−i6ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ2300000000000000000000000000000000000
χ934-4-44-2-240024222-4-4-2-21-2-2-11-22-2-12220000−3i3i003i−3i1-11-100003i−3i−3i3i00−666−6i6−i6−i6i6−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ2300000000000000000000000000000000000
χ948888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-422-4-422-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000
χ958888-4-4-4-8-8-4-4-4-4-4-4-4-4-42222222222224444-2-244-2-2-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ9688-8-88-4-400-44-848-44-84-4-42-4442-244-2-4000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ9788-8-8-48-400844-8-4-444-8-42-4-44-2-444-242000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-400-4444-4-44442222-2-22-2-2-2-2200006i−6i006i−6i-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-400-4444-4-44442222-2-22-2-2-2-220000−6i6i00−6i6i-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-48-844-4-444-444222-2-2-2-2-2222-244-44-2-2-4-422-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4-4-8844-4-444-444222-2-2-2-2-2222-2-4-44-42244-2-2-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000
χ1028-8-888-4-4004-4-84-8448-4-4-424-4-4-2244-2400000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-48-400-8-44-8444-48-42-44-424-44-24-200000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-4004-444444-4-4222-222-22-2-2-2-200006i−6i00−6i6i-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-4004-444444-4-4222-222-22-2-2-2-20000−6i6i006i−6i-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000

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