Finite Group Databasebeta

← Group #13156328

Character table — Group #13156328

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222222222444444444444444444444488888888888812121212121212121212121212121212121212122424242424242424242424242424242424363636363636363654547272727272108
order1222333446666666663336666666661212121212121212121236661212121212121212448824242424242424242424242424242424412121212121212121212121212121212448824242424444121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1
χ3111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-111-111-1-11
χ51111111111111111111111111111111111111111111111111111-1-1111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1
χ61111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111-1
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χ894-4-444-2-200-422-42-242-2-2-2122-1122-1-2-20003i−3i00−3i3i01-11-100003i−3i−3i3i0000−i6i6i6−i6−666−6ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000000
χ904-4-444-2-200-422-42-242-2-2-2122-1122-1-2-2000−3i3i003i−3i01-11-10000−3i3i3i−3i0000i6−i6−i6i6−666−6−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000000
χ914-4-444-2-200-422-42-242-2-2-2122-1122-1-2-2000−3i3i003i−3i01-11-10000−3i3i3i−3i0000−i6i6i6−i66−6−66ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000000
χ924-4-44-244002-4-42-44-2-44-2-2422-4422-4-2-20000000000-22-220000000000000000000000000000000000000000000000000i6−i6−i6i600000000
χ934-4-44-244002-4-42-44-2-44-2-2422-4422-4-2-20000000000-22-220000000000000000000000000000000000000000000000000−i6i6i6−i600000000
χ948888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-422-4-422-4-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000
χ958888-4-4-4-8-8-4-4-4-4-4-4-4-4-4222222222222444-2-244-2-24-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-48-8444-4-444-44222-2-2-2-2222-2-2-4-4-42244-2-24-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4-4-88444-4-444-44222-2-2-2-2222-2-2444-2-2-4-422-4-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000
χ988-88-8-48-400-48-44-8444-8-42-4-42-444-244-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4800-4-4844-84-842-4-42-4-44-244-24000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-400-4-4-4444444222222-2-2-2-2-2-20006i−6i006i−6i0-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4-400-4-4-4444444222222-2-2-2-2-2-2000−6i6i00−6i6i0-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ1028-8-88-48-4004-844-8-4-448-42-44-24-44-24-4200000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1038-8-88-4-480044-8448-4-8-42-4-4-244-4-2442-400000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-40044444-4-44-4222-2-2-22-2-2-2220006i−6i00−6i6i0-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-40044444-4-44-4222-2-2-22-2-2-222000−6i6i006i−6i0-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000

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