Finite Group Databasebeta

← Group #13155898

Character table — Group #13155898

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363672727272108108
order122233344666666666333666666666121212121212121212123666121212121212121288242424242424242424242424242424244444121212121212121212121212121212122224466121266121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-111
χ31111111111111111111111111111111111111111111111111111111111111111111111-1-11-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-11-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1-111-1-1-1-1
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
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-111-1-111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-111-1-1-1-1-1-11111
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χ422-2-22-122-221-2-2-21-222-1-1-12111-2-2-1-1122-22-1-1-1-2111-111-11-1-2211-1-100−33−330000−33−33−33−330000−33000000−33−3300000002-2000000-1100
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χ874-4-44-24-24-42-4222-4-24-2-21-22-1-122-212-224-42-1-1-2-2111-1-11-22-2211-1-10000002i3−2i32i3−2i3−i3−i3i3i3−i3−i3i3i300000000000000000000000000000000000
χ884-4-44-24-2-442-4222-4-24-2-21-22-1-122-212-2-2-44-21122-1-11-1-112-22-2-1-1110023−2323−230000−33−33−33−3300000000000000000000000000000000000
χ894-4-44-24-2-442-4222-4-24-2-21-22-1-122-212-2-2-44-21122-1-11-1-112-22-2-1-11100−2323−232300003−33−33−33−300000000000000000000000000000000000
χ904-4-44-2-244-422-4-4224-2-21-2-2-122221-2-1-2-4-222224-2-2-21-1-111-1-2211-1-10000000000000000000000000000003i−3i−3i3i0000000000000000000
χ914-4-44-2-244-422-4-4224-2-21-2-2-122221-2-1-2-4-222224-2-2-21-1-111-1-2211-1-1000000000000000000000000000000−3i3i3i−3i0000000000000000000
χ924-4-44-2-24-4422-4-4224-2-21-2-2-122221-2-1-242-2-2-2-2-42221-1-11-112-2-1-111000000000000000000000023−23000000−33−330000000000000000000
χ934-4-44-2-24-4422-4-4224-2-21-2-2-122221-2-1-242-2-2-2-2-42221-1-11-112-2-1-1110000000000000000000000−23230000003−33−30000000000000000000
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
χ9688-8-88-4-4008-44-4-8444-8-4-42-44-4-22444-200000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ9788-8-8-4-4800-4-4-8844-8442-4-424-44-4-24-2400000000002-22-20000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-4-4-400-4-44-4444442222-22-22-2-2-2-200006i−6i006i−6i-11-110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-400-4-44-4444442222-22-22-2-2-2-20000−6i6i00−6i6i-11-1100003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ1008-88-88-4-400-84-448-444-8-4-424-442-244-4-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1018-88-8-4-4800448-8-4-4-8442-4-4-2-44-44-2424000000000022-2-20000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4-40044-44-4-4444222-22-22-2-2-22-200006i−6i00−6i6i-1-11100003i−3i−3i3i00000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-40044-44-4-4444222-22-22-2-2-22-20000−6i6i006i−6i-1-1110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000
χ1048-8-88-4-4-48-8444444-4-4-4222-2-2-2-2-222-224-444-2-2-4-422-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-4-88444444-4-4-4222-2-2-2-2-222-22-44-4-42244-2-2-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000

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