Finite Group Databasebeta

← Group #197939

Character table — Group #197939

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12222222444444444444444422444444444444444444448888888888888888888888888888888888888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-1-1-1-1-1111111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ101111111111-1-1-1-1-1-1-1-1111111-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ111111111111-1-1-1-1-1-1-1-1111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-111
χ121111111111-1-1-1-1-1-1-1-1111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-11111-1-1
χ131111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111-1-111
χ141111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-111-1-1
χ151111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ161111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
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χ181-1-1-1-1111111111-1-1-1-111-1-1-1-11-11-11-11111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i-1-111-1-111-11−ii−ii-11−ii−ii
χ191-1-1-1-1111111111-1-1-1-111-1-1-1-11-11-11-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-11-1−ii−ii1-1−ii−ii
χ201-1-1-1-1111111111-1-1-1-111-1-1-1-11-11-11-11111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111-11i−ii−i-11i−ii−i
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χ241-1-1-1-1111111111-1-1-1-111-1-1-1-11-11-11-1-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-1111-1i−ii−i1-1−ii−ii
χ251-1-1-1-111111-1-1-1-1111111-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-1-1111-1i−i−ii-11i−i−ii
χ261-1-1-1-111111-1-1-1-1111111-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1-11−iii−i1-1−iii−i
χ271-1-1-1-111111-1-1-1-1111111-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-1111-1−iii−i-11−iii−i
χ281-1-1-1-111111-1-1-1-1111111-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1-11i−i−ii1-1i−i−ii
χ291-1-1-1-111111-1-1-1-1111111-1-1-1-1-111-1-11-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111-11i−i−ii1-1−iii−i
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χ782-2-2-2-22222222-2-2-2-222-2-222-2-22-2-22-2200000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ792-2-2-2-222222-2-22222-2-2-2-222-2-2-22-222-2000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ802-2-2-2-222222-2-22222-2-2-2-222-2-2-22-222-200000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000
χ812-2-2-2-2222-2-22222-2-2-2-222-2-222-22-22-2222-2-2-2-22222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ822-2-2-2-2222-2-22222-2-2-2-222-2-222-22-22-22-2-22222-2-2-2-22222-2-20000000000000000000000000000000000000000000000000000
χ832-2-2-2-2222-2-222-2-2-2-222-2-22222-222-22-2000000000000000022-2-2-2-22222-2-2-2-222000000000000000000000000000000000000
χ842-2-2-2-2222-2-222-2-2-2-222-2-22222-222-22-20000000000000000-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000
χ852-2-2-2-2222-2-2-2-22222-2-2-2-222222-22-2-22000000000000000022-2-2-2-222-2-22222-2-2000000000000000000000000000000000000
χ862-2-2-2-2222-2-2-2-22222-2-2-2-222222-22-2-220000000000000000-2-22222-2-222-2-2-2-222000000000000000000000000000000000000
χ872-2-2-2-2222-2-2-2-2-2-2222222-2-2222-2-222-222-2-2-2-222-2-22222-2-20000000000000000000000000000000000000000000000000000
χ882-2-2-2-2222-2-2-2-2-2-2222222-2-2222-2-222-2-2-22222-2-222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ8944-4-44-44-44-40000000000004-40000000000000000000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ9044-4-44-44-44-40000000000004-4000000000000000000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ9144-4-44-44-4-44000000000000-4400000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ9244-4-44-44-4-44000000000000-440000000000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ934-444-4-44-44-4000000000000-440000000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ944-444-4-44-44-4000000000000-44000000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ954-444-4-44-4-440000000000004-400000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ964-444-4-44-4-440000000000004-40000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ97888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).