Finite Group Databasebeta

← Group #197857

Character table — Group #197857

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12222222222244444444444444444444444444444444448888888888888888888888888888888888888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
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
χ911111111-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ1111111111-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111-1-111
χ1211111111-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-111-1-1
χ1311111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-111
χ1411111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-11111-1-1
χ1511111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ1611111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
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χ181-1-1-111-1111-1-1111-111-1-1-1-11-11-11-11-111-1-111-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-11−ii−ii-11-11-11
χ191-1-1-111-1111-1-1111-111-1-1-1-11-11-11-11-111-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-11i−ii−i-11-11-11
χ201-1-1-111-1111-1-1111-111-1-1-1-11-11-11-11-111-1-111-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-1−ii−ii1-11-11-1
χ211-1-1-111-1111-1-1111-111-1-1-1-11-11-11-11-1-1-111-1-111-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i1-1−ii−ii1-1-11-11
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χ231-1-1-111-1111-1-1111-111-1-1-1-11-11-11-11-1-1-111-1-111-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i-11−ii−ii-111-11-1
χ241-1-1-111-1111-1-1111-111-1-1-1-11-11-11-11-1-1-111-1-111-1-111-1-111−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii1-1i−ii−i1-1-11-11
χ251-1-1-111-11-1-111111-1-1-111-1-11-1-111-1-1111-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1i−i−ii-111-1-11
χ261-1-1-111-11-1-111111-1-1-111-1-11-1-111-1-1111-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-11−iii−i1-1-111-1
χ271-1-1-111-11-1-111111-1-1-111-1-11-1-111-1-1111-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-11i−i−ii1-1-111-1
χ281-1-1-111-11-1-111111-1-1-111-1-11-1-111-1-1111-1-1-1-11111-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1−iii−i-111-1-11
χ291-1-1-111-11-1-111111-1-1-111-1-11-1-111-1-11-1-11111-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii1-1−iii−i-11-111-1
χ301-1-1-111-11-1-111111-1-1-111-1-11-1-111-1-11-1-11111-1-1-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-11i−i−ii1-11-1-11
χ311-1-1-111-11-1-111111-1-1-111-1-11-1-111-1-11-1-11111-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-11−iii−i1-11-1-11
χ321-1-1-111-11-1-111111-1-1-111-1-11-1-111-1-11-1-11111-1-1-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i1-1i−i−ii-11-111-1
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χ852-2-2-222-22-2-222-2-22-2-2-222222-22-2-222-222-2-2-2-222-2-22222-2-20000000000000000000000000000000000000000000000000000
χ862-2-2-222-22-2-222-2-22-2-2-222222-22-2-222-2-2-22222-2-222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ872-2-2-222-22-2-222-2-2-2222-2-222-222-22-2-22000000000000000022-2-2-2-222-2-22222-2-2000000000000000000000000000000000000
χ882-2-2-222-22-2-222-2-2-2222-2-222-222-22-2-220000000000000000-2-22222-2-222-2-2-2-222000000000000000000000000000000000000
χ8944-444-4-4-400004-40000004-40000000000000000000000000000000000000000000000000000000022−2222−220000000000000000
χ9044-444-4-4-400004-40000004-400000000000000000000000000000000000000000000000000000000−2222−22220000000000000000
χ9144-444-4-4-40000-44000000-4400000000000000000000000000000000000000000000000000000000000022−2222−22000000000000
χ9244-444-4-4-40000-44000000-44000000000000000000000000000000000000000000000000000000000000−2222−2222000000000000
χ934-44-44-44-400004-4000000-44000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ944-44-44-44-400004-4000000-4400000000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ954-44-44-44-40000-440000004-40000000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ964-44-44-44-40000-440000004-4000000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ9788-8-8-888-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-888-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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