Finite Group Databasebeta

← Group #196734

Character table — Group #196734

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12222222444444444444444422222244444444444444448888888888888888888888888888888888888888224444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ611111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ711111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-11111-1-1-1-1-1-1
χ811111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111
χ9111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1-111-1-11-1ii−i−i
χ10111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-11-1-111-11−i−iii
χ11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-11-1-111-11ii−i−i
χ12111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1-111-1-11-1−i−iii
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i1-1-1-1111-1−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii-1111-1-1-11ii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i-1111-1-1-11−i−iii
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii1-1-1-1111-1ii−i−i
χ1711111111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1111-11-1-1-11-11-1
χ1811111111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-11-1111-11-11
χ1911111111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-11-11111-11-1
χ2011111111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-111-1-111111-11-1-1-1-11-11
χ2111111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-11-11-1-1-11-11
χ2211111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-11-11-1111-11-1
χ2311111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11-11-111-11-11
χ2411111111-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-11111-11-11-1-11-11-1
χ2511111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-11-1-11-11i−i−ii
χ2611111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-11-111-11-1−iii−i
χ2711111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-11-111-11-1i−i−ii
χ2811111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-11-1-11-11−iii−i
χ2911111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii1-1-111-1-11−iii−i
χ3011111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-111-1-111-1i−i−ii
χ3111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-111-1-111-1−iii−i
χ3211111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i1-1-111-1-11i−i−ii
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χ782-2-22-2-2222-2-22-2-22-2-2222-2-222-220000-2200000000-220000-222-2-222-2-222-2-222-2000000000000000000000000000000000000
χ792-2-22-2-2222-2-22-2-2-222-22-222-22-2200002-2000000002-2000000000000000000002-2-22-222-2-222-22-2-2200000000000000000000
χ802-2-22-2-2222-2-22-2-2-222-22-222-22-2200002-2000000002-200000000000000000000-222-22-2-222-2-22-222-200000000000000000000
χ812-2-22-2-222-222-2222-2-22-2-222-2-2-2200002-200000000-2200002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000
χ822-2-22-2-222-222-2222-2-22-2-222-2-2-2200002-200000000-220000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000
χ832-2-22-2-222-222-222-222-2-22-2-22-2-220000-22000000002-2000000000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i00000000000000000000
χ842-2-22-2-222-222-222-222-2-22-2-22-2-220000-22000000002-200000000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ852-2-22-2-222-222-2-2-22-2-222-222-222-20000-22000000002-2000000000000000000002-2-222-2-22-222-2-222-200000000000000000000
χ862-2-22-2-222-222-2-2-22-2-222-222-222-20000-22000000002-200000000000000000000-222-2-222-22-2-222-2-2200000000000000000000
χ872-2-22-2-222-222-2-2-2-222-222-2-2222-200002-200000000-2200002-2-222-2-22-222-2-222-2000000000000000000000000000000000000
χ882-2-22-2-222-222-2-2-2-222-222-2-2222-200002-200000000-220000-222-2-222-22-2-222-2-22000000000000000000000000000000000000
χ89444-4-4-44-400004-4000040000-400000000000000000000000000000000000000000000000000000022−220022−2200000000000000
χ90444-4-4-44-400004-4000040000-4000000000000000000000000000000000000000000000000000000−222200−222200000000000000
χ91444-4-4-44-40000-440000-4000040000000000000000000000000000000000000000000000000000002i2−2i200−2i22i200000000000000
χ92444-4-4-44-40000-440000-400004000000000000000000000000000000000000000000000000000000−2i22i2002i2−2i200000000000000
χ934-4-4-4444-400004-40000-4000040000000000000000000000000000000000000000000000000000000022−220022−22000000000000
χ944-4-4-4444-400004-40000-40000400000000000000000000000000000000000000000000000000000000−222200−2222000000000000
χ954-4-4-4444-40000-44000040000-4000000000000000000000000000000000000000000000000000000002i2−2i200−2i22i2000000000000
χ964-4-4-4444-40000-44000040000-400000000000000000000000000000000000000000000000000000000−2i22i2002i2−2i2000000000000
χ9788-8-8-88-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-88-88-8-88000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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