Finite Group Databasebeta

← Group #197855

Character table — Group #197855

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222244444444444444444444444444444444444444444444444444444488888888161616161616161616161616
order12222222444444444444444422222222224444444444448888888888888888888888888888888888888888444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ1111111111-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-111-1-1
χ1311111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-11111-1-1
χ1511111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
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χ291-1-11-1-111-1-11111-1-11111-1-1-1-1-11-1-11111-1-11-1-11-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii−iii−i1-1-11-111-1
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χ782-2-22-2-22222-2-222-2-222-2-222-2-2-2200000000-222-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ792-2-22-2-22222-2-2-2-222-2-222-2-222-2222-2-2-2-222-22-22-2-22222-2-20000000000000000000000000000000000000000000000000000
χ802-2-22-2-22222-2-2-2-222-2-222-2-222-22-2-22222-2-2-22-2222-2-2-2-2220000000000000000000000000000000000000000000000000000
χ812-2-22-2-22222-2-2-2-2-2-222-2-222222-2000000002-2-220000000022-2-2-2-22222-2-2-2-222000000000000000000000000000000000000
χ822-2-22-2-22222-2-2-2-2-2-222-2-222222-2000000002-2-2200000000-2-22222-2-2-2-22222-2-2000000000000000000000000000000000000
χ832-2-22-2-222-2-2222222-2-2-2-222-2-22-200000000-22-220000000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ842-2-22-2-222-2-2222222-2-2-2-222-2-22-200000000-22-22000000000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i00000000000000000000
χ852-2-22-2-222-2-222-2-222-2-2-2-22222-22000000002-22-20000000022-2-2-2-222-2-22222-2-2000000000000000000000000000000000000
χ862-2-22-2-222-2-222-2-222-2-2-2-22222-22000000002-22-200000000-2-22222-2-222-2-2-2-222000000000000000000000000000000000000
χ872-2-22-2-222-2-222-2-2-2-22222-2-2222-222-2-222-2-2-222-2-2-222-2-2220000000000000000000000000000000000000000000000000000
χ882-2-22-2-222-2-222-2-2-2-22222-2-2222-2-2-222-2-222-222-222-2-222-2-20000000000000000000000000000000000000000000000000000
χ89444-4-4-4-4400004-4000000004-40000000000000000000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ90444-4-4-4-4400004-4000000004-4000000000000000000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ91444-4-4-4-440000-4400000000-4400000000000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ92444-4-4-4-440000-4400000000-440000000000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ934-4-4-444-4400004-400000000-4400000000000000000000000000000000000000000000000000000022−22−22220000000000000000
χ944-4-4-444-4400004-400000000-44000000000000000000000000000000000000000000000000000000−222222−220000000000000000
χ954-4-4-444-440000-44000000004-4000000000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ964-4-4-444-440000-44000000004-40000000000000000000000000000000000000000000000000000000000−222222−22000000000000
χ9788-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-8888-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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