Finite Group Databasebeta

← Group #686196

Character table — Group #686196

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222222222224444444444444444222244444444444444444444444444444444444444444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111
χ5111111111111111111111111111111111111-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1
χ9111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-11-1
χ10111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-11-11
χ11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-11-11
χ12111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-11-11-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-11-11
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111-11-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111-11-1
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-11-11
χ171111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-1-1-11-1-11
χ181111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-111-1-111-1-111-1-111-1-1-111-1
χ191111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-111-1-1-1-111-1-111-1-1-111-1
χ201111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-111-1-111-1-11111-1-111-1-1-1-11-1-11
χ211111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-11111-1-111-1-111-111-1
χ221111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111111-1-111-1-111-1-1-1-111-1-111111-1-11
χ231111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-111111-1-11
χ241111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-11111-1-111-1-111-1-111-1-111-111-1
χ251111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ261111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-111
χ271111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-111-1-1-1-111-1-11111-1-111-1-111
χ281111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1111111-1-1
χ291111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-11111-1-111-1-1-1-111-1-1-1-111
χ301111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1
χ311111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ321111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111
χ3322222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222-2-2000000000000000000000000000000002-22-22-22-20000000000000000000000000000
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χ6122-222-2-2-22-222-2-22-200000000−2i2i−2i2i−2i2i−2i2i00002-22-200000000−2i2i−2i2i00002i2i−2i−2i0000-2-22200000000000000002i−2i00-2200000000000000
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χ6422-222-2-2-22-222-2-22-200000000−2i2i−2i2i−2i2i−2i2i0000-22-22000000002i−2i2i−2i0000−2i−2i2i2i000022-2-200000000000000002i−2i00-2200000000000000
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χ9144-4-4-444-44-4-4-4444-4000000004i−4i−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ9244-4-4-444-44-4-4-4444-400000000−4i4i4i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ934-444-44-4-4-44-44-444-44i−4i4i−4i−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ944-444-44-4-4-44-44-444-4−4i4i−4i4i4i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ954-44-44-44-4-444-44-44-44i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ964-44-44-44-4-444-44-44-4−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ974-4-44-4-444444-4-44-4-400000000000000000000000000000000000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ984-4-44-4-444444-4-44-4-40000000000000000000000000000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ994-4-44-4-444-4-4-444-444000000000000000000000000000000000000000000004-4-440000000000000000000000000000000000000000
χ1004-4-44-4-444-4-4-444-44400000000000000000000000000000000000000000000-444-40000000000000000000000000000000000000000
χ1014-4-4-444-4444-444-4-4-40000000000000000000000000000000000000000000000004i−4i−4i4i000000000000000000000000000000000000
χ1024-4-4-444-4444-444-4-4-4000000000000000000000000000000000000000000000000−4i4i4i−4i000000000000000000000000000000000000
χ1034-4-4-444-44-4-44-4-44440000000000000000000000000000000000004-4-44000000000000000000000000000000000000000000000000
χ1044-4-4-444-44-4-44-4-4444000000000000000000000000000000000000-444-4000000000000000000000000000000000000000000000000

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