Finite Group Databasebeta

← Group #657166

Character table — Group #657166

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222224444444444444444444444444444444444448888888888888888888888888888888816161616
order12222222222222222222222244444444222244444444444444444444444444444444224444444444444444444444444444442444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111
χ511111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ811111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1111111111111-1-1-1-1
χ9111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-111-1
χ10111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11
χ11111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11-1-11
χ12111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-111-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111111-111-1
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111111-1-11
χ171111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-1
χ181111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1-1-11111-1-1-1-111
χ191111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ201111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1
χ211111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111-1-111
χ221111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-111-1-111-1-11111-1-1
χ231111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1111111-1-1-1-11111-1-111-1-1
χ241111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-111-1-11111-1-111-1-111-1-1-1-111
χ251111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111-1-111-1-111-1-11111-1-1-11-11
χ261111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-111-1-11111-1-11111-1-111-1-11-11-1
χ271111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-11111-1-111-1-1-1-1111-11-1
χ281111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-1-1-1111111-1-1-1-111-1-111-11-11
χ291111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-11111-1-111-1-1-1-111-1-111-1-1-1-111-1-1111-11-1
χ301111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-111-11-11
χ311111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-11111-1-111-1-1-11-11
χ321111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111-1-11111-1-11-11-1
χ3322222-2-2-2-222-2-2-2-222222-2-2-2-2000000000000000022-2-222-2-22i2i−2i−2i2i2i−2i−2i00000000000000000000002i−2i2i−2i0000000000000000000000
χ3422222-2-2-2-222-2-2-2-222222-2-2-2-2000000000000000022-2-222-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000−2i2i−2i2i0000000000000000000000
χ3522222-2-2-2-222-2-2-2-222222-2-2-2-20000000000000000-2-222-2-2222i2i−2i−2i2i2i−2i−2i0000000000000000000000−2i2i−2i2i0000000000000000000000
χ3622222-2-2-2-222-2-2-2-222222-2-2-2-20000000000000000-2-222-2-222−2i−2i2i2i−2i−2i2i2i00000000000000000000002i−2i2i−2i0000000000000000000000
χ3722222-2-2-2-222-2-2-2-22-2-2-2-22222000000000000000022-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000002i−2i−2i2i0000000000000000000000
χ3822222-2-2-2-222-2-2-2-22-2-2-2-22222000000000000000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i0000000000000000000000−2i2i2i−2i0000000000000000000000
χ3922222-2-2-2-222-2-2-2-22-2-2-2-222220000000000000000-2-22222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000−2i2i2i−2i0000000000000000000000
χ4022222-2-2-2-222-2-2-2-22-2-2-2-222220000000000000000-2-22222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000002i−2i−2i2i0000000000000000000000
χ41222-2-222-2-2-2-222-2-2222-2-222-2-22i2i2i2i−2i−2i−2i−2i00002i2i−2i−2i00000000000000000000000000000000002i−2i2i−2i00002-22-2000000000000000000
χ42222-2-222-2-2-2-222-2-2222-2-222-2-22i2i2i2i−2i−2i−2i−2i00002i2i−2i−2i0000000000000000000000000000000000−2i2i−2i2i0000-22-22000000000000000000
χ43222-2-222-2-2-2-222-2-2222-2-222-2-2−2i−2i−2i−2i2i2i2i2i0000−2i−2i2i2i00000000000000000000000000000000002i−2i2i−2i0000-22-22000000000000000000
χ44222-2-222-2-2-2-222-2-2222-2-222-2-2−2i−2i−2i−2i2i2i2i2i0000−2i−2i2i2i0000000000000000000000000000000000−2i2i−2i2i00002-22-2000000000000000000
χ45222-2-222-2-2-2-222-2-22-2-222-2-2222i2i2i2i−2i−2i−2i−2i0000−2i−2i2i2i00000000000000000000000000000000002i−2i−2i2i00002-2-22000000000000000000
χ46222-2-222-2-2-2-222-2-22-2-222-2-2222i2i2i2i−2i−2i−2i−2i0000−2i−2i2i2i0000000000000000000000000000000000−2i2i2i−2i0000-222-2000000000000000000
χ47222-2-222-2-2-2-222-2-22-2-222-2-222−2i−2i−2i−2i2i2i2i2i00002i2i−2i−2i00000000000000000000000000000000002i−2i−2i2i0000-222-2000000000000000000
χ48222-2-222-2-2-2-222-2-22-2-222-2-222−2i−2i−2i−2i2i2i2i2i00002i2i−2i−2i0000000000000000000000000000000000−2i2i2i−2i00002-2-22000000000000000000
χ4922-22-22-22-22-22-22-2-20000000022-2-222-2-222-2-2000000002i−2i2i−2i0000000022-2-200002i2i−2i−2i00000000000000000000002i−2i0000002i−2i0000
χ5022-22-22-22-22-22-22-2-20000000022-2-222-2-222-2-200000000−2i2i−2i2i0000000022-2-20000−2i−2i2i2i0000000000000000000000−2i2i000000−2i2i0000
χ5122-22-22-22-22-22-22-2-20000000022-2-222-2-2-2-222000000002i−2i2i−2i00000000-2-22200002i2i−2i−2i0000000000000000000000−2i2i000000−2i2i0000
χ5222-22-22-22-22-22-22-2-20000000022-2-222-2-2-2-22200000000−2i2i−2i2i00000000-2-2220000−2i−2i2i2i00000000000000000000002i−2i0000002i−2i0000
χ5322-22-22-22-22-22-22-2-200000000-2-222-2-22222-2-2000000002i−2i2i−2i00000000-2-2220000−2i−2i2i2i0000000000000000000000−2i2i0000002i−2i0000
χ5422-22-22-22-22-22-22-2-200000000-2-222-2-22222-2-200000000−2i2i−2i2i00000000-2-22200002i2i−2i−2i00000000000000000000002i−2i000000−2i2i0000
χ5522-22-22-22-22-22-22-2-200000000-2-222-2-222-2-222000000002i−2i2i−2i0000000022-2-20000−2i−2i2i2i00000000000000000000002i−2i000000−2i2i0000
χ5622-22-22-22-22-22-22-2-200000000-2-222-2-222-2-22200000000−2i2i−2i2i0000000022-2-200002i2i−2i−2i0000000000000000000000−2i2i0000002i−2i0000
χ572-22-222-2-222-2-222-2-2000000002-22-22-22-22-22-200002i−2i2i−2i0000000000002-22-22i2i−2i−2i0000000000000000000000002i−2i0000002i−2i000000
χ582-22-222-2-222-2-222-2-2000000002-22-22-22-22-22-20000−2i2i−2i2i0000000000002-22-2−2i−2i2i2i000000000000000000000000−2i2i000000−2i2i000000
χ592-22-222-2-222-2-222-2-2000000002-22-22-22-2-22-2200002i−2i2i−2i000000000000-22-222i2i−2i−2i000000000000000000000000−2i2i000000−2i2i000000
χ602-22-222-2-222-2-222-2-2000000002-22-22-22-2-22-220000−2i2i−2i2i000000000000-22-22−2i−2i2i2i0000000000000000000000002i−2i0000002i−2i000000
χ612-22-222-2-222-2-222-2-200000000-22-22-22-222-22-200002i−2i2i−2i000000000000-22-22−2i−2i2i2i000000000000000000000000−2i2i0000002i−2i000000
χ622-22-222-2-222-2-222-2-200000000-22-22-22-222-22-20000−2i2i−2i2i000000000000-22-222i2i−2i−2i0000000000000000000000002i−2i000000−2i2i000000
χ632-22-222-2-222-2-222-2-200000000-22-22-22-22-22-2200002i−2i2i−2i0000000000002-22-2−2i−2i2i2i0000000000000000000000002i−2i000000−2i2i000000
χ642-22-222-2-222-2-222-2-200000000-22-22-22-22-22-220000−2i2i−2i2i0000000000002-22-22i2i−2i−2i000000000000000000000000−2i2i0000002i−2i000000
χ652-2-2222222-2-2-2-2-2-222-22-22-22-22i−2i−2i2i−2i2i2i−2i00002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i000000000000002-22-2000000000000000000000000000000
χ662-2-2222222-2-2-2-2-2-222-22-22-22-22i−2i−2i2i−2i2i2i−2i00002i−2i2i−2i00000000−2i2i−2i2i−2i2i−2i2i00000000000000-22-22000000000000000000000000000000
χ672-2-2222222-2-2-2-2-2-222-22-22-22-2−2i2i2i−2i2i−2i−2i2i0000−2i2i−2i2i000000002i−2i2i−2i2i−2i2i−2i00000000000000-22-22000000000000000000000000000000
χ682-2-2222222-2-2-2-2-2-222-22-22-22-2−2i2i2i−2i2i−2i−2i2i0000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i000000000000002-22-2000000000000000000000000000000
χ692-2-2222222-2-2-2-2-2-22-22-22-22-222i−2i−2i2i−2i2i2i−2i0000−2i2i−2i2i000000002i−2i2i−2i−2i2i−2i2i000000000000002-2-22000000000000000000000000000000
χ702-2-2222222-2-2-2-2-2-22-22-22-22-222i−2i−2i2i−2i2i2i−2i0000−2i2i−2i2i00000000−2i2i−2i2i2i−2i2i−2i00000000000000-222-2000000000000000000000000000000
χ712-2-2222222-2-2-2-2-2-22-22-22-22-22−2i2i2i−2i2i−2i−2i2i00002i−2i2i−2i000000002i−2i2i−2i−2i2i−2i2i00000000000000-222-2000000000000000000000000000000
χ722-2-2222222-2-2-2-2-2-22-22-22-22-22−2i2i2i−2i2i−2i−2i2i00002i−2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i000000000000002-2-22000000000000000000000000000000
χ732-2-222-2-2-2-2-2-2222222-22-2-22-220000000000000000000000002-2-222-2-2200002-22-22-22-20000000000000000000000002-22-200000000
χ742-2-222-2-2-2-2-2-2222222-22-2-22-220000000000000000000000002-2-222-2-220000-22-22-22-22000000000000000000000000-22-2200000000
χ752-2-222-2-2-2-2-2-2222222-22-2-22-22000000000000000000000000-222-2-222-200002-22-22-22-2000000000000000000000000-22-2200000000
χ762-2-222-2-2-2-2-2-2222222-22-2-22-22000000000000000000000000-222-2-222-20000-22-22-22-220000000000000000000000002-22-200000000
χ772-2-222-2-2-2-2-2-222222-22-222-22-20000000000000000000000002-2-22-222-200002-22-2-22-220000000000000000000000002-2-2200000000
χ782-2-222-2-2-2-2-2-222222-22-222-22-20000000000000000000000002-2-22-222-20000-22-222-22-2000000000000000000000000-222-200000000
χ792-2-222-2-2-2-2-2-222222-22-222-22-2000000000000000000000000-222-22-2-2200002-22-2-22-22000000000000000000000000-222-200000000
χ802-2-222-2-2-2-2-2-222222-22-222-22-2000000000000000000000000-222-22-2-220000-22-222-22-20000000000000000000000002-2-2200000000
χ812-2-2-2-222-2-222-2-22222-2-222-2-222-2-222-2-222-2-222-2-2200000000000000002-2-22000000002-200000000000000002-20000000000000000
χ822-2-2-2-222-2-222-2-22222-2-222-2-222-2-222-2-22-222-22-2-220000000000000000-222-200000000-220000000000000000-220000000000000000
χ832-2-2-2-222-2-222-2-22222-2-222-2-22-222-2-222-22-2-22-222-20000000000000000-222-2000000002-20000000000000000-220000000000000000
χ842-2-2-2-222-2-222-2-22222-2-222-2-22-222-2-222-2-222-2-222-200000000000000002-2-2200000000-2200000000000000002-20000000000000000
χ852-2-2-2-222-2-222-2-2222-222-2-222-22-2-222-2-222-2-22-222-200000000000000002-2-2200000000-220000000000000000-220000000000000000
χ862-2-2-2-222-2-222-2-2222-222-2-222-22-2-222-2-22-222-2-222-20000000000000000-222-2000000002-200000000000000002-20000000000000000
χ872-2-2-2-222-2-222-2-2222-222-2-222-2-222-2-222-22-2-222-2-220000000000000000-222-200000000-2200000000000000002-20000000000000000
χ882-2-2-2-222-2-222-2-2222-222-2-222-2-222-2-222-2-222-22-2-2200000000000000002-2-22000000002-20000000000000000-220000000000000000
χ89444-4-4-4-444-4-4-4-444444-4-4-4-44400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ90444-4-4-4-444-4-4-4-4444-4-44444-4-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9144-44-4-44-444-4-44-44-400000000000000000000000000004i−4i−4i4i00000000000000000000000000000000000000000000000000000000
χ9244-44-4-44-444-4-44-44-40000000000000000000000000000−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ9344-4-444-4-44-444-4-44-4000000004i4i−4i−4i−4i−4i4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ9444-4-444-4-44-444-4-44-400000000−4i−4i4i4i4i4i−4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ9544-4-44-444-4-44-444-4-4000000000000000000000000000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ9644-4-44-444-4-44-444-4-400000000000000000000000000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ974-444-44-44-4-44-44-44-4000000004i−4i4i−4i−4i4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000
χ984-444-44-44-4-44-44-44-400000000−4i4i−4i4i4i−4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000
χ994-444-4-44-44-444-44-4-40000000000000000000000000000000000000000000000004i−4i−4i4i000000000000000000000000000000000000
χ1004-444-4-44-44-444-44-4-4000000000000000000000000000000000000000000000000−4i4i4i−4i000000000000000000000000000000000000
χ1014-44-44-444-44-44-4-44-40000000000000000000000004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000
χ1024-44-44-444-44-44-4-44-4000000000000000000000000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-4-4-4-4444444-4-444-4-44-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-4-4-4-4444444-4-44-444-44-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000

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