Finite Group Databasebeta

← Group #412205

Character table — Group #412205

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222222222222244444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222222224444444488888888888888884444444444444444444444448888888888888888888888884444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ9111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-111
χ12111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-11111-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-111-1-111
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-111-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
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χ822-2-2-2-222222-2-2-2-222-22222-2-2-20000000000000000000000002-2-22-222-200000000−2i2i2i−2i−2i2i2i−2i000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ832-2-2-2-222222-2-2-2-222-22222-2-2-2000000000000000000000000-222-22-2-22000000002i−2i−2i2i2i−2i−2i2i000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ842-2-2-2-222222-2-2-2-222-22222-2-2-2000000000000000000000000-222-22-2-2200000000−2i2i2i−2i−2i2i2i−2i00000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ852-2-2-2-2-2-22222222-2-22-2-222-2-22000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i-222-22-2-22000000000000000000000000
χ862-2-2-2-2-2-22222222-2-22-2-222-2-22000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2-2-22-222-2000000000000000000000000
χ872-2-2-2-2-2-22222222-2-22-2-222-2-2200000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i2-2-22-222-2000000000000000000000000
χ882-2-2-2-2-2-22222222-2-22-2-222-2-2200000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i-222-22-2-22000000000000000000000000
χ892-2-2-2-2-2-22222222-2-2-222-2-222-22-2-222-2-22-222-2-222-200000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ902-2-2-2-2-2-22222222-2-2-222-2-222-22-2-222-2-22-222-2-222-20000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ912-2-2-2-2-2-22222222-2-2-222-2-222-2-222-2-222-22-2-222-2-2200000000000000002i−2i−2i2i2i−2i−2i2i00000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ922-2-2-2-2-2-22222222-2-2-222-2-222-2-222-2-222-22-2-222-2-220000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ93444-4-4444-4-444-4-4-4-4-4-44-44-44400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ94444-4-4-4-44-4-4-4-4444444-4-44-44-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9544-4-444-4-4-444-4-44-44000000002i22i2−2i2−2i2−2i2−2i22i22i22i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000000000000000000000000000000000
χ9644-4-444-4-4-444-4-44-4400000000−2i2−2i22i22i22i22i2−2i2−2i2−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000000000000000000000000000000000
χ9744-4-44-44-4-44-444-44-4000000002i22i2−2i2−2i2−2i2−2i22i22i2−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000000000000000000000000000000000
χ9844-4-44-44-4-44-444-44-400000000−2i2−2i22i22i22i22i2−2i2−2i22i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000000000000000000000000000000000
χ994-444-44-4-4-44-444-4-44000000002i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000000000000000000000000000
χ1004-444-44-4-4-44-444-4-4400000000−2i22i2−2i22i22i2−2i22i2−2i2−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000000000000000000000000000
χ1014-444-4-44-4-444-4-444-4000000002i2−2i22i2−2i2−2i22i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000000000000000000000000000
χ1024-444-4-44-4-444-4-444-400000000−2i22i2−2i22i22i2−2i22i2−2i22i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000000000000000000000000000
χ1034-4-444444-4-4-4-444-4-4-44-44-4-44400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-444-4-44-4-444-4-4444-444-4-44-400000000000000000000000000000000000000000000000000000000000000000000000000000000

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