Finite Group Databasebeta

← Group #397019

Character table — Group #397019

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222222222222244444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222222224444444488888888888888882222444444444444444444448888888888888888888888884444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111
χ51111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111
χ61111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111
χ9111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111
χ10111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1
χ11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ12111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1111111
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111111111-1-1-1-1-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111
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χ802-2-22-2-2-2-22-222-2222-222-2-2-222-222-2-222-22-2-222-2-22000000000000000000000000000000000000000000000000000000-220000002-2
χ812-2-2-22-222-22-2-2-2222222-22-2-2-22i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i00002-2-222-2-22000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ822-2-2-22-222-22-2-2-2222222-22-2-2-22i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i0000-222-2-222-20000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ832-2-2-22-222-22-2-2-2222222-22-2-2-2−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i00002-2-222-2-220000000000002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000
χ842-2-2-22-222-22-2-2-2222222-22-2-2-2−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i0000-222-2-222-2000000000000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000
χ852-2-2-22-222-22-2-2-2222-2-2-22-2222000000000000000000002-2-22-222-2000000000000000000002-2-22-222-2-222-22-2-220000000000000000
χ862-2-2-22-222-22-2-2-2222-2-2-22-2222000000000000000000002-2-22-222-200000000000000000000-222-22-2-222-2-22-222-20000000000000000
χ872-2-2-22-222-22-2-2-2222-2-2-22-222200000000000000000000-222-22-2-22000000000000000000002-2-22-222-22-2-22-222-20000000000000000
χ882-2-2-22-222-22-2-2-2222-2-2-22-222200000000000000000000-222-22-2-2200000000000000000000-222-22-2-22-222-22-2-220000000000000000
χ892-2-2-2-2222-2-2222-2-2222-22-2-22-22i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000000000000000000000000000002-2002i−2i00
χ902-2-2-2-2222-2-2222-2-2222-22-2-22-22i−2i−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000000000000000000000000000-2200−2i2i00
χ912-2-2-2-2222-2-2222-2-2222-22-2-22-2−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i000000000000000000000000000000000000000000000000000000002-200−2i2i00
χ922-2-2-2-2222-2-2222-2-2222-22-2-22-2−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000000000000000000000000000-22002i−2i00
χ934444-4-4444-4-4-4-4-4-44-4-4444-44-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ94444-4-44-4-4-4-4-4-444444-4-4-44-44400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9544-44444-4-4-4-44-4-44-4000000002222−22−222222−22−22−22−222222−22−2222220000000000000000000000000000000000000000000000000000000000000000
χ9644-44444-4-4-4-44-4-44-400000000−22−222222−22−2222222222−22−222222−22−220000000000000000000000000000000000000000000000000000000000000000
χ9744-4-44-4-444-4-4444-4-4000000002i22i2−2i2−2i2−2i2−2i22i22i2−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000000000000000000000000000000000
χ9844-4-44-4-444-4-4444-4-400000000−2i2−2i22i22i22i22i2−2i2−2i22i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000000000000000000000000000000000
χ994-44444-44-4-44-4-44-4-40000000022−2222−2222−2222−22−2222−2222−2222−22220000000000000000000000000000000000000000000000000000000000000000
χ1004-44444-44-4-44-4-44-4-400000000−2222−2222−2222−222222−2222−2222−2222−220000000000000000000000000000000000000000000000000000000000000000
χ1014-44-44-44-44-44-44-44-4000000002i2−2i22i2−2i2−2i22i2−2i22i2−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000000000000000000000000000
χ1024-44-44-44-44-44-44-44-400000000−2i22i2−2i22i22i2−2i22i2−2i22i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000000000000000000000000000
χ1034-4-44-4-4-4-44-444-44444-4-4444-4-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-4-4444-4-4444-4-44-4-44-444-4400000000000000000000000000000000000000000000000000000000000000000000000000000000

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