Finite Group Databasebeta

← Group #414469

Character table — Group #414469

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size111111111111111122222222222222222222222244444444444444444444444444444444444444444444444416161616161616161616161616161616
order12222222222222224444444488888888888888884444444444444444444444448888888888888888888888884444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1
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
χ11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-111
χ12111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1111111-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111
χ14111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
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χ192222222222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ202222222222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ2122222-2-2222-2-2-2-2-2-222-2-222-2-200000000000000000000000022-2-222-2-2000000002222-2-2-2-2000000002222-2-2-2-20000000000000000
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χ2722222-2-2222-2-2-2-2-2-2-2-222-2-222-2-2-2-2-2-2-2-2222222220000000022-2-2-2-2220000000000000000-2-2-2-22222000000000000000000000000
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χ5422-22-2-22-22-2-22-222-200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22i−2i2i−2i00000000-222-20000−2i2i−2i2i2−22−2−22−22i2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000000000
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χ812-2-222-2-22-2-222-22-2222-22-2-22-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000002i−2i2-2000000000000
χ822-2-222-2-22-2-222-22-2222-22-2-22-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000−2i2i-22000000000000
χ832-2-222-2-22-2-222-22-2222-22-2-22-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000002i−2i-22000000000000
χ842-2-222-2-22-2-222-22-2222-22-2-22-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000−2i2i2-2000000000000
χ852-2-2-2-222222-2-2-22-222-222-22-2-22i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000000000000000002i−2i00002-2
χ862-2-2-2-222222-2-2-22-222-222-22-2-22i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000000000000000000000−2i2i0000-22
χ872-2-2-2-222222-2-2-22-222-222-22-2-2−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000000000000000002i−2i0000-22
χ882-2-2-2-222222-2-2-22-222-222-22-2-2−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000000000000000−2i2i00002-2
χ892-2-2-2-2-2-2222222-22-2-22222-2-2-22i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000000000002-200002i−2i0000
χ902-2-2-2-2-2-2222222-22-2-22222-2-2-22i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000-220000−2i2i0000
χ912-2-2-2-2-2-2222222-22-2-22222-2-2-2−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000000000000000000000002-20000−2i2i0000
χ922-2-2-2-2-2-2222222-22-2-22222-2-2-2−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000-2200002i−2i0000
χ934-444-44-4-4-44-4444-4-40000000022−22−222222−22−222222−22−222222−22−22220000000000000000000000000000000000000000000000000000000000000000
χ944-444-44-4-4-44-4444-4-400000000−222222−22−222222−22−222222−22−222222−220000000000000000000000000000000000000000000000000000000000000000
χ954-444-4-44-4-444-4-4-4440000000022−22−222222−22−2222−222222−22−222222−220000000000000000000000000000000000000000000000000000000000000000
χ964-444-4-44-4-444-4-4-44400000000−222222−22−222222−2222−22−222222−22−22220000000000000000000000000000000000000000000000000000000000000000
χ974-44-444-4-44-4-44-4-4440000000022−22−2222−222222−2222−22−2222−222222−220000000000000000000000000000000000000000000000000000000000000000
χ984-44-444-4-44-4-44-4-44400000000−222222−2222−22−2222−222222−2222−22−22220000000000000000000000000000000000000000000000000000000000000000
χ994-44-44-44-44-44-444-4-40000000022−22−2222−222222−22−222222−2222−22−22220000000000000000000000000000000000000000000000000000000000000000
χ1004-44-44-44-44-44-444-4-400000000−222222−2222−22−222222−22−2222−222222−220000000000000000000000000000000000000000000000000000000000000000
χ1014-4-444444-4-4-4-44-44-4444-4-4-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-4-444-4-44-4-444-44-44-4-44-444-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-4-4-444444-4-4-44-44-44-4-44-44400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-4-4-4-4-4444444-44-44-4-4-4-444400000000000000000000000000000000000000000000000000000000000000000000000000000000

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