Finite Group Databasebeta

← Group #157621

Character table — Group #157621

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111111111111111111111444444444444444444444444888888888888888888888888888888888888888888888888
order12222222222222222222222222222222222222224444444444444444222244444444444444444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ911111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ1011111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ1111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ1211111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ1311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ1411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ1511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1
χ1611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ172222222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-2222222-2-2-2-200000000000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-2222222-2-2-2-20000000000000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ192222222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ202222222222222-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ2122222222-2-2-2-2-2222-2-2-2-2-2-222222-2-2-2-2-200000000000000002i2i2i2i−2i−2i−2i−2i000000000000000000000000000022-2-20000000000002i2i−2i−2i
χ2222222222-2-2-2-2-2222-2-2-2-2-2-222222-2-2-2-2-200000000000000002i2i2i2i−2i−2i−2i−2i0000000000000000000000000000-2-222000000000000−2i−2i2i2i
χ2322222222-2-2-2-2-2222-2-2-2-2-2-222222-2-2-2-2-20000000000000000−2i−2i−2i−2i2i2i2i2i000000000000000000000000000022-2-2000000000000−2i−2i2i2i
χ2422222222-2-2-2-2-2222-2-2-2-2-2-222222-2-2-2-2-20000000000000000−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000-2-2220000000000002i2i−2i−2i
χ252222-2-2-2-22222-22-2-222-2-2-2-2222-2-222-2-2-200000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000022-2-22i2i−2i−2i00000000
χ262222-2-2-2-22222-22-2-222-2-2-2-2222-2-222-2-2-200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000-2-222−2i−2i2i2i00000000
χ272222-2-2-2-22222-22-2-222-2-2-2-2222-2-222-2-2-20000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000022-2-2−2i−2i2i2i00000000
χ282222-2-2-2-22222-22-2-222-2-2-2-2222-2-222-2-2-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000-2-2222i2i−2i−2i00000000
χ292222-2-2-2-2-2-2-2-222-2-2-2-22222222-2-2-2-222222-2-222-2-22222-2-2-2-222-2-2-2-222000000000000000000000000000000000000000000000000
χ302222-2-2-2-2-2-2-2-222-2-2-2-22222222-2-2-2-222222-2-222-2-2-2-2-2-22222-2-22222-2-2000000000000000000000000000000000000000000000000
χ312222-2-2-2-2-2-2-2-222-2-2-2-22222222-2-2-2-2222-2-222-2-2222222-2-2-2-2-2-22222-2-2000000000000000000000000000000000000000000000000
χ322222-2-2-2-2-2-2-2-222-2-2-2-22222222-2-2-2-2222-2-222-2-222-2-2-2-2222222-2-2-2-222000000000000000000000000000000000000000000000000
χ332222-2-2-2-2-2-2-2-22-22222-2-2-22-2-2-22222-22222-2-2-2-22200000000000000000000000000000000000022-2-222-2-200000000000000000000
χ342222-2-2-2-2-2-2-2-22-22222-2-2-22-2-2-22222-22222-2-2-2-222000000000000000000000000000000000000-2-222-2-22200000000000000000000
χ352222-2-2-2-2-2-2-2-22-22222-2-2-22-2-2-22222-222-2-22222-2-200000000000000000000000000000000000022-2-2-2-22200000000000000000000
χ362222-2-2-2-2-2-2-2-22-22222-2-2-22-2-2-22222-222-2-22222-2-2000000000000000000000000000000000000-2-22222-2-200000000000000000000
χ3722-2-222-2-222-2-22222-2-222-2-22-2-2-2-222-22-20000000022-2-222-2-20000000000000000000000000000000000002i−2i2i−2i00002i−2i2i−2i00000000
χ3822-2-222-2-222-2-22222-2-222-2-22-2-2-2-222-22-20000000022-2-222-2-2000000000000000000000000000000000000−2i2i−2i2i0000−2i2i−2i2i00000000
χ3922-2-222-2-222-2-22222-2-222-2-22-2-2-2-222-22-200000000-2-222-2-2220000000000000000000000000000000000002i−2i2i−2i0000−2i2i−2i2i00000000
χ4022-2-222-2-222-2-22222-2-222-2-22-2-2-2-222-22-200000000-2-222-2-222000000000000000000000000000000000000−2i2i−2i2i00002i−2i2i−2i00000000
χ4122-2-222-2-2-2-222-222222-2-2222-2-2-2-2-2-22-222-22-22-22-2000000000000000000000000000000000000000000002i−2i−2i2i2i−2i2i−2i000000000000
χ4222-2-222-2-2-2-222-222222-2-2222-2-2-2-2-2-22-222-22-22-22-200000000000000000000000000000000000000000000−2i2i2i−2i−2i2i−2i2i000000000000
χ4322-2-222-2-2-2-222-222222-2-2222-2-2-2-2-2-22-22-22-22-22-22000000000000000000000000000000000000000000002i−2i−2i2i−2i2i−2i2i000000000000
χ4422-2-222-2-2-2-222-222222-2-2222-2-2-2-2-2-22-22-22-22-22-2200000000000000000000000000000000000000000000−2i2i2i−2i2i−2i2i−2i000000000000
χ4522-2-222-2-2-2-222-2-2-2-2-2-222-22-2222222-2-222-22-2-22-22000000000000000022-2-200000000000000000000000000000000000022-2-20000
χ4622-2-222-2-2-2-222-2-2-2-2-2-222-22-2222222-2-222-22-2-22-220000000000000000-2-222000000000000000000000000000000000000-2-2220000
χ4722-2-222-2-2-2-222-2-2-2-2-2-222-22-2222222-2-22-22-222-22-2000000000000000022-2-2000000000000000000000000000000000000-2-2220000
χ4822-2-222-2-2-2-222-2-2-2-2-2-222-22-2222222-2-22-22-222-22-20000000000000000-2-22200000000000000000000000000000000000022-2-20000
χ4922-2-2-2-22222-2-2-22-2-2-2-2-2-2222-2-222222-222-2-222-2-2200000000000000000000000000000000000000000000000000002-2-2200002-22-2
χ5022-2-2-2-22222-2-2-22-2-2-2-2-2-2222-2-222222-222-2-222-2-220000000000000000000000000000000000000000000000000000-222-20000-22-22
χ5122-2-2-2-22222-2-2-22-2-2-2-2-2-2222-2-222222-22-222-2-222-200000000000000000000000000000000000000000000000000002-2-220000-22-22
χ5222-2-2-2-22222-2-2-22-2-2-2-2-2-2222-2-222222-22-222-2-222-20000000000000000000000000000000000000000000000000000-222-200002-22-2
χ5322-2-2-2-22222-2-2-2-2222222-22-222-2-2-2-2-2-222-2-22-222-2000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000
χ5422-2-2-2-22222-2-2-2-2222222-22-222-2-2-2-2-2-222-2-22-222-200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000
χ5522-2-2-2-22222-2-2-2-2222222-22-222-2-2-2-2-2-22-222-22-2-22000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ5622-2-2-2-22222-2-2-2-2222222-22-222-2-2-2-2-2-22-222-22-2-2200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ5722-2-2-2-222-2-22222-2-22222-2-22-2-222-2-2-22-20000000022-2-2-2-22200000000000000000000000000000000000000002i−2i−2i2i000000002i−2i−2i2i
χ5822-2-2-2-222-2-22222-2-22222-2-22-2-222-2-2-22-20000000022-2-2-2-2220000000000000000000000000000000000000000−2i2i2i−2i00000000−2i2i2i−2i
χ5922-2-2-2-222-2-22222-2-22222-2-22-2-222-2-2-22-200000000-2-22222-2-200000000000000000000000000000000000000002i−2i−2i2i00000000−2i2i2i−2i
χ6022-2-2-2-222-2-22222-2-22222-2-22-2-222-2-2-22-200000000-2-22222-2-20000000000000000000000000000000000000000−2i2i2i−2i000000002i−2i−2i2i
χ612-22-22-22-22-22-2222-22-22-22-2-22-22-22-2-2-22000000002i−2i2i−2i2i−2i2i−2i00000000000000002i−2i2i−2i00000000000000000000000000002-22-20000
χ622-22-22-22-22-22-2222-22-22-22-2-22-22-22-2-2-22000000002i−2i2i−2i2i−2i2i−2i0000000000000000−2i2i−2i2i0000000000000000000000000000-22-220000
χ632-22-22-22-22-22-2222-22-22-22-2-22-22-22-2-2-2200000000−2i2i−2i2i−2i2i−2i2i00000000000000002i−2i2i−2i0000000000000000000000000000-22-220000
χ642-22-22-22-22-22-2222-22-22-22-2-22-22-22-2-2-2200000000−2i2i−2i2i−2i2i−2i2i0000000000000000−2i2i−2i2i00000000000000000000000000002-22-20000
χ652-22-2-22-22-22-2222-22-222-22-2-22-2-22-22-2-22000000002i−2i2i−2i−2i2i−2i2i000000002-22-22i−2i2i−2i0000000000000000000000000000000000000000
χ662-22-2-22-22-22-2222-22-222-22-2-22-2-22-22-2-22000000002i−2i2i−2i−2i2i−2i2i00000000-22-22−2i2i−2i2i0000000000000000000000000000000000000000
χ672-22-2-22-22-22-2222-22-222-22-2-22-2-22-22-2-2200000000−2i2i−2i2i2i−2i2i−2i000000002-22-2−2i2i−2i2i0000000000000000000000000000000000000000
χ682-22-2-22-22-22-2222-22-222-22-2-22-2-22-22-2-2200000000−2i2i−2i2i2i−2i2i−2i00000000-22-222i−2i2i−2i0000000000000000000000000000000000000000
χ692-2-222-2-222-2-22222-2-222-2-22-2-22-222-22-2-2000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000002-22-200002i−2i2i−2i00000000000000000000
χ702-2-222-2-222-2-22222-2-222-2-22-2-22-222-22-2-2000000002i−2i−2i2i2i−2i−2i2i000000000000000000000000-22-220000−2i2i−2i2i00000000000000000000
χ712-2-222-2-222-2-22222-2-222-2-22-2-22-222-22-2-200000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000002-22-20000−2i2i−2i2i00000000000000000000
χ722-2-222-2-222-2-22222-2-222-2-22-2-22-222-22-2-200000000−2i2i2i−2i−2i2i2i−2i000000000000000000000000-22-2200002i−2i2i−2i00000000000000000000
χ732-2-222-2-222-2-222-2-222-2-222222-22-2-22-2-2-200000000000000002i−2i2i−2i2i−2i2i−2i00000000000000002i−2i−2i2i2-22-2000000000000000000000000
χ742-2-222-2-222-2-222-2-222-2-222222-22-2-22-2-2-200000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000−2i2i2i−2i-22-22000000000000000000000000
χ752-2-222-2-222-2-222-2-222-2-222222-22-2-22-2-2-20000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000002i−2i−2i2i-22-22000000000000000000000000
χ762-2-222-2-222-2-222-2-222-2-222222-22-2-22-2-2-20000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000−2i2i2i−2i2-22-2000000000000000000000000
χ772-2-222-2-22-222-2-2-2-22-222-2-2-222-22-22-222200000000000000002-22-2-22-2200002-2-22000000000000000000000000000000002-2-220000
χ782-2-222-2-22-222-2-2-2-22-222-2-2-222-22-22-222200000000000000002-22-2-22-220000-222-200000000000000000000000000000000-222-20000
χ792-2-222-2-22-222-2-2-2-22-222-2-2-222-22-22-22220000000000000000-22-222-22-200002-2-2200000000000000000000000000000000-222-20000
χ802-2-222-2-22-222-2-2-2-22-222-2-2-222-22-22-22220000000000000000-22-222-22-20000-222-2000000000000000000000000000000002-2-220000
χ812-2-22-222-22-2-22-2-22-22-22-2-2-222-2-22-2222200000000000000002-2-222-2-222-2-2200002-2-22000000000000000000000000000000000000
χ822-2-22-222-22-2-22-2-22-22-22-2-2-222-2-22-2222200000000000000002-2-222-2-22-222-20000-222-2000000000000000000000000000000000000
χ832-2-22-222-22-2-22-2-22-22-22-2-2-222-2-22-222220000000000000000-222-2-222-22-2-220000-222-2000000000000000000000000000000000000
χ842-2-22-222-22-2-22-2-22-22-22-2-2-222-2-22-222220000000000000000-222-2-222-2-222-200002-2-22000000000000000000000000000000000000
χ852-2-22-222-2-222-222-222-22-2-22-2-222-2-222-2-2000000002i−2i−2i2i−2i2i2i−2i000000000000000000002i−2i2i−2i00002-2-22000000000000000000000000
χ862-2-22-222-2-222-222-222-22-2-22-2-222-2-222-2-2000000002i−2i−2i2i−2i2i2i−2i00000000000000000000−2i2i−2i2i0000-222-2000000000000000000000000
χ872-2-22-222-2-222-222-222-22-2-22-2-222-2-222-2-200000000−2i2i2i−2i2i−2i−2i2i000000000000000000002i−2i2i−2i0000-222-2000000000000000000000000
χ882-2-22-222-2-222-222-222-22-2-22-2-222-2-222-2-200000000−2i2i2i−2i2i−2i−2i2i00000000000000000000−2i2i−2i2i00002-2-22000000000000000000000000
χ892-2-22-222-2-222-22-22-2-22-222222-2-222-2-2-2-200000000000000002i−2i−2i2i−2i2i2i−2i0000000000002-2-22000000002i−2i−2i2i00000000000000000000
χ902-2-22-222-2-222-22-22-2-22-222222-2-222-2-2-2-200000000000000002i−2i−2i2i−2i2i2i−2i000000000000-222-200000000−2i2i2i−2i00000000000000000000
χ912-2-22-222-2-222-22-22-2-22-222222-2-222-2-2-2-20000000000000000−2i2i2i−2i2i−2i−2i2i0000000000002-2-2200000000−2i2i2i−2i00000000000000000000
χ922-2-22-222-2-222-22-22-2-22-222222-2-222-2-2-2-20000000000000000−2i2i2i−2i2i−2i−2i2i000000000000-222-2000000002i−2i−2i2i00000000000000000000
χ9344444444-4-4-4-4-4-4-4-444444-4-4-4-4-4-4444-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ944444-4-4-4-44444-4-444-4-4444-4-4-4-444-4-44-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ9544-4-444-4-444-4-44-4-4-444-4-44-4-44444-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ9644-4-4-4-444-4-4444-444-4-4-4-44-4-444-4-44444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ974-44-44-44-44-44-44-4-44-44-44-4-44-44-44-444-44000000000000000000000000000000000000000000000000000000000000000000000000
χ984-44-44-44-4-44-44-444-4-44-44-44-44-44-4-4444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ994-44-44-44-4-44-44-4-4-444-44-4444-44-444-4-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1004-44-4-44-444-44-4-44-444-4-44-44-44-4-444-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1014-44-4-44-444-44-4-4-44-4-444-4444-444-4-44-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1024-44-4-44-44-44-444-44-44-4-44-4-44-444-44-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ1034-4-444-4-44-444-4-444-44-4-444-4-4-44-44-44-444000000000000000000000000000000000000000000000000000000000000000000000000
χ1044-4-44-444-44-4-44-44-44-44-444-4-4-444-44-4-444000000000000000000000000000000000000000000000000000000000000000000000000

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