Finite Group Databasebeta

← Group #115931

Character table — Group #115931

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444442222444444444444444488888888888888884444444444444444888888888888888822448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111
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χ342222-2-2-2-2−2i−2i−2i2i2i2i−2i2i000022-2-2−2i2i000−2i2i0000000002ζ2ζ−2ζ−2ζ00002ζ32ζ3−2ζ3−2ζ300000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000022−2−2−i2−i2i2i200000000
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χ4322-2-222-2-2−2i−2i2i−2i2i2i2i−2i00002-22-22i−2i000−2i2i00000−2ζ3−2ζ32ζ32ζ30000−2ζ−2ζ2ζ2ζ0000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000−i2i2−i2i22−22−200000000
χ4422-2-222-2-2−2i−2i2i−2i2i2i2i−2i00002-22-22i−2i000−2i2i00000−2ζ3−2ζ32ζ32ζ30000−2ζ−2ζ2ζ2ζ000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000i2−i2i2−i2−22−2200000000
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χ924-4-44-44-44-4444-44-4-4-444-40000004-4400-4000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.