Finite Group Databasebeta

← Group #6629707

Character table — Group #6629707

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122222244444444444444444444444444441616161616161616111122222244444444444444444444444444441616161616161616
order12222244442244444444448888888888888888244488882222224444224444444444888888888888888824448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111
χ5111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111
χ8111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1
χ91111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11-11-11111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11-11-1
χ101111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-11-111111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-11-11
χ111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111-1-111-1-111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111-1-111-1-11
χ121111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-111-1-111-11111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-111-1-111-1
χ131111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-11-111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-11-11
χ141111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111-11-11111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111-11-1
χ151111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-11-111-11111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-11-111-1
χ161111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-111-11-1-111111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-111-11-1-11
χ17222222-2-2-2-2220000-2-20000000000002i2i−2i−2i2i2i−2i−2i00000000222222-2-2-2-2220000-2-20000000000002i2i−2i−2i2i2i−2i−2i00000000
χ18222222-2-2-2-2220000-2-2000000000000−2i−2i2i2i−2i−2i2i2i00000000222222-2-2-2-2220000-2-2000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ19222222-2-2-2-2-2-20000220000000000002i2i−2i−2i−2i−2i2i2i00000000222222-2-2-2-2-2-20000220000000000002i2i−2i−2i−2i−2i2i2i00000000
χ20222222-2-2-2-2-2-2000022000000000000−2i−2i2i2i2i2i−2i−2i00000000222222-2-2-2-2-2-2000022000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ212222-2-222-2-22-200002-2000022-2-222-2-200000000000000002222-2-222-2-22-200002-2000022-2-222-2-20000000000000000
χ222222-2-222-2-22-200002-20000-2-222-2-22200000000000000002222-2-222-2-22-200002-20000-2-222-2-2220000000000000000
χ232222-2-222-2-2-220000-22000022-2-2-2-22200000000000000002222-2-222-2-2-220000-22000022-2-2-2-2220000000000000000
χ242222-2-222-2-2-220000-220000-2-22222-2-200000000000000002222-2-222-2-2-220000-220000-2-22222-2-20000000000000000
χ252222-2-2-2-2222-22222-22-2-2-2-20000000000000000000000002222-2-2-2-2222-22222-22-2-2-2-2000000000000000000000000
χ262222-2-2-2-2222-2-2-2-2-2-2222220000000000000000000000002222-2-2-2-2222-2-2-2-2-2-222222000000000000000000000000
χ272222-2-2-2-222-2222-2-22-2-2-2220000000000000000000000002222-2-2-2-222-2222-2-22-2-2-222000000000000000000000000
χ282222-2-2-2-222-22-2-2222-222-2-20000000000000000000000002222-2-2-2-222-22-2-2222-222-2-2000000000000000000000000
χ292-22-22-22-22-200002i−2i00002i−2i00002i−2i2i−2i2-22-20000000000002-22-22-22-22-200002i−2i00002i−2i00002i−2i2i−2i2-22-2000000000000
χ302-22-22-22-22-200002i−2i00002i−2i0000−2i2i−2i2i-22-220000000000002-22-22-22-22-200002i−2i00002i−2i0000−2i2i−2i2i-22-22000000000000
χ312-22-22-22-22-20000−2i2i0000−2i2i00002i−2i2i−2i-22-220000000000002-22-22-22-22-20000−2i2i0000−2i2i00002i−2i2i−2i-22-22000000000000
χ322-22-22-22-22-20000−2i2i0000−2i2i0000−2i2i−2i2i2-22-20000000000002-22-22-22-22-20000−2i2i0000−2i2i0000−2i2i−2i2i2-22-2000000000000
χ332-22-22-2-22-22002i−2i00002i−2i002-22-200002i−2i−2i2i0000000000002-22-22-2-22-22002i−2i00002i−2i002-22-200002i−2i−2i2i000000000000
χ342-22-22-2-22-22002i−2i00002i−2i00-22-220000−2i2i2i−2i0000000000002-22-22-2-22-22002i−2i00002i−2i00-22-220000−2i2i2i−2i000000000000
χ352-22-22-2-22-2200−2i2i0000−2i2i002-22-20000−2i2i2i−2i0000000000002-22-22-2-22-2200−2i2i0000−2i2i002-22-20000−2i2i2i−2i000000000000
χ362-22-22-2-22-2200−2i2i0000−2i2i00-22-2200002i−2i−2i2i0000000000002-22-22-2-22-2200−2i2i0000−2i2i00-22-2200002i−2i−2i2i000000000000
χ372-22-2-222-2-22002i−2i0000−2i2i0000002i−2i−2i2i00002-22-2000000002-22-2-222-2-22002i−2i0000−2i2i0000002i−2i−2i2i00002-22-200000000
χ382-22-2-222-2-22002i−2i0000−2i2i000000−2i2i2i−2i0000-22-22000000002-22-2-222-2-22002i−2i0000−2i2i000000−2i2i2i−2i0000-22-2200000000
χ392-22-2-222-2-2200−2i2i00002i−2i0000002i−2i−2i2i0000-22-22000000002-22-2-222-2-2200−2i2i00002i−2i0000002i−2i−2i2i0000-22-2200000000
χ402-22-2-222-2-2200−2i2i00002i−2i000000−2i2i2i−2i00002-22-2000000002-22-2-222-2-2200−2i2i00002i−2i000000−2i2i2i−2i00002-22-200000000
χ412-22-2-22-222-200002i−2i0000−2i2i2-2-22000000002i−2i−2i2i000000002-22-2-22-222-200002i−2i0000−2i2i2-2-22000000002i−2i−2i2i00000000
χ422-22-2-22-222-200002i−2i0000−2i2i-222-200000000−2i2i2i−2i000000002-22-2-22-222-200002i−2i0000−2i2i-222-200000000−2i2i2i−2i00000000
χ432-22-2-22-222-20000−2i2i00002i−2i2-2-2200000000−2i2i2i−2i000000002-22-2-22-222-20000−2i2i00002i−2i2-2-2200000000−2i2i2i−2i00000000
χ442-22-2-22-222-20000−2i2i00002i−2i-222-2000000002i−2i−2i2i000000002-22-2-22-222-20000−2i2i00002i−2i-222-2000000002i−2i−2i2i00000000
χ4588-8-800000000000000000000000000000000000000000088-8-8000000000000000000000000000000000000000000
χ468-8-880000000000000000000000000000000000000000008-8-88000000000000000000000000000000000000000000
χ471111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ491111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-11-1-111
χ501111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-11-111-1-1
χ51111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ52111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ53111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-11-1111-1-1
χ54111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-11-11-1-1-111
χ551111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11-11-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-111-11-11
χ561111111111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-11-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1111111-1-11-11-1
χ571111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111-1-111-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-11111-1-1-1-1-111-1-111-1
χ581111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-11111-1-1-1-11-1-111-1-11
χ591111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-11-11-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1111-11-1
χ601111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1111-11-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-11-11
χ611111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-11-1-11-111-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-11111-111-11-1-11
χ621111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-111-11-1-11-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-111111-1-11-111-1
χ63222222-2-2-2-2220000-2-20000000000002i2i−2i−2i2i2i−2i−2i00000000-2-2-2-2-2-22222-2-2000022000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ64222222-2-2-2-2220000-2-2000000000000−2i−2i2i2i−2i−2i2i2i00000000-2-2-2-2-2-22222-2-20000220000000000002i2i−2i−2i2i2i−2i−2i00000000
χ65222222-2-2-2-2-2-20000220000000000002i2i−2i−2i−2i−2i2i2i00000000-2-2-2-2-2-22222220000-2-2000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ66222222-2-2-2-2-2-2000022000000000000−2i−2i2i2i2i2i−2i−2i00000000-2-2-2-2-2-22222220000-2-20000000000002i2i−2i−2i−2i−2i2i2i00000000
χ672222-2-222-2-22-200002-2000022-2-222-2-20000000000000000-2-2-2-222-2-222-220000-220000-2-222-2-2220000000000000000
χ682222-2-222-2-22-200002-20000-2-222-2-2220000000000000000-2-2-2-222-2-222-220000-22000022-2-222-2-20000000000000000
χ692222-2-222-2-2-220000-22000022-2-2-2-2220000000000000000-2-2-2-222-2-2222-200002-20000-2-22222-2-20000000000000000
χ702222-2-222-2-2-220000-220000-2-22222-2-20000000000000000-2-2-2-222-2-2222-200002-2000022-2-2-2-2220000000000000000
χ712222-2-2-2-2222-22222-22-2-2-2-2000000000000000000000000-2-2-2-22222-2-2-22-2-2-2-22-22222000000000000000000000000
χ722222-2-2-2-2222-2-2-2-2-2-222222000000000000000000000000-2-2-2-22222-2-2-2222222-2-2-2-2-2000000000000000000000000
χ732222-2-2-2-222-2222-2-22-2-2-222000000000000000000000000-2-2-2-22222-2-22-2-2-222-2222-2-2000000000000000000000000
χ742222-2-2-2-222-22-2-2222-222-2-2000000000000000000000000-2-2-2-22222-2-22-222-2-2-22-2-222000000000000000000000000
χ752-22-22-22-22-200002i−2i00002i−2i00002i−2i2i−2i2-22-2000000000000-22-22-22-22-220000−2i2i0000−2i2i0000−2i2i−2i2i-22-22000000000000
χ762-22-22-22-22-200002i−2i00002i−2i0000−2i2i−2i2i-22-22000000000000-22-22-22-22-220000−2i2i0000−2i2i00002i−2i2i−2i2-22-2000000000000
χ772-22-22-22-22-20000−2i2i0000−2i2i00002i−2i2i−2i-22-22000000000000-22-22-22-22-2200002i−2i00002i−2i0000−2i2i−2i2i2-22-2000000000000
χ782-22-22-22-22-20000−2i2i0000−2i2i0000−2i2i−2i2i2-22-2000000000000-22-22-22-22-2200002i−2i00002i−2i00002i−2i2i−2i-22-22000000000000
χ792-22-22-2-22-22002i−2i00002i−2i002-22-200002i−2i−2i2i000000000000-22-22-222-22-200−2i2i0000−2i2i00-22-220000−2i2i2i−2i000000000000
χ802-22-22-2-22-22002i−2i00002i−2i00-22-220000−2i2i2i−2i000000000000-22-22-222-22-200−2i2i0000−2i2i002-22-200002i−2i−2i2i000000000000
χ812-22-22-2-22-2200−2i2i0000−2i2i002-22-20000−2i2i2i−2i000000000000-22-22-222-22-2002i−2i00002i−2i00-22-2200002i−2i−2i2i000000000000
χ822-22-22-2-22-2200−2i2i0000−2i2i00-22-2200002i−2i−2i2i000000000000-22-22-222-22-2002i−2i00002i−2i002-22-20000−2i2i2i−2i000000000000
χ832-22-2-222-2-22002i−2i0000−2i2i0000002i−2i−2i2i00002-22-200000000-22-222-2-222-200−2i2i00002i−2i000000−2i2i2i−2i0000-22-2200000000
χ842-22-2-222-2-22002i−2i0000−2i2i000000−2i2i2i−2i0000-22-2200000000-22-222-2-222-200−2i2i00002i−2i0000002i−2i−2i2i00002-22-200000000
χ852-22-2-222-2-2200−2i2i00002i−2i0000002i−2i−2i2i0000-22-2200000000-22-222-2-222-2002i−2i0000−2i2i000000−2i2i2i−2i00002-22-200000000
χ862-22-2-222-2-2200−2i2i00002i−2i000000−2i2i2i−2i00002-22-200000000-22-222-2-222-2002i−2i0000−2i2i0000002i−2i−2i2i0000-22-2200000000
χ872-22-2-22-222-200002i−2i0000−2i2i2-2-22000000002i−2i−2i2i00000000-22-222-22-2-220000−2i2i00002i−2i-222-200000000−2i2i2i−2i00000000
χ882-22-2-22-222-200002i−2i0000−2i2i-222-200000000−2i2i2i−2i00000000-22-222-22-2-220000−2i2i00002i−2i2-2-22000000002i−2i−2i2i00000000
χ892-22-2-22-222-20000−2i2i00002i−2i2-2-2200000000−2i2i2i−2i00000000-22-222-22-2-2200002i−2i0000−2i2i-222-2000000002i−2i−2i2i00000000
χ902-22-2-22-222-20000−2i2i00002i−2i-222-2000000002i−2i−2i2i00000000-22-222-22-2-2200002i−2i0000−2i2i2-2-2200000000−2i2i2i−2i00000000
χ9188-8-8000000000000000000000000000000000000000000-8-888000000000000000000000000000000000000000000
χ928-8-88000000000000000000000000000000000000000000-888-8000000000000000000000000000000000000000000

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