Finite Group Databasebeta

← Group #196239

Character table — Group #196239

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222222222222288888888888888888888888888881111222222222222228888888888888888888888888888
order12222244444444444422444444444488888888888888882222224444444444442244444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222-2-2-2-222-2-2-2-2222-2002-20000000000000000000000222222-2-2-2-222-2-2-2-2222-2002-20000000000000000000000
χ18222222-2-2-2-222-2-2-2-222-2200-220000000000000000000000222222-2-2-2-222-2-2-2-222-2200-220000000000000000000000
χ19222222-2-2-2-2-2-22222-2-22-200-220000000000000000000000222222-2-2-2-2-2-22222-2-22-200-220000000000000000000000
χ20222222-2-2-2-2-2-22222-2-2-22002-20000000000000000000000222222-2-2-2-2-2-22222-2-2-22002-20000000000000000000000
χ212222-2-222-2-22222-2-2-2-20000000000000000000000002i−2i2i−2i2222-2-222-2-22222-2-2-2-20000000000000000000000002i−2i2i−2i
χ222222-2-222-2-22222-2-2-2-2000000000000000000000000−2i2i−2i2i2222-2-222-2-22222-2-2-2-2000000000000000000000000−2i2i−2i2i
χ232222-2-222-2-2-2-2-2-222220000000000000000000000002-2-222222-2-222-2-2-2-2-2-222220000000000000000000000002-2-22
χ242222-2-222-2-2-2-2-2-22222000000000000000000000000-222-22222-2-222-2-2-2-2-2-22222000000000000000000000000-222-2
χ252222-2-2-2-22222-2-222-2-2000000000000000000002i−2i2i−2i00002222-2-2-2-22222-2-222-2-2000000000000000000002i−2i2i−2i0000
χ262222-2-2-2-22222-2-222-2-200000000000000000000−2i2i−2i2i00002222-2-2-2-22222-2-222-2-200000000000000000000−2i2i−2i2i0000
χ272222-2-2-2-222-2-222-2-222000000000000000000002-2-2200002222-2-2-2-222-2-222-2-222000000000000000000002-2-220000
χ282222-2-2-2-222-2-222-2-22200000000000000000000-222-200002222-2-2-2-222-2-222-2-22200000000000000000000-222-20000
χ292-22-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000002ζ−2ζ2ζ3−2ζ3000000002-22-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000002ζ−2ζ2ζ3−2ζ300000000
χ302-22-22-22-22-22i−2i2i−2i2i−2i2i−2i0000000000000000−2ζ2ζ−2ζ32ζ3000000002-22-22-22-22-22i−2i2i−2i2i−2i2i−2i0000000000000000−2ζ2ζ−2ζ32ζ300000000
χ312-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000002ζ3−2ζ32ζ−2ζ000000002-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000002ζ3−2ζ32ζ−2ζ00000000
χ322-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000−2ζ32ζ3−2ζ2ζ000000002-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ332-22-22-2-22-222i−2i−2i2i−2i2i2i−2i0000000000002ζ3−2ζ32ζ−2ζ0000000000002-22-22-2-22-222i−2i−2i2i−2i2i2i−2i0000000000002ζ3−2ζ32ζ−2ζ000000000000
χ342-22-22-2-22-222i−2i−2i2i−2i2i2i−2i000000000000−2ζ32ζ3−2ζ2ζ0000000000002-22-22-2-22-222i−2i−2i2i−2i2i2i−2i000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ352-22-22-2-22-22−2i2i2i−2i2i−2i−2i2i0000000000002ζ−2ζ2ζ3−2ζ30000000000002-22-22-2-22-22−2i2i2i−2i2i−2i−2i2i0000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ362-22-22-2-22-22−2i2i2i−2i2i−2i−2i2i000000000000−2ζ2ζ−2ζ32ζ30000000000002-22-22-2-22-22−2i2i2i−2i2i−2i−2i2i000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ372-22-2-222-2-222i−2i2i−2i−2i2i−2i2i002-2002i−2i000000000000000000002-22-2-222-2-222i−2i2i−2i−2i2i−2i2i002-2002i−2i00000000000000000000
χ382-22-2-222-2-222i−2i2i−2i−2i2i−2i2i00-2200−2i2i000000000000000000002-22-2-222-2-222i−2i2i−2i−2i2i−2i2i00-2200−2i2i00000000000000000000
χ392-22-2-222-2-22−2i2i−2i2i2i−2i2i−2i002-200−2i2i000000000000000000002-22-2-222-2-22−2i2i−2i2i2i−2i2i−2i002-200−2i2i00000000000000000000
χ402-22-2-222-2-22−2i2i−2i2i2i−2i2i−2i00-22002i−2i000000000000000000002-22-2-222-2-22−2i2i−2i2i2i−2i2i−2i00-22002i−2i00000000000000000000
χ412-22-2-22-222-22i−2i−2i2i2i−2i−2i2i000000002-22i−2i00000000000000002-22-2-22-222-22i−2i−2i2i2i−2i−2i2i000000002-22i−2i0000000000000000
χ422-22-2-22-222-22i−2i−2i2i2i−2i−2i2i00000000-22−2i2i00000000000000002-22-2-22-222-22i−2i−2i2i2i−2i−2i2i00000000-22−2i2i0000000000000000
χ432-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i000000002-2−2i2i00000000000000002-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i000000002-2−2i2i0000000000000000
χ442-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i00000000-222i−2i00000000000000002-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i00000000-222i−2i0000000000000000
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
χ48111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ4911111111111111111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111111
χ5011111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111111111-1-1-1-1-1-1-1-1
χ51111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111
χ52111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-11111-1-1-1-1
χ53111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ54111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ551111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1ii−i−iii−i−iii−i−iii−i−i-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111−i−iii−i−iii−i−iii−i−iii
χ561111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1−i−iii−i−iii−i−iii−i−iii-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111ii−i−iii−i−iii−i−iii−i−i
χ571111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i
χ581111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii
χ591111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ601111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ611111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1ii−i−i−i−iii−i−iiiii−i−i-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ621111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−iiiii−i−iii−i−i−i−iii-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i
χ63222222-2-2-2-222-2-2-2-2222-2002-20000000000000000000000-2-2-2-2-2-22222-2-22222-2-2-2200-220000000000000000000000
χ64222222-2-2-2-222-2-2-2-222-2200-220000000000000000000000-2-2-2-2-2-22222-2-22222-2-22-2002-20000000000000000000000
χ65222222-2-2-2-2-2-22222-2-22-200-220000000000000000000000-2-2-2-2-2-2222222-2-2-2-222-22002-20000000000000000000000
χ66222222-2-2-2-2-2-22222-2-2-22002-20000000000000000000000-2-2-2-2-2-2222222-2-2-2-2222-200-220000000000000000000000
χ672222-2-222-2-22222-2-2-2-20000000000000000000000002i−2i2i−2i-2-2-2-222-2-222-2-2-2-22222000000000000000000000000−2i2i−2i2i
χ682222-2-222-2-22222-2-2-2-2000000000000000000000000−2i2i−2i2i-2-2-2-222-2-222-2-2-2-222220000000000000000000000002i−2i2i−2i
χ692222-2-222-2-2-2-2-2-222220000000000000000000000002-2-22-2-2-2-222-2-2222222-2-2-2-2000000000000000000000000-222-2
χ702222-2-222-2-2-2-2-2-22222000000000000000000000000-222-2-2-2-2-222-2-2222222-2-2-2-20000000000000000000000002-2-22
χ712222-2-2-2-22222-2-222-2-2000000000000000000002i−2i2i−2i0000-2-2-2-22222-2-2-2-222-2-22200000000000000000000−2i2i−2i2i0000
χ722222-2-2-2-22222-2-222-2-200000000000000000000−2i2i−2i2i0000-2-2-2-22222-2-2-2-222-2-222000000000000000000002i−2i2i−2i0000
χ732222-2-2-2-222-2-222-2-222000000000000000000002-2-220000-2-2-2-22222-2-222-2-222-2-200000000000000000000-222-20000
χ742222-2-2-2-222-2-222-2-22200000000000000000000-222-20000-2-2-2-22222-2-222-2-222-2-2000000000000000000002-2-220000
χ752-22-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000002ζ−2ζ2ζ3−2ζ300000000-22-22-22-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000−2ζ2ζ−2ζ32ζ300000000
χ762-22-22-22-22-22i−2i2i−2i2i−2i2i−2i0000000000000000−2ζ2ζ−2ζ32ζ300000000-22-22-22-22-22−2i2i−2i2i−2i2i−2i2i00000000000000002ζ−2ζ2ζ3−2ζ300000000
χ772-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000002ζ3−2ζ32ζ−2ζ00000000-22-22-22-22-222i−2i2i−2i2i−2i2i−2i0000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ782-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000−2ζ32ζ3−2ζ2ζ00000000-22-22-22-22-222i−2i2i−2i2i−2i2i−2i00000000000000002ζ3−2ζ32ζ−2ζ00000000
χ792-22-22-2-22-222i−2i−2i2i−2i2i2i−2i0000000000002ζ3−2ζ32ζ−2ζ000000000000-22-22-222-22-2−2i2i2i−2i2i−2i−2i2i000000000000−2ζ32ζ3−2ζ2ζ000000000000
χ802-22-22-2-22-222i−2i−2i2i−2i2i2i−2i000000000000−2ζ32ζ3−2ζ2ζ000000000000-22-22-222-22-2−2i2i2i−2i2i−2i−2i2i0000000000002ζ3−2ζ32ζ−2ζ000000000000
χ812-22-22-2-22-22−2i2i2i−2i2i−2i−2i2i0000000000002ζ−2ζ2ζ3−2ζ3000000000000-22-22-222-22-22i−2i−2i2i−2i2i2i−2i000000000000−2ζ2ζ−2ζ32ζ3000000000000
χ822-22-22-2-22-22−2i2i2i−2i2i−2i−2i2i000000000000−2ζ2ζ−2ζ32ζ3000000000000-22-22-222-22-22i−2i−2i2i−2i2i2i−2i0000000000002ζ−2ζ2ζ3−2ζ3000000000000
χ832-22-2-222-2-222i−2i2i−2i−2i2i−2i2i002-2002i−2i00000000000000000000-22-222-2-222-2−2i2i−2i2i2i−2i2i−2i00-2200−2i2i00000000000000000000
χ842-22-2-222-2-222i−2i2i−2i−2i2i−2i2i00-2200−2i2i00000000000000000000-22-222-2-222-2−2i2i−2i2i2i−2i2i−2i002-2002i−2i00000000000000000000
χ852-22-2-222-2-22−2i2i−2i2i2i−2i2i−2i002-200−2i2i00000000000000000000-22-222-2-222-22i−2i2i−2i−2i2i−2i2i00-22002i−2i00000000000000000000
χ862-22-2-222-2-22−2i2i−2i2i2i−2i2i−2i00-22002i−2i00000000000000000000-22-222-2-222-22i−2i2i−2i−2i2i−2i2i002-200−2i2i00000000000000000000
χ872-22-2-22-222-22i−2i−2i2i2i−2i−2i2i000000002-22i−2i0000000000000000-22-222-22-2-22−2i2i2i−2i−2i2i2i−2i00000000-22−2i2i0000000000000000
χ882-22-2-22-222-22i−2i−2i2i2i−2i−2i2i00000000-22−2i2i0000000000000000-22-222-22-2-22−2i2i2i−2i−2i2i2i−2i000000002-22i−2i0000000000000000
χ892-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i000000002-2−2i2i0000000000000000-22-222-22-2-222i−2i−2i2i2i−2i−2i2i00000000-222i−2i0000000000000000
χ902-22-2-22-222-2−2i2i2i−2i−2i2i2i−2i00000000-222i−2i0000000000000000-22-222-22-2-222i−2i−2i2i2i−2i−2i2i000000002-2−2i2i0000000000000000
χ9188-8-8000000000000000000000000000000000000000000-8-888000000000000000000000000000000000000000000
χ928-8-88000000000000000000000000000000000000000000-888-8000000000000000000000000000000000000000000

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