Finite Group Databasebeta

← Group #357491

Character table — Group #357491

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222222222222288888888888888888888888888881111222222222222228888888888888888888888888888
order12222222224444444422222244444444444444888888882222222222444444442222224444444444444488888888
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
χ31111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ6111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ7111111111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1
χ8111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111
χ9111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ12111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ13111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1ii−i−i−i−iii−i−iiiii−i−i111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ14111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1−i−iiiii−i−iii−i−i−i−iii111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1−i−iiiii−i−iii−i−i−i−iii
χ15111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111ii−i−iii−i−i−i−iii−i−iii111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ16111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111−i−iii−i−iiiii−i−iii−i−i111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ172222222222-2-2-2-2-2-2-2-20000002-22-20000000000000000002222222222-2-2-2-2-2-2-2-20000002-22-2000000000000000000
χ182222222222-2-2-2-2-2-2-2-2000000-22-220000000000000000002222222222-2-2-2-2-2-2-2-2000000-22-22000000000000000000
χ19222222-2-2-2-2-2-2-2-222220000002-2-22000000000000000000222222-2-2-2-2-2-2-2-222220000002-2-22000000000000000000
χ20222222-2-2-2-2-2-2-2-22222000000-222-2000000000000000000222222-2-2-2-2-2-2-2-22222000000-222-2000000000000000000
χ212222-2-22-22-222-2-22-22-200002-200002-200000000000000002222-2-22-22-222-2-22-22-200002-200002-20000000000000000
χ222222-2-22-22-222-2-22-22-20000-220000-2200000000000000002222-2-22-22-222-2-22-22-20000-220000-220000000000000000
χ232222-2-22-22-2-2-222-22-222-22-20000000000000000000000002222-2-22-22-2-2-222-22-222-22-2000000000000000000000000
χ242222-2-22-22-2-2-222-22-22-22-220000000000000000000000002222-2-22-22-2-2-222-22-22-22-22000000000000000000000000
χ252222-2-2-22-2222-2-2-22-2200002-20000-2200000000000000002222-2-2-22-2222-2-2-22-2200002-20000-220000000000000000
χ262222-2-2-22-2222-2-2-22-220000-2200002-200000000000000002222-2-2-22-2222-2-2-22-220000-2200002-20000000000000000
χ272222-2-2-22-22-2-2222-22-22-2-220000000000000000000000002222-2-2-22-22-2-2222-22-22-2-22000000000000000000000000
χ282222-2-2-22-22-2-2222-22-2-222-20000000000000000000000002222-2-2-22-22-2-2222-22-2-222-2000000000000000000000000
χ292-2-222-222-2-22-22-22-2-220000000000000000000000002i−2i2i−2i2-2-222-222-2-22-22-22-2-220000000000000000000000002i−2i2i−2i
χ302-2-222-222-2-22-22-22-2-22000000000000000000000000−2i2i−2i2i2-2-222-222-2-22-22-22-2-22000000000000000000000000−2i2i−2i2i
χ312-2-222-222-2-2-22-22-222-2000000000000000000002i−2i2i−2i00002-2-222-222-2-2-22-22-222-2000000000000000000002i−2i2i−2i0000
χ322-2-222-222-2-2-22-22-222-200000000000000000000−2i2i−2i2i00002-2-222-222-2-2-22-22-222-200000000000000000000−2i2i−2i2i0000
χ332-2-222-2-2-2222-22-2-222-20000000000000000000000002-2-222-2-222-2-2-2222-22-2-222-20000000000000000000000002-2-22
χ342-2-222-2-2-2222-22-2-222-2000000000000000000000000-222-22-2-222-2-2-2222-22-2-222-2000000000000000000000000-222-2
χ352-2-222-2-2-222-22-222-2-22000000000000000000002-2-2200002-2-222-2-2-222-22-222-2-22000000000000000000002-2-220000
χ362-2-222-2-2-222-22-222-2-2200000000000000000000-222-200002-2-222-2-2-222-22-222-2-2200000000000000000000-222-20000
χ372-2-22-222-2-222-2-2222-2-20000000000002i−2i2i−2i0000000000002-2-22-222-2-222-2-2222-2-20000000000002i−2i2i−2i000000000000
χ382-2-22-222-2-222-2-2222-2-2000000000000−2i2i−2i2i0000000000002-2-22-222-2-222-2-2222-2-2000000000000−2i2i−2i2i000000000000
χ392-2-22-222-2-22-222-2-2-22200000000000000002-22-2000000002-2-22-222-2-22-222-2-2-22200000000000000002-22-200000000
χ402-2-22-222-2-22-222-2-2-2220000000000000000-22-22000000002-2-22-222-2-22-222-2-2-2220000000000000000-22-2200000000
χ412-2-22-22-222-22-2-22-2-2220000000000002-2-220000000000002-2-22-22-222-22-2-22-2-2220000000000002-2-22000000000000
χ422-2-22-22-222-22-2-22-2-222000000000000-222-20000000000002-2-22-22-222-22-2-22-2-222000000000000-222-2000000000000
χ432-2-22-22-222-2-222-222-2-200000000000000002i−2i−2i2i000000002-2-22-22-222-2-222-222-2-200000000000000002i−2i−2i2i00000000
χ442-2-22-22-222-2-222-222-2-20000000000000000−2i2i2i−2i000000002-2-22-22-222-2-222-222-2-20000000000000000−2i2i2i−2i00000000
χ4588-8-800000000000000000000000000000000000000000088-8-8000000000000000000000000000000000000000000
χ468-88-80000000000000000000000000000000000000000008-88-8000000000000000000000000000000000000000000
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
χ491111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ501111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ51111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ52111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-11111
χ53111111111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111111111
χ54111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ55111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111−i−iii−i−iii−i−iii−i−iii
χ56111111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i
χ57111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ58111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ59111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1ii−i−i−i−iii−i−iiiii−i−i-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111−i−iiiii−i−iii−i−i−i−iii
χ60111111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1−i−iiiii−i−iii−i−i−i−iii-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-111ii−i−i−i−iii−i−iiiii−i−i
χ61111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111ii−i−iii−i−i−i−iii−i−iii-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i
χ62111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111−i−iii−i−iiiii−i−iii−i−i-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii
χ632222222222-2-2-2-2-2-2-2-20000002-22-2000000000000000000-2-2-2-2-2-2-2-2-2-222222222000000-22-22000000000000000000
χ642222222222-2-2-2-2-2-2-2-2000000-22-22000000000000000000-2-2-2-2-2-2-2-2-2-2222222220000002-22-2000000000000000000
χ65222222-2-2-2-2-2-2-2-222220000002-2-22000000000000000000-2-2-2-2-2-222222222-2-2-2-2000000-222-2000000000000000000
χ66222222-2-2-2-2-2-2-2-22222000000-222-2000000000000000000-2-2-2-2-2-222222222-2-2-2-20000002-2-22000000000000000000
χ672222-2-22-22-222-2-22-22-200002-200002-20000000000000000-2-2-2-222-22-22-2-222-22-220000-220000-220000000000000000
χ682222-2-22-22-222-2-22-22-20000-220000-220000000000000000-2-2-2-222-22-22-2-222-22-2200002-200002-20000000000000000
χ692222-2-22-22-2-2-222-22-222-22-2000000000000000000000000-2-2-2-222-22-2222-2-22-22-2-22-22000000000000000000000000
χ702222-2-22-22-2-2-222-22-22-22-22000000000000000000000000-2-2-2-222-22-2222-2-22-22-22-22-2000000000000000000000000
χ712222-2-2-22-2222-2-2-22-2200002-20000-220000000000000000-2-2-2-2222-22-2-2-2222-22-20000-2200002-20000000000000000
χ722222-2-2-22-2222-2-2-22-220000-2200002-20000000000000000-2-2-2-2222-22-2-2-2222-22-200002-20000-220000000000000000
χ732222-2-2-22-22-2-2222-22-22-2-22000000000000000000000000-2-2-2-2222-22-222-2-2-22-22-222-2000000000000000000000000
χ742222-2-2-22-22-2-2222-22-2-222-2000000000000000000000000-2-2-2-2222-22-222-2-2-22-222-2-22000000000000000000000000
χ752-2-222-222-2-22-22-22-2-220000000000000000000000002i−2i2i−2i-222-2-22-2-222-22-22-222-2000000000000000000000000−2i2i−2i2i
χ762-2-222-222-2-22-22-22-2-22000000000000000000000000−2i2i−2i2i-222-2-22-2-222-22-22-222-20000000000000000000000002i−2i2i−2i
χ772-2-222-222-2-2-22-22-222-2000000000000000000002i−2i2i−2i0000-222-2-22-2-2222-22-22-2-2200000000000000000000−2i2i−2i2i0000
χ782-2-222-222-2-2-22-22-222-200000000000000000000−2i2i−2i2i0000-222-2-22-2-2222-22-22-2-22000000000000000000002i−2i2i−2i0000
χ792-2-222-2-2-2222-22-2-222-20000000000000000000000002-2-22-222-2-2222-2-2-22-222-2-22000000000000000000000000-222-2
χ802-2-222-2-2-2222-22-2-222-2000000000000000000000000-222-2-222-2-2222-2-2-22-222-2-220000000000000000000000002-2-22
χ812-2-222-2-2-222-22-222-2-22000000000000000000002-2-220000-222-2-2222-2-22-22-2-222-200000000000000000000-222-20000
χ822-2-222-2-2-222-22-222-2-2200000000000000000000-222-20000-222-2-2222-2-22-22-2-222-2000000000000000000002-2-220000
χ832-2-22-222-2-222-2-2222-2-20000000000002i−2i2i−2i000000000000-222-22-2-222-2-222-2-2-222000000000000−2i2i−2i2i000000000000
χ842-2-22-222-2-222-2-2222-2-2000000000000−2i2i−2i2i000000000000-222-22-2-222-2-222-2-2-2220000000000002i−2i2i−2i000000000000
χ852-2-22-222-2-22-222-2-2-22200000000000000002-22-200000000-222-22-2-222-22-2-2222-2-20000000000000000-22-2200000000
χ862-2-22-222-2-22-222-2-2-2220000000000000000-22-2200000000-222-22-2-222-22-2-2222-2-200000000000000002-22-200000000
χ872-2-22-22-222-22-2-22-2-2220000000000002-2-22000000000000-222-22-22-2-22-222-222-2-2000000000000-222-2000000000000
χ882-2-22-22-222-22-2-22-2-222000000000000-222-2000000000000-222-22-22-2-22-222-222-2-20000000000002-2-22000000000000
χ892-2-22-22-222-2-222-222-2-200000000000000002i−2i−2i2i00000000-222-22-22-2-222-2-22-2-2220000000000000000−2i2i2i−2i00000000
χ902-2-22-22-222-2-222-222-2-20000000000000000−2i2i2i−2i00000000-222-22-22-2-222-2-22-2-22200000000000000002i−2i−2i2i00000000
χ9188-8-8000000000000000000000000000000000000000000-8-888000000000000000000000000000000000000000000
χ928-88-8000000000000000000000000000000000000000000-88-88000000000000000000000000000000000000000000

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