Finite Group Databasebeta

← Group #358271

Character table — Group #358271

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222222222444444448888888888888888888888881111111122222222222244444444888888888888888888888888
order12224444222222444444444444444444444488888888888888882222444422222244444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91-1-1111-1-11-1-111-1111-1-1-11111-1-1-1-111-1-1ii−i−i11-1-1ii−i−iii−i−iii−i−i1-1-1111-1-11-1-111-1111-1-1-11111-1-1-1-111-1-1ii−i−i11-1-1ii−i−iii−i−iii−i−i
χ101-1-1111-1-11-1-111-1111-1-1-11111-1-1-1-111-1-1−i−iii11-1-1−i−iii−i−iii−i−iii1-1-1111-1-11-1-111-1111-1-1-11111-1-1-1-111-1-1−i−iii11-1-1−i−iii−i−iii−i−iii
χ111-1-1111-1-11-1-111-1111-1-1-11111-1-1-1-1-1-111ii−i−i-1-111ii−i−i−i−iii−i−iii1-1-1111-1-11-1-111-1111-1-1-11111-1-1-1-1-1-111ii−i−i-1-111ii−i−i−i−iii−i−iii
χ121-1-1111-1-11-1-111-1111-1-1-11111-1-1-1-1-1-111−i−iii-1-111−i−iiiii−i−iii−i−i1-1-1111-1-11-1-111-1111-1-1-11111-1-1-1-1-1-111−i−iii-1-111−i−iiiii−i−iii−i−i
χ131-1-1111-1-11-1-111-1111-1-1-1-1-1-1-1111111-1-1ii−i−i-1-111−i−iiiii−i−i−i−iii1-1-1111-1-11-1-111-1111-1-1-1-1-1-1-1111111-1-1ii−i−i-1-111−i−iiiii−i−i−i−iii
χ141-1-1111-1-11-1-111-1111-1-1-1-1-1-1-1111111-1-1−i−iii-1-111ii−i−i−i−iiiii−i−i1-1-1111-1-11-1-111-1111-1-1-1-1-1-1-1111111-1-1−i−iii-1-111ii−i−i−i−iiiii−i−i
χ151-1-1111-1-11-1-111-1111-1-1-1-1-1-1-11111-1-111ii−i−i11-1-1−i−iii−i−iiiii−i−i1-1-1111-1-11-1-111-1111-1-1-1-1-1-1-11111-1-111ii−i−i11-1-1−i−iii−i−iiiii−i−i
χ161-1-1111-1-11-1-111-1111-1-1-1-1-1-1-11111-1-111−i−iii11-1-1ii−i−iii−i−i−i−iii1-1-1111-1-11-1-111-1111-1-1-1-1-1-1-11111-1-111−i−iii11-1-1ii−i−iii−i−i−i−iii
χ17222222222-2-2-2-222-2-22-2-2000000002i−2i2i−2i00000000000000000000222222222-2-2-2-222-2-22-2-2000000002i−2i2i−2i00000000000000000000
χ18222222222-2-2-2-222-2-22-2-200000000−2i2i−2i2i00000000000000000000222222222-2-2-2-222-2-22-2-200000000−2i2i−2i2i00000000000000000000
χ1922222222-22-22-2-2-22-2-22-20000000000002i−2i2i−2i000000000000000022222222-22-22-2-2-22-2-22-20000000000002i−2i2i−2i0000000000000000
χ2022222222-22-22-2-2-22-2-22-2000000000000−2i2i−2i2i000000000000000022222222-22-22-2-2-22-2-22-2000000000000−2i2i−2i2i0000000000000000
χ2122222222-2-22-22-2-2-22-2-220000000000000000000000002-22-2000022222222-2-22-22-2-2-22-2-220000000000000000000000002-22-20000
χ2222222222-2-22-22-2-2-22-2-22000000000000000000000000-22-22000022222222-2-22-22-2-2-22-2-22000000000000000000000000-22-220000
χ232222-2-2-2-2222222-2-2-2-2-2-200000000000000000000000000002i−2i2i−2i2222-2-2-2-2222222-2-2-2-2-2-200000000000000000000000000002i−2i2i−2i
χ242222-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000−2i2i−2i2i2222-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000−2i2i−2i2i
χ252222-2-2-2-22-2-2-2-22-222-222000000000000000000002i−2i2i−2i000000002222-2-2-2-22-2-2-2-22-222-222000000000000000000002i−2i2i−2i00000000
χ262222-2-2-2-22-2-2-2-22-222-22200000000000000000000−2i2i−2i2i000000002222-2-2-2-22-2-2-2-22-222-22200000000000000000000−2i2i−2i2i00000000
χ272222-2-2-2-2-22-22-2-22-222-2200000000000000002i−2i2i−2i0000000000002222-2-2-2-2-22-22-2-22-222-2200000000000000002i−2i2i−2i000000000000
χ282222-2-2-2-2-22-22-2-22-222-220000000000000000−2i2i−2i2i0000000000002222-2-2-2-2-22-22-2-22-222-220000000000000000−2i2i−2i2i000000000000
χ292222-2-2-2-2-2-22-22-222-222-222-2-222-2-20000000000000000000000002222-2-2-2-2-2-22-22-222-222-222-2-222-2-2000000000000000000000000
χ302222-2-2-2-2-2-22-22-222-222-2-2-222-2-2220000000000000000000000002222-2-2-2-2-2-22-22-222-222-2-2-222-2-222000000000000000000000000
χ312-2-2222-2-2222-2-2-22-2-2-222000000002i−2i−2i2i000000000000000000002-2-2222-2-2222-2-2-22-2-2-222000000002i−2i−2i2i00000000000000000000
χ322-2-2222-2-2222-2-2-22-2-2-22200000000−2i2i2i−2i000000000000000000002-2-2222-2-2222-2-2-22-2-2-22200000000−2i2i2i−2i00000000000000000000
χ332-2-2222-2-2-22-2-222-2-2222-20000000000000000000000002i−2i−2i2i00002-2-2222-2-2-22-2-222-2-2222-20000000000000000000000002i−2i−2i2i0000
χ342-2-2222-2-2-22-2-222-2-2222-2000000000000000000000000−2i2i2i−2i00002-2-2222-2-2-22-2-222-2-2222-2000000000000000000000000−2i2i2i−2i0000
χ352-2-2222-2-2-2-222-22-22-22-220000000000002-2-2200000000000000002-2-2222-2-2-2-222-22-22-22-220000000000002-2-220000000000000000
χ362-2-2222-2-2-2-222-22-22-22-22000000000000-222-200000000000000002-2-2222-2-2-2-222-22-22-22-22000000000000-222-20000000000000000
χ372-2-22-2-222222-2-2-2-2222-2-2000000000000000000002-2-22000000002-2-22-2-222222-2-2-2-2222-2-2000000000000000000002-2-2200000000
χ382-2-22-2-222222-2-2-2-2222-2-200000000000000000000-222-2000000002-2-22-2-222222-2-2-2-2222-2-200000000000000000000-222-200000000
χ392-2-22-2-2222-2-222-2-2-2-222200000000000000000000000000002-2-222-2-22-2-2222-2-222-2-2-2-222200000000000000000000000000002-2-22
χ402-2-22-2-2222-2-222-2-2-2-22220000000000000000000000000000-222-22-2-22-2-2222-2-222-2-2-2-22220000000000000000000000000000-222-2
χ412-2-22-2-222-22-2-22222-2-2-2222-2-2-2-2220000000000000000000000002-2-22-2-222-22-2-22222-2-2-2222-2-2-2-222000000000000000000000000
χ422-2-22-2-222-22-2-22222-2-2-22-2-22222-2-20000000000000000000000002-2-22-2-222-22-2-22222-2-2-22-2-22222-2-2000000000000000000000000
χ432-2-22-2-222-2-222-222-22-22-200000000000000002i−2i−2i2i0000000000002-2-22-2-222-2-222-222-22-22-200000000000000002i−2i−2i2i000000000000
χ442-2-22-2-222-2-222-222-22-22-20000000000000000−2i2i2i−2i0000000000002-2-22-2-222-2-222-222-22-22-20000000000000000−2i2i2i−2i000000000000
χ4544-4-44i−4i4i−4i0000000000002-22i−2i2-22i−2i00000000000000000000000044-4-44i−4i4i−4i0000000000002-22i−2i2-22i−2i000000000000000000000000
χ4644-4-44i−4i4i−4i000000000000-22−2i2i-22−2i2i00000000000000000000000044-4-44i−4i4i−4i000000000000-22−2i2i-22−2i2i000000000000000000000000
χ4744-4-4−4i4i−4i4i0000000000002-2−2i2i2-2−2i2i00000000000000000000000044-4-4−4i4i−4i4i0000000000002-2−2i2i2-2−2i2i000000000000000000000000
χ4844-4-4−4i4i−4i4i000000000000-222i−2i-222i−2i00000000000000000000000044-4-4−4i4i−4i4i000000000000-222i−2i-222i−2i000000000000000000000000
χ494-44-44i−4i−4i4i0000000000002-22i−2i-22−2i2i0000000000000000000000004-44-44i−4i−4i4i0000000000002-22i−2i-22−2i2i000000000000000000000000
χ504-44-44i−4i−4i4i000000000000-22−2i2i2-22i−2i0000000000000000000000004-44-44i−4i−4i4i000000000000-22−2i2i2-22i−2i000000000000000000000000
χ514-44-4−4i4i4i−4i0000000000002-2−2i2i-222i−2i0000000000000000000000004-44-4−4i4i4i−4i0000000000002-2−2i2i-222i−2i000000000000000000000000
χ524-44-4−4i4i4i−4i000000000000-222i−2i2-2−2i2i0000000000000000000000004-44-4−4i4i4i−4i000000000000-222i−2i2-2−2i2i000000000000000000000000
χ531111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ5411111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111
χ551111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111
χ561111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ5711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ5811111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ5911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ6011111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ611-1-1111-1-11-1-111-1111-1-1-11111-1-1-1-111-1-1ii−i−i11-1-1ii−i−iii−i−iii−i−i-111-1-1-111-111-1-11-1-1-1111-1-1-1-11111-1-111−i−iii-1-111−i−iii−i−iii−i−iii
χ621-1-1111-1-11-1-111-1111-1-1-11111-1-1-1-111-1-1−i−iii11-1-1−i−iii−i−iii−i−iii-111-1-1-111-111-1-11-1-1-1111-1-1-1-11111-1-111ii−i−i-1-111ii−i−iii−i−iii−i−i
χ631-1-1111-1-11-1-111-1111-1-1-11111-1-1-1-1-1-111ii−i−i-1-111ii−i−i−i−iii−i−iii-111-1-1-111-111-1-11-1-1-1111-1-1-1-1111111-1-1−i−iii11-1-1−i−iiiii−i−iii−i−i
χ641-1-1111-1-11-1-111-1111-1-1-11111-1-1-1-1-1-111−i−iii-1-111−i−iiiii−i−iii−i−i-111-1-1-111-111-1-11-1-1-1111-1-1-1-1111111-1-1ii−i−i11-1-1ii−i−i−i−iii−i−iii
χ651-1-1111-1-11-1-111-1111-1-1-1-1-1-1-1111111-1-1ii−i−i-1-111−i−iiiii−i−i−i−iii-111-1-1-111-111-1-11-1-1-11111111-1-1-1-1-1-111−i−iii11-1-1ii−i−i−i−iiiii−i−i
χ661-1-1111-1-11-1-111-1111-1-1-1-1-1-1-1111111-1-1−i−iii-1-111ii−i−i−i−iiiii−i−i-111-1-1-111-111-1-11-1-1-11111111-1-1-1-1-1-111ii−i−i11-1-1−i−iiiii−i−i−i−iii
χ671-1-1111-1-11-1-111-1111-1-1-1-1-1-1-11111-1-111ii−i−i11-1-1−i−iii−i−iiiii−i−i-111-1-1-111-111-1-11-1-1-11111111-1-1-1-111-1-1−i−iii-1-111ii−i−iii−i−i−i−iii
χ681-1-1111-1-11-1-111-1111-1-1-1-1-1-1-11111-1-111−i−iii11-1-1ii−i−iii−i−i−i−iii-111-1-1-111-111-1-11-1-1-11111111-1-1-1-111-1-1ii−i−i-1-111−i−iii−i−iiiii−i−i
χ69222222222-2-2-2-222-2-22-2-2000000002i−2i2i−2i00000000000000000000-2-2-2-2-2-2-2-2-22222-2-222-22200000000−2i2i−2i2i00000000000000000000
χ70222222222-2-2-2-222-2-22-2-200000000−2i2i−2i2i00000000000000000000-2-2-2-2-2-2-2-2-22222-2-222-222000000002i−2i2i−2i00000000000000000000
χ7122222222-22-22-2-2-22-2-22-20000000000002i−2i2i−2i0000000000000000-2-2-2-2-2-2-2-22-22-2222-222-22000000000000−2i2i−2i2i0000000000000000
χ7222222222-22-22-2-2-22-2-22-2000000000000−2i2i−2i2i0000000000000000-2-2-2-2-2-2-2-22-22-2222-222-220000000000002i−2i2i−2i0000000000000000
χ7322222222-2-22-22-2-2-22-2-220000000000000000000000002-22-20000-2-2-2-2-2-2-2-222-22-2222-222-2000000000000000000000000-22-220000
χ7422222222-2-22-22-2-2-22-2-22000000000000000000000000-22-220000-2-2-2-2-2-2-2-222-22-2222-222-20000000000000000000000002-22-20000
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χ762222-2-2-2-2222222-2-2-2-2-2-20000000000000000000000000000−2i2i−2i2i-2-2-2-22222-2-2-2-2-2-222222200000000000000000000000000002i−2i2i−2i
χ772222-2-2-2-22-2-2-2-22-222-222000000000000000000002i−2i2i−2i00000000-2-2-2-22222-22222-22-2-22-2-200000000000000000000−2i2i−2i2i00000000
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χ792222-2-2-2-2-22-22-2-22-222-2200000000000000002i−2i2i−2i000000000000-2-2-2-222222-22-222-22-2-22-20000000000000000−2i2i−2i2i000000000000
χ802222-2-2-2-2-22-22-2-22-222-220000000000000000−2i2i−2i2i000000000000-2-2-2-222222-22-222-22-2-22-200000000000000002i−2i2i−2i000000000000
χ812222-2-2-2-2-2-22-22-222-222-222-2-222-2-2000000000000000000000000-2-2-2-2222222-22-22-2-22-2-22-2-222-2-222000000000000000000000000
χ822222-2-2-2-2-2-22-22-222-222-2-2-222-2-222000000000000000000000000-2-2-2-2222222-22-22-2-22-2-2222-2-222-2-2000000000000000000000000
χ832-2-2222-2-2222-2-2-22-2-2-222000000002i−2i−2i2i00000000000000000000-222-2-2-222-2-2-2222-2222-2-200000000−2i2i2i−2i00000000000000000000
χ842-2-2222-2-2222-2-2-22-2-2-22200000000−2i2i2i−2i00000000000000000000-222-2-2-222-2-2-2222-2222-2-2000000002i−2i−2i2i00000000000000000000
χ852-2-2222-2-2-22-2-222-2-2222-20000000000000000000000002i−2i−2i2i0000-222-2-2-2222-222-2-222-2-2-22000000000000000000000000−2i2i2i−2i0000
χ862-2-2222-2-2-22-2-222-2-2222-2000000000000000000000000−2i2i2i−2i0000-222-2-2-2222-222-2-222-2-2-220000000000000000000000002i−2i−2i2i0000
χ872-2-2222-2-2-2-222-22-22-22-220000000000002-2-220000000000000000-222-2-2-22222-2-22-22-22-22-2000000000000-222-20000000000000000
χ882-2-2222-2-2-2-222-22-22-22-22000000000000-222-20000000000000000-222-2-2-22222-2-22-22-22-22-20000000000002-2-220000000000000000
χ892-2-22-2-222222-2-2-2-2222-2-2000000000000000000002-2-2200000000-222-222-2-2-2-2-22222-2-2-22200000000000000000000-222-200000000
χ902-2-22-2-222222-2-2-2-2222-2-200000000000000000000-222-200000000-222-222-2-2-2-2-22222-2-2-222000000000000000000002-2-2200000000
χ912-2-22-2-2222-2-222-2-2-2-222200000000000000000000000000002-2-22-222-222-2-2-222-2-22222-2-2-20000000000000000000000000000-222-2
χ922-2-22-2-2222-2-222-2-2-2-22220000000000000000000000000000-222-2-222-222-2-2-222-2-22222-2-2-200000000000000000000000000002-2-22
χ932-2-22-2-222-22-2-22222-2-2-2222-2-2-2-222000000000000000000000000-222-222-2-22-222-2-2-2-2222-2-2-22222-2-2000000000000000000000000
χ942-2-22-2-222-22-2-22222-2-2-22-2-22222-2-2000000000000000000000000-222-222-2-22-222-2-2-2-2222-222-2-2-2-222000000000000000000000000
χ952-2-22-2-222-2-222-222-22-22-200000000000000002i−2i−2i2i000000000000-222-222-2-222-2-22-2-22-22-220000000000000000−2i2i2i−2i000000000000
χ962-2-22-2-222-2-222-222-22-22-20000000000000000−2i2i2i−2i000000000000-222-222-2-222-2-22-2-22-22-2200000000000000002i−2i−2i2i000000000000
χ9744-4-44i−4i4i−4i0000000000002-22i−2i2-22i−2i000000000000000000000000-4-444−4i4i−4i4i000000000000-22−2i2i-22−2i2i000000000000000000000000
χ9844-4-44i−4i4i−4i000000000000-22−2i2i-22−2i2i000000000000000000000000-4-444−4i4i−4i4i0000000000002-22i−2i2-22i−2i000000000000000000000000
χ9944-4-4−4i4i−4i4i0000000000002-2−2i2i2-2−2i2i000000000000000000000000-4-4444i−4i4i−4i000000000000-222i−2i-222i−2i000000000000000000000000
χ10044-4-4−4i4i−4i4i000000000000-222i−2i-222i−2i000000000000000000000000-4-4444i−4i4i−4i0000000000002-2−2i2i2-2−2i2i000000000000000000000000
χ1014-44-44i−4i−4i4i0000000000002-22i−2i-22−2i2i000000000000000000000000-44-44−4i4i4i−4i000000000000-22−2i2i2-22i−2i000000000000000000000000
χ1024-44-44i−4i−4i4i000000000000-22−2i2i2-22i−2i000000000000000000000000-44-44−4i4i4i−4i0000000000002-22i−2i-22−2i2i000000000000000000000000
χ1034-44-4−4i4i4i−4i0000000000002-2−2i2i-222i−2i000000000000000000000000-44-444i−4i−4i4i000000000000-222i−2i2-2−2i2i000000000000000000000000
χ1044-44-4−4i4i4i−4i000000000000-222i−2i2-2−2i2i000000000000000000000000-44-444i−4i−4i4i0000000000002-2−2i2i-222i−2i000000000000000000000000

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