Finite Group Databasebeta

← Group #357487

Character table — Group #357487

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222222222444444448888888888888888888888881111111122222222222244444444888888888888888888888888
order12222222222244444444444444442222444444444444888888882222222222224444444444444444222244444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ31111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ41111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ911-1-1-11-1111-1-11111-1-1-1-1iiii−i−i−i−i1-11-111-1-1ii−i−i1-11-1ii−i−iii−i−i11-1-1-11-1111-1-11111-1-1-1-1iiii−i−i−i−i1-11-111-1-1ii−i−i1-11-1ii−i−iii−i−i
χ1011-1-1-11-1111-1-11111-1-1-1-1iiii−i−i−i−i1-1-11-1-111−i−iii1-1-11ii−i−i−i−iii11-1-1-11-1111-1-11111-1-1-1-1iiii−i−i−i−i1-1-11-1-111−i−iii1-1-11ii−i−i−i−iii
χ1111-1-1-11-1111-1-11111-1-1-1-1iiii−i−i−i−i-111-1-1-111−i−iii-111-1−i−iiiii−i−i11-1-1-11-1111-1-11111-1-1-1-1iiii−i−i−i−i-111-1-1-111−i−iii-111-1−i−iiiii−i−i
χ1211-1-1-11-1111-1-11111-1-1-1-1iiii−i−i−i−i-11-1111-1-1ii−i−i-11-11−i−iii−i−iii11-1-1-11-1111-1-11111-1-1-1-1iiii−i−i−i−i-11-1111-1-1ii−i−i-11-11−i−iii−i−iii
χ1311-1-1-11-1111-1-11111-1-1-1-1−i−i−i−iiiii1-11-111-1-1−i−iii1-11-1−i−iii−i−iii11-1-1-11-1111-1-11111-1-1-1-1−i−i−i−iiiii1-11-111-1-1−i−iii1-11-1−i−iii−i−iii
χ1411-1-1-11-1111-1-11111-1-1-1-1−i−i−i−iiiii1-1-11-1-111ii−i−i1-1-11−i−iiiii−i−i11-1-1-11-1111-1-11111-1-1-1-1−i−i−i−iiiii1-1-11-1-111ii−i−i1-1-11−i−iiiii−i−i
χ1511-1-1-11-1111-1-11111-1-1-1-1−i−i−i−iiiii-111-1-1-111ii−i−i-111-1ii−i−i−i−iii11-1-1-11-1111-1-11111-1-1-1-1−i−i−i−iiiii-111-1-1-111ii−i−i-111-1ii−i−i−i−iii
χ1611-1-1-11-1111-1-11111-1-1-1-1−i−i−i−iiiii-11-1111-1-1−i−iii-11-11ii−i−iii−i−i11-1-1-11-1111-1-11111-1-1-1-1−i−i−i−iiiii-11-1111-1-1−i−iii-11-11ii−i−iii−i−i
χ17222222222222-2-2-2-2-2-2-2-20000000000002-22-20000000000000000222222222222-2-2-2-2-2-2-2-20000000000002-22-20000000000000000
χ18222222222222-2-2-2-2-2-2-2-2000000000000-22-220000000000000000222222222222-2-2-2-2-2-2-2-2000000000000-22-220000000000000000
χ1922222222-2-2-2-222-2-22-22-20000000000220000000000-2-20000000022222222-2-2-2-222-2-22-22-20000000000220000000000-2-200000000
χ2022222222-2-2-2-222-2-22-22-20000000000-2-20000000000220000000022222222-2-2-2-222-2-22-22-20000000000-2-200000000002200000000
χ2122222222-2-2-2-2-2-222-22-2200000000220000000000-2-2000000000022222222-2-2-2-2-2-222-22-2200000000220000000000-2-20000000000
χ2222222222-2-2-2-2-2-222-22-2200000000-2-2000000000022000000000022222222-2-2-2-2-2-222-22-2200000000-2-20000000000220000000000
χ2322-2-2-22-2222-2-2-2-2-2-222220000000000002-2-22000000000000000022-2-2-22-2222-2-2-2-2-2-222220000000000002-2-220000000000000000
χ2422-2-2-22-2222-2-2-2-2-2-22222000000000000-222-2000000000000000022-2-2-22-2222-2-2-2-2-2-22222000000000000-222-20000000000000000
χ2522-2-2-22-22-2-22222-2-2-22-2200000000002-20000000000-220000000022-2-2-22-22-2-22222-2-2-22-2200000000002-20000000000-2200000000
χ2622-2-2-22-22-2-22222-2-2-22-220000000000-2200000000002-20000000022-2-2-22-22-2-22222-2-2-22-220000000000-2200000000002-200000000
χ2722-2-2-22-22-2-222-2-2222-22-2000000002-20000000000-22000000000022-2-2-22-22-2-222-2-2222-22-2000000002-20000000000-220000000000
χ2822-2-2-22-22-2-222-2-2222-22-200000000-2200000000002-2000000000022-2-2-22-22-2-222-2-2222-22-200000000-2200000000002-20000000000
χ292-222-2-2-222-22-22-22-22-2-220000000000000000000000002i−2i2i−2i00002-222-2-2-222-22-22-22-22-2-220000000000000000000000002i−2i2i−2i0000
χ302-222-2-2-222-22-22-22-22-2-22000000000000000000000000−2i2i−2i2i00002-222-2-2-222-22-22-22-22-2-22000000000000000000000000−2i2i−2i2i0000
χ312-222-2-2-222-22-2-22-22-222-200000000000000000000000000002i−2i2i−2i2-222-2-2-222-22-2-22-22-222-200000000000000000000000000002i−2i2i−2i
χ322-222-2-2-222-22-2-22-22-222-20000000000000000000000000000−2i2i−2i2i2-222-2-2-222-22-2-22-22-222-20000000000000000000000000000−2i2i−2i2i
χ332-222-2-2-22-22-222-2-2222-2-200000000000000002i−2i2i−2i0000000000002-222-2-2-22-22-222-2-2222-2-200000000000000002i−2i2i−2i000000000000
χ342-222-2-2-22-22-222-2-2222-2-20000000000000000−2i2i−2i2i0000000000002-222-2-2-22-22-222-2-2222-2-20000000000000000−2i2i−2i2i000000000000
χ352-222-2-2-22-22-22-222-2-2-22222-2-222-2-20000000000000000000000002-222-2-2-22-22-22-222-2-2-22222-2-222-2-2000000000000000000000000
χ362-222-2-2-22-22-22-222-2-2-222-2-222-2-2220000000000000000000000002-222-2-2-22-22-22-222-2-2-222-2-222-2-222000000000000000000000000
χ372-2-2-22-2222-2-222-22-2-222-20000000000000000000000002-2-2200002-2-2-22-2222-2-222-22-2-222-20000000000000000000000002-2-220000
χ382-2-2-22-2222-2-222-22-2-222-2000000000000000000000000-222-200002-2-2-22-2222-2-222-22-2-222-2000000000000000000000000-222-20000
χ392-2-2-22-2222-2-22-22-222-2-2200000000000000000000000000002-2-222-2-2-22-2222-2-22-22-222-2-2200000000000000000000000000002-2-22
χ402-2-2-22-2222-2-22-22-222-2-220000000000000000000000000000-222-22-2-2-22-2222-2-22-22-222-2-220000000000000000000000000000-222-2
χ412-2-2-22-222-222-22-2-22-2-22200000000000000002-2-220000000000002-2-2-22-222-222-22-2-22-2-22200000000000000002-2-22000000000000
χ422-2-2-22-222-222-22-2-22-2-2220000000000000000-222-20000000000002-2-2-22-222-222-22-2-22-2-2220000000000000000-222-2000000000000
χ432-2-2-22-222-222-2-222-222-2-22i2i−2i−2i−2i−2i2i2i0000000000000000000000002-2-2-22-222-222-2-222-222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ442-2-2-22-222-222-2-222-222-2-2−2i−2i2i2i2i2i−2i−2i0000000000000000000000002-2-2-22-222-222-2-222-222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ45444-44-4-4-40000000000002-22-22-22-2000000000000000000000000444-44-4-4-40000000000002-22-22-22-2000000000000000000000000
χ46444-44-4-4-4000000000000-22-22-22-22000000000000000000000000444-44-4-4-4000000000000-22-22-22-22000000000000000000000000
χ4744-44-4-44-40000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000000044-44-4-44-40000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ4844-44-4-44-4000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000000044-44-4-44-4000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ494-44-4-444-40000000000002-2-222-2-220000000000000000000000004-44-4-444-40000000000002-2-222-2-22000000000000000000000000
χ504-44-4-444-4000000000000-222-2-222-20000000000000000000000004-44-4-444-4000000000000-222-2-222-2000000000000000000000000
χ514-4-4444-4-40000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000004-4-4444-4-40000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ524-4-4444-4-4000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000004-4-4444-4-4000000000000−2i2i2i−2i2i−2i−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
χ54111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111
χ551111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-11111-1-1-1-1
χ561111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111
χ5711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ5811111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1111111-1-1-1-1
χ5911111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1-1-11111
χ6011111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111-1-1-11-1111-1-11111-1-1-1-1iiii−i−i−i−i1-11-111-1-1ii−i−i1-11-1ii−i−iii−i−i-1-1111-11-1-1-111-1-1-1-11111−i−i−i−iiiii-11-11-1-111−i−iii-11-11−i−iii−i−iii
χ6211-1-1-11-1111-1-11111-1-1-1-1iiii−i−i−i−i1-1-11-1-111−i−iii1-1-11ii−i−i−i−iii-1-1111-11-1-1-111-1-1-1-11111−i−i−i−iiiii-111-111-1-1ii−i−i-111-1−i−iiiii−i−i
χ6311-1-1-11-1111-1-11111-1-1-1-1iiii−i−i−i−i-111-1-1-111−i−iii-111-1−i−iiiii−i−i-1-1111-11-1-1-111-1-1-1-11111−i−i−i−iiiii1-1-1111-1-1ii−i−i1-1-11ii−i−i−i−iii
χ6411-1-1-11-1111-1-11111-1-1-1-1iiii−i−i−i−i-11-1111-1-1ii−i−i-11-11−i−iii−i−iii-1-1111-11-1-1-111-1-1-1-11111−i−i−i−iiiii1-11-1-1-111−i−iii1-11-1ii−i−iii−i−i
χ6511-1-1-11-1111-1-11111-1-1-1-1−i−i−i−iiiii1-11-111-1-1−i−iii1-11-1−i−iii−i−iii-1-1111-11-1-1-111-1-1-1-11111iiii−i−i−i−i-11-11-1-111ii−i−i-11-11ii−i−iii−i−i
χ6611-1-1-11-1111-1-11111-1-1-1-1−i−i−i−iiiii1-1-11-1-111ii−i−i1-1-11−i−iiiii−i−i-1-1111-11-1-1-111-1-1-1-11111iiii−i−i−i−i-111-111-1-1−i−iii-111-1ii−i−i−i−iii
χ6711-1-1-11-1111-1-11111-1-1-1-1−i−i−i−iiiii-111-1-1-111ii−i−i-111-1ii−i−i−i−iii-1-1111-11-1-1-111-1-1-1-11111iiii−i−i−i−i1-1-1111-1-1−i−iii1-1-11−i−iiiii−i−i
χ6811-1-1-11-1111-1-11111-1-1-1-1−i−i−i−iiiii-11-1111-1-1−i−iii-11-11ii−i−iii−i−i-1-1111-11-1-1-111-1-1-1-11111iiii−i−i−i−i1-11-1-1-111ii−i−i1-11-1−i−iii−i−iii
χ69222222222222-2-2-2-2-2-2-2-20000000000002-22-20000000000000000-2-2-2-2-2-2-2-2-2-2-2-222222222000000000000-22-220000000000000000
χ70222222222222-2-2-2-2-2-2-2-2000000000000-22-220000000000000000-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000002-22-20000000000000000
χ7122222222-2-2-2-222-2-22-22-20000000000220000000000-2-200000000-2-2-2-2-2-2-2-22222-2-222-22-220000000000-2-200000000002200000000
χ7222222222-2-2-2-222-2-22-22-20000000000-2-200000000002200000000-2-2-2-2-2-2-2-22222-2-222-22-220000000000220000000000-2-200000000
χ7322222222-2-2-2-2-2-222-22-2200000000220000000000-2-20000000000-2-2-2-2-2-2-2-2222222-2-22-22-200000000-2-20000000000220000000000
χ7422222222-2-2-2-2-2-222-22-2200000000-2-20000000000220000000000-2-2-2-2-2-2-2-2222222-2-22-22-200000000220000000000-2-20000000000
χ7522-2-2-22-2222-2-2-2-2-2-222220000000000002-2-220000000000000000-2-2222-22-2-2-2222222-2-2-2-2000000000000-222-20000000000000000
χ7622-2-2-22-2222-2-2-2-2-2-22222000000000000-222-20000000000000000-2-2222-22-2-2-2222222-2-2-2-20000000000002-2-220000000000000000
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χ7822-2-2-22-22-2-22222-2-2-22-220000000000-2200000000002-200000000-2-2222-22-222-2-2-2-2222-22-200000000002-20000000000-2200000000
χ7922-2-2-22-22-2-222-2-2222-22-2000000002-20000000000-220000000000-2-2222-22-222-2-222-2-2-22-2200000000-2200000000002-20000000000
χ8022-2-2-22-22-2-222-2-2222-22-200000000-2200000000002-20000000000-2-2222-22-222-2-222-2-2-22-22000000002-20000000000-220000000000
χ812-222-2-2-222-22-22-22-22-2-220000000000000000000000002i−2i2i−2i0000-22-2-2222-2-22-22-22-22-222-2000000000000000000000000−2i2i−2i2i0000
χ822-222-2-2-222-22-22-22-22-2-22000000000000000000000000−2i2i−2i2i0000-22-2-2222-2-22-22-22-22-222-20000000000000000000000002i−2i2i−2i0000
χ832-222-2-2-222-22-2-22-22-222-200000000000000000000000000002i−2i2i−2i-22-2-2222-2-22-222-22-22-2-220000000000000000000000000000−2i2i−2i2i
χ842-222-2-2-222-22-2-22-22-222-20000000000000000000000000000−2i2i−2i2i-22-2-2222-2-22-222-22-22-2-2200000000000000000000000000002i−2i2i−2i
χ852-222-2-2-22-22-222-2-2222-2-200000000000000002i−2i2i−2i000000000000-22-2-2222-22-22-2-222-2-2-2220000000000000000−2i2i−2i2i000000000000
χ862-222-2-2-22-22-222-2-2222-2-20000000000000000−2i2i−2i2i000000000000-22-2-2222-22-22-2-222-2-2-22200000000000000002i−2i2i−2i000000000000
χ872-222-2-2-22-22-22-222-2-2-22222-2-222-2-2000000000000000000000000-22-2-2222-22-22-22-2-2222-2-2-2-222-2-222000000000000000000000000
χ882-222-2-2-22-22-22-222-2-2-222-2-222-2-222000000000000000000000000-22-2-2222-22-22-22-2-2222-2-222-2-222-2-2000000000000000000000000
χ892-2-2-22-2222-2-222-22-2-222-20000000000000000000000002-2-220000-2222-22-2-2-222-2-22-222-2-22000000000000000000000000-222-20000
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χ912-2-2-22-2222-2-22-22-222-2-2200000000000000000000000000002-2-22-2222-22-2-2-222-22-22-2-222-20000000000000000000000000000-222-2
χ922-2-2-22-2222-2-22-22-222-2-220000000000000000000000000000-222-2-2222-22-2-2-222-22-22-2-222-200000000000000000000000000002-2-22
χ932-2-2-22-222-222-22-2-22-2-22200000000000000002-2-22000000000000-2222-22-2-22-2-22-222-222-2-20000000000000000-222-2000000000000
χ942-2-2-22-222-222-22-2-22-2-2220000000000000000-222-2000000000000-2222-22-2-22-2-22-222-222-2-200000000000000002-2-22000000000000
χ952-2-2-22-222-222-2-222-222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000000000-2222-22-2-22-2-222-2-22-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ962-2-2-22-222-222-2-222-222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000-2222-22-2-22-2-222-2-22-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ97444-44-4-4-40000000000002-22-22-22-2000000000000000000000000-4-4-44-4444000000000000-22-22-22-22000000000000000000000000
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χ9944-44-4-44-40000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000-4-44-444-44000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ10044-44-4-44-4000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000-4-44-444-440000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ1014-44-4-444-40000000000002-2-222-2-22000000000000000000000000-44-444-4-44000000000000-222-2-222-2000000000000000000000000
χ1024-44-4-444-4000000000000-222-2-222-2000000000000000000000000-44-444-4-440000000000002-2-222-2-22000000000000000000000000
χ1034-4-4444-4-40000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000-444-4-4-444000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ1044-4-4444-4-4000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000000-444-4-4-4440000000000002i−2i−2i2i−2i2i2i−2i000000000000000000000000

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