Finite Group Databasebeta

← Group #357463

Character table — Group #357463

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111222222222222444444448888888888888888888888881111111122222222222244444444888888888888888888888888
order12222222222244444444444444442222444488888888888888882222222222224444444444444444222244448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
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
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ12111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222-2-2-2-222-2-222-2-222-2-222-2-200000000000000000000000022222222-2-2-2-222-2-222-2-222-2-222-2-2000000000000000000000000
χ1822222222-2-2-2-222-2-222-2-2-2-222-2-22200000000000000000000000022222222-2-2-2-222-2-222-2-2-2-222-2-222000000000000000000000000
χ1922222222-2-2-2-2-2-222-2-22222-2-2-2-22200000000000000000000000022222222-2-2-2-2-2-222-2-22222-2-2-2-222000000000000000000000000
χ2022222222-2-2-2-2-2-222-2-222-2-22222-2-200000000000000000000000022222222-2-2-2-2-2-222-2-222-2-22222-2-2000000000000000000000000
χ21222-2-2-2-2222-2-2222-2-2-22-200000000000000000000000000002i−2i2i−2i222-2-2-2-2222-2-2222-2-2-22-200000000000000000000000000002i−2i2i−2i
χ22222-2-2-2-2222-2-2222-2-2-22-20000000000000000000000000000−2i2i−2i2i222-2-2-2-2222-2-2222-2-2-22-20000000000000000000000000000−2i2i−2i2i
χ23222-2-2-2-2222-2-2-2-2-2222-2200000000000000000000000000002-2-22222-2-2-2-2222-2-2-2-2-2222-2200000000000000000000000000002-2-22
χ24222-2-2-2-2222-2-2-2-2-2222-220000000000000000000000000000-222-2222-2-2-2-2222-2-2-2-2-2222-220000000000000000000000000000-222-2
χ25222-2-2-2-22-2-22222-22-2-2-220000000000000000000000002i−2i2i−2i0000222-2-2-2-22-2-22222-22-2-2-220000000000000000000000002i−2i2i−2i0000
χ26222-2-2-2-22-2-22222-22-2-2-22000000000000000000000000−2i2i−2i2i0000222-2-2-2-22-2-22222-22-2-2-22000000000000000000000000−2i2i−2i2i0000
χ27222-2-2-2-22-2-222-2-22-2222-20000000000000000000000002-2-220000222-2-2-2-22-2-222-2-22-2222-20000000000000000000000002-2-220000
χ28222-2-2-2-22-2-222-2-22-2222-2000000000000000000000000-222-20000222-2-2-2-22-2-222-2-22-2222-2000000000000000000000000-222-20000
χ292-2-222-2-222-22-22-2222-2-2-2000000000000000000002i−2i2i−2i000000002-2-222-2-222-22-22-2222-2-2-2000000000000000000002i−2i2i−2i00000000
χ302-2-222-2-222-22-22-2222-2-2-200000000000000000000−2i2i−2i2i000000002-2-222-2-222-22-22-2222-2-2-200000000000000000000−2i2i−2i2i00000000
χ312-2-222-2-222-22-2-22-2-2-2222000000000000000000002-2-22000000002-2-222-2-222-22-2-22-2-2-2222000000000000000000002-2-2200000000
χ322-2-222-2-222-22-2-22-2-2-222200000000000000000000-222-2000000002-2-222-2-222-22-2-22-2-2-222200000000000000000000-222-200000000
χ332-2-222-2-22-22-222-2-2-22-22200000000000000002-22-20000000000002-2-222-2-22-22-222-2-2-22-22200000000000000002-22-2000000000000
χ342-2-222-2-22-22-222-2-2-22-2220000000000000000-22-220000000000002-2-222-2-22-22-222-2-2-22-2220000000000000000-22-22000000000000
χ352-2-222-2-22-22-22-2222-22-2-200000000000000002i−2i−2i2i0000000000002-2-222-2-22-22-22-2222-22-2-200000000000000002i−2i−2i2i000000000000
χ362-2-222-2-22-22-22-2222-22-2-20000000000000000−2i2i2i−2i0000000000002-2-222-2-22-22-22-2222-22-2-20000000000000000−2i2i2i−2i000000000000
χ372-2-2-2-22222-2-222-22-2-22-22000000002-22-2000000000000000000002-2-2-2-22222-2-222-22-2-22-22000000002-22-200000000000000000000
χ382-2-2-2-22222-2-222-22-2-22-2200000000-22-22000000000000000000002-2-2-2-22222-2-222-22-2-22-2200000000-22-2200000000000000000000
χ392-2-2-2-22222-2-22-22-222-22-2000000002-2-22000000000000000000002-2-2-2-22222-2-22-22-222-22-2000000002-2-2200000000000000000000
χ402-2-2-2-22222-2-22-22-222-22-200000000-222-2000000000000000000002-2-2-2-22222-2-22-22-222-22-200000000-222-200000000000000000000
χ412-2-2-2-2222-222-22-2-22-222-20000000000002-22-200000000000000002-2-2-2-2222-222-22-2-22-222-20000000000002-22-20000000000000000
χ422-2-2-2-2222-222-22-2-22-222-2000000000000-22-2200000000000000002-2-2-2-2222-222-22-2-22-222-2000000000000-22-220000000000000000
χ432-2-2-2-2222-222-2-222-22-2-220000000000002-2-2200000000000000002-2-2-2-2222-222-2-222-22-2-220000000000002-2-220000000000000000
χ442-2-2-2-2222-222-2-222-22-2-22000000000000-222-200000000000000002-2-2-2-2222-222-2-222-22-2-22000000000000-222-20000000000000000
χ4544-44-44-4-40000000000000000004i−4i00000000000000000000000044-44-44-4-40000000000000000004i−4i000000000000000000000000
χ4644-44-44-4-4000000000000000000−4i4i00000000000000000000000044-44-44-4-4000000000000000000−4i4i000000000000000000000000
χ4744-4-44-44-40000000000004i−4i00000000000000000000000000000044-4-44-44-40000000000004i−4i000000000000000000000000000000
χ4844-4-44-44-4000000000000−4i4i00000000000000000000000000000044-4-44-44-4000000000000−4i4i000000000000000000000000000000
χ494-444-4-44-4000000000000004i−4i00000000000000000000000000004-444-4-44-4000000000000004i−4i0000000000000000000000000000
χ504-444-4-44-400000000000000−4i4i00000000000000000000000000004-444-4-44-400000000000000−4i4i0000000000000000000000000000
χ514-44-444-4-400000000000000004i−4i000000000000000000000000004-44-444-4-400000000000000004i−4i00000000000000000000000000
χ524-44-444-4-40000000000000000−4i4i000000000000000000000000004-44-444-4-40000000000000000−4i4i00000000000000000000000000
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
χ54111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ551111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111
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
χ5711111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111
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
χ6011111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ61111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-111−i−iii−i−iii−i−iii−i−iii
χ62111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-111ii−i−iii−i−iii−i−iii−i−i
χ63111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111ii−i−iii−i−i−i−iii−i−iii-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1−i−iii−i−iiiii−i−iii−i−i
χ64111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111−i−iii−i−iiiii−i−iii−i−i-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1ii−i−iii−i−i−i−iii−i−iii
χ65111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i
χ66111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iii
χ67111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111−i−iiiii−i−iii−i−i−i−iii
χ68111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-111ii−i−i−i−iii−i−iiiii−i−i
χ6922222222-2-2-2-222-2-222-2-222-2-222-2-2000000000000000000000000-2-2-2-2-2-2-2-22222-2-222-2-222-2-222-2-222000000000000000000000000
χ7022222222-2-2-2-222-2-222-2-2-2-222-2-222000000000000000000000000-2-2-2-2-2-2-2-22222-2-222-2-22222-2-222-2-2000000000000000000000000
χ7122222222-2-2-2-2-2-222-2-22222-2-2-2-222000000000000000000000000-2-2-2-2-2-2-2-2222222-2-222-2-2-2-22222-2-2000000000000000000000000
χ7222222222-2-2-2-2-2-222-2-222-2-22222-2-2000000000000000000000000-2-2-2-2-2-2-2-2222222-2-222-2-222-2-2-2-222000000000000000000000000
χ73222-2-2-2-2222-2-2222-2-2-22-200000000000000000000000000002i−2i2i−2i-2-2-22222-2-2-222-2-2-2222-220000000000000000000000000000−2i2i−2i2i
χ74222-2-2-2-2222-2-2222-2-2-22-20000000000000000000000000000−2i2i−2i2i-2-2-22222-2-2-222-2-2-2222-2200000000000000000000000000002i−2i2i−2i
χ75222-2-2-2-2222-2-2-2-2-2222-2200000000000000000000000000002-2-22-2-2-22222-2-2-222222-2-2-22-20000000000000000000000000000-222-2
χ76222-2-2-2-2222-2-2-2-2-2222-220000000000000000000000000000-222-2-2-2-22222-2-2-222222-2-2-22-200000000000000000000000000002-2-22
χ77222-2-2-2-22-2-22222-22-2-2-220000000000000000000000002i−2i2i−2i0000-2-2-22222-222-2-2-2-22-2222-2000000000000000000000000−2i2i−2i2i0000
χ78222-2-2-2-22-2-22222-22-2-2-22000000000000000000000000−2i2i−2i2i0000-2-2-22222-222-2-2-2-22-2222-20000000000000000000000002i−2i2i−2i0000
χ79222-2-2-2-22-2-222-2-22-2222-20000000000000000000000002-2-220000-2-2-22222-222-2-222-22-2-2-22000000000000000000000000-222-20000
χ80222-2-2-2-22-2-222-2-22-2222-2000000000000000000000000-222-20000-2-2-22222-222-2-222-22-2-2-220000000000000000000000002-2-220000
χ812-2-222-2-222-22-22-2222-2-2-2000000000000000000002i−2i2i−2i00000000-222-2-222-2-22-22-22-2-2-222200000000000000000000−2i2i−2i2i00000000
χ822-2-222-2-222-22-22-2222-2-2-200000000000000000000−2i2i−2i2i00000000-222-2-222-2-22-22-22-2-2-2222000000000000000000002i−2i2i−2i00000000
χ832-2-222-2-222-22-2-22-2-2-2222000000000000000000002-2-2200000000-222-2-222-2-22-222-2222-2-2-200000000000000000000-222-200000000
χ842-2-222-2-222-22-2-22-2-2-222200000000000000000000-222-200000000-222-2-222-2-22-222-2222-2-2-2000000000000000000002-2-2200000000
χ852-2-222-2-22-22-222-2-2-22-22200000000000000002-22-2000000000000-222-2-222-22-22-2-2222-22-2-20000000000000000-22-22000000000000
χ862-2-222-2-22-22-222-2-2-22-2220000000000000000-22-22000000000000-222-2-222-22-22-2-2222-22-2-200000000000000002-22-2000000000000
χ872-2-222-2-22-22-22-2222-22-2-200000000000000002i−2i−2i2i000000000000-222-2-222-22-22-22-2-2-22-2220000000000000000−2i2i2i−2i000000000000
χ882-2-222-2-22-22-22-2222-22-2-20000000000000000−2i2i2i−2i000000000000-222-2-222-22-22-22-2-2-22-22200000000000000002i−2i−2i2i000000000000
χ892-2-2-2-22222-2-222-22-2-22-22000000002-22-200000000000000000000-22222-2-2-2-222-2-22-222-22-200000000-22-2200000000000000000000
χ902-2-2-2-22222-2-222-22-2-22-2200000000-22-2200000000000000000000-22222-2-2-2-222-2-22-222-22-2000000002-22-200000000000000000000
χ912-2-2-2-22222-2-22-22-222-22-2000000002-2-2200000000000000000000-22222-2-2-2-222-22-22-2-22-2200000000-222-200000000000000000000
χ922-2-2-2-22222-2-22-22-222-22-200000000-222-200000000000000000000-22222-2-2-2-222-22-22-2-22-22000000002-2-2200000000000000000000
χ932-2-2-2-2222-222-22-2-22-222-20000000000002-22-20000000000000000-22222-2-2-22-2-22-222-22-2-22000000000000-22-220000000000000000
χ942-2-2-2-2222-222-22-2-22-222-2000000000000-22-220000000000000000-22222-2-2-22-2-22-222-22-2-220000000000002-22-20000000000000000
χ952-2-2-2-2222-222-2-222-22-2-220000000000002-2-220000000000000000-22222-2-2-22-2-222-2-22-222-2000000000000-222-20000000000000000
χ962-2-2-2-2222-222-2-222-22-2-22000000000000-222-20000000000000000-22222-2-2-22-2-222-2-22-222-20000000000002-2-220000000000000000
χ9744-44-44-4-40000000000000000004i−4i000000000000000000000000-4-44-44-444000000000000000000−4i4i000000000000000000000000
χ9844-44-44-4-4000000000000000000−4i4i000000000000000000000000-4-44-44-4440000000000000000004i−4i000000000000000000000000
χ9944-4-44-44-40000000000004i−4i000000000000000000000000000000-4-444-44-44000000000000−4i4i000000000000000000000000000000
χ10044-4-44-44-4000000000000−4i4i000000000000000000000000000000-4-444-44-440000000000004i−4i000000000000000000000000000000
χ1014-444-4-44-4000000000000004i−4i0000000000000000000000000000-44-4-444-4400000000000000−4i4i0000000000000000000000000000
χ1024-444-4-44-400000000000000−4i4i0000000000000000000000000000-44-4-444-44000000000000004i−4i0000000000000000000000000000
χ1034-44-444-4-400000000000000004i−4i00000000000000000000000000-44-44-4-4440000000000000000−4i4i00000000000000000000000000
χ1044-44-444-4-40000000000000000−4i4i00000000000000000000000000-44-44-4-44400000000000000004i−4i00000000000000000000000000

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