Finite Group Databasebeta

← Group #72342845

Character table — Group #72342845

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122
size1111222222444444444444888888888888888888888888888888881616161616161616161616161616161616161616161616161616161616161616161616161616161632323232323232323232323232323232323232323232646464646464
order12442224442222224444442222444488888888888888888888888822222244444444444444888888888888888888884444444444444488888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-11111-1-11111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ611111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111111111-1-1-1-1
χ9111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ10111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111
χ11111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111-1-1111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ12111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1
χ13111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ14111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ15111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ16111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
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χ1811-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i−i−iii1-11-1-111-11-1-1111-1-1-1-111i−i−iiii−i−iii−i−iii−i−i−i−iii1-111-1-1-1-111-1-111ii−i−i−i−iii−ii−ii-11
χ1911-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iiiii−i−i1-1-111-11-1-111-1-1-11111-1-1−iii−iii−i−iii−i−i−i−iiiii−i−i1-1-1-11111-1-1-1-111−i−iiiii−i−i−ii−ii-11
χ2011-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii1-1-11-111-1-11-11-1-111-1-111−ii−iiii−i−iii−i−i−i−iii−i−iii1-1-1-111-1-11111-1-1−i−iii−i−iiii−ii−i1-1
χ2111-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−iii−i−i-111-1-11-111-1-1111-1-1-1-111i−ii−iii−i−i−i−iiiii−i−iii−i−i-11-1-11111-1-111-1-1−i−iii−i−iiii−i−ii-11
χ2211-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-111-11-1-111-11-111-1-111-1-1i−i−iiii−i−i−i−iiiii−i−i−i−iii-11-1-111-1-111-1-111−i−iiiii−i−i−iii−i1-1
χ2311-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-11-11-11-11-11-11-1-111-1-111−iii−iii−i−i−i−iii−i−iiiii−i−i-1111-1-111-1-1-1-111ii−i−i−i−iii−iii−i1-1
χ2411-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iii−i−iii-11-111-1-11-111-1-1-11111-1-1−ii−iiii−i−i−i−iii−i−iii−i−iii-1111-1-1-1-11111-1-1ii−i−iii−i−ii−i−ii-11
χ2511-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−iii−i−i-11-111-1-11-111-1-1-11111-1-1i−ii−i−i−iiiii−i−iii−i−iii−i−i-1111-1-1-1-11111-1-1−i−iii−i−iii−iii−i-11
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χ2811-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iii−i−iii-111-1-11-111-1-1111-1-1-1-111−ii−ii−i−iiiii−i−i−i−iii−i−iii-11-1-11111-1-111-1-1ii−i−iii−i−i−iii−i-11
χ2911-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i1-1-11-111-1-11-11-1-111-1-111i−ii−i−i−iii−i−iiiii−i−iii−i−i1-1-1-111-1-11111-1-1ii−i−iii−i−i−ii−ii1-1
χ3011-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−iii1-1-111-11-1-111-1-1-11111-1-1i−i−ii−i−iii−i−iiiii−i−i−i−iii1-1-1-11111-1-1-1-111ii−i−i−i−iiii−ii−i-11
χ3111-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iiiii−i−i1-11-1-111-11-1-1111-1-1-1-111−iii−i−i−iii−i−iii−i−iiiii−i−i1-111-1-1-1-111-1-111−i−iiiii−i−ii−ii−i-11
χ3211-1-1111-1-1-1111111-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii1-11-11-11-11-11-111-1-111-1-1−ii−ii−i−iii−i−iii−i−iii−i−iii1-111-1-111-1-111-1-1−i−iii−i−iii−ii−ii1-1
χ3322222222222222-2-22222-2-22-2-2-2-2-22-20000000022-2-222-2-22222000000000000000000000000220000002-22-2-2-2-2-20000002-22-20000000000000000000000
χ3422222222222222-2-22222-2-22-2-2-2-2-22-20000000022-2-222-2-2-2-2-2-2000000000000000000000000-2-20000002-22-22222000000-22-220000000000000000000000
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χ37222222222222-2-22222-2-222-22-2-2-2-2-2222-2-222-2-200000000000022220000000000000000000000222-22-200000000-2-2-2-20000002-22-2000000000000000000
χ38222222222222-2-22222-2-222-22-2-2-2-2-2222-2-222-2-2000000000000-2-2-2-20000000000000000000000-2-22-22-2000000002222000000-22-22000000000000000000
χ39222222222222-2-22222-2-222-22-2-2-2-2-22-2-222-2-2220000000000002222000000000000000000000022-22-2200000000-2-2-2-2000000-22-22000000000000000000
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χ412222222222-2-22222-2-22222-2-22-22-2-2-2222222222222222200000000220000220000000000000000-2-2-2-2-2-2-2-200000000-2-200000000000000000000000000
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χ472222222222-2-222-2-2-2-222-2-2-22-22-22-2200000000-2-222-2-22200000000002200002200-2-2-2-20000000000002-22-20000000000000000000000-22-220000000000
χ482222222222-2-222-2-2-2-222-2-2-22-22-22-2200000000-2-222-2-2220000000000-2-20000-2-20022220000000000002-22-200000000000000000000002-22-20000000000
χ492222222222-2-2-2-222-2-2-2-2222-2-22-222-222-2-222-2-200000000000000000000220000220000-2-2-2-20000-22-220000000000000000000000000000002-22-2000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.