Finite Group Databasebeta

← Group #72342849

Character table — Group #72342849

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122
size1111222222444444444444888888888888888888888888888888881616161616161616161616161616161616161616161616161616161616161616161616161616161632323232323232323232323232323232323232323232646464646464
order12442224442222224444442222222222444444444488888888888824444444448888888888888888888888888888884444444444448888888888448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ511111111111111111111111111111-1-11111111-1-111111111111111-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ611111111111111111111111111111-1-11111111-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111
χ711111111111111111111111111111-1-11111111-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ811111111111111111111111111111-1-11111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-111-1-1
χ91111111111111111111111111-1-1-1-111111-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ101111111111111111111111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ111111111111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-111
χ121111111111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1
χ131111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-11111
χ141111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-11111111111-1-1-1-1
χ151111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1
χ161111111111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ1711-1-1111-1-1-1111111-1-1-1-1-1-11-1-111-1-11111-111-1-1-1-11-1iiii−i−i−i−iii−i−i1-111-1-111-1-1ii−i−iii−i−ii−iii−i−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-111-1-1i−iii−i−iii−i−i1-1i−i1-1
χ1811-1-1111-1-1-1111111-1-1-1-1-1-11-1-111-1-11111-111-1-1-1-11-1iiii−i−i−i−i−i−iii1-111-1-111-1-1ii−i−iii−i−i−ii−i−iiiii−i−iii−i−i−i−iii−i−iii11-1-1-1-111-1-111i−iii−i−i−i−iii-11−ii-11
χ1911-1-1111-1-1-1111111-1-1-1-1-1-11-1-111-1-11111-111-1-1-1-11-1−i−i−i−iiiiiii−i−i1-111-1-111-1-1−i−iii−i−iiii−iii−i−i−i−iii−i−iiiii−i−iii−i−i11-1-1-1-111-1-111−ii−i−iiiii−i−i-11i−i-11
χ2011-1-1111-1-1-1111111-1-1-1-1-1-11-1-111-1-11111-111-1-1-1-11-1−i−i−i−iiiii−i−iii1-111-1-111-1-1−i−iii−i−iii−ii−i−iii−i−iii−i−iii−i−iii−i−iii11-1-111-1-111-1-1−ii−i−iii−i−iii1-1−ii1-1
χ2111-1-1111-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-111-111-1-1111-1iiii−i−i−i−iii−i−i-1111-1-1-1-111ii−i−i−i−iiii−iii−i−iii−i−i−i−iiiii−i−iii−i−i-1-11111-1-111-1-1i−i−i−iii−i−iii-11−ii-11
χ2211-1-1111-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-111-111-1-1111-1iiii−i−i−i−i−i−iii-1111-1-1-1-111ii−i−i−i−iii−ii−i−iiiii−i−i−i−iii−i−iii−i−iii-1-111-1-111-1-111i−i−i−iiiii−i−i1-1i−i1-1
χ2311-1-1111-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-111-111-1-1111-1−i−i−i−iiiiiii−i−i-1111-1-1-1-111−i−iiiii−i−ii−iii−i−i−i−iiiii−i−iii−i−iii−i−i-1-111-1-111-1-111−iiii−i−i−i−iii1-1−ii1-1
χ2411-1-1111-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-111-111-1-1111-1−i−i−i−iiiii−i−iii-1111-1-1-1-111−i−iiiii−i−i−ii−i−iii−i−iiiii−i−i−i−iii−i−iii-1-11111-1-111-1-1−iiii−i−iii−i−i-11i−i-11
χ2511-1-1111-1-1-1111111-1-1-1-1-1-11-1-1-1-1111111-1-1-111-1-11-1iiii−i−i−i−iii−i−i1-1-1-11111-1-1−i−iiiii−i−ii−i−i−iiiii−i−iii−i−iii−i−i−i−iii-1-11111-1-1-1-111−ii−i−iiiii−i−i1-1−ii-11
χ2611-1-1111-1-1-1111111-1-1-1-1-1-11-1-1-1-1111111-1-1-111-1-11-1iiii−i−i−i−i−i−iii1-1-1-11111-1-1−i−iiiii−i−i−iiii−i−iii−i−iii−i−i−i−iiiii−i−i-1-111-1-11111-1-1−ii−i−iii−i−iii-11i−i1-1
χ2711-1-1111-1-1-1111111-1-1-1-1-1-11-1-1-1-1111111-1-1-111-1-11-1−i−i−i−iiiiiii−i−i1-1-1-11111-1-1ii−i−i−i−iiii−i−i−iii−i−iii−i−iiiii−i−i−i−iii-1-111-1-11111-1-1i−iii−i−iii−i−i-11−ii1-1
χ2811-1-1111-1-1-1111111-1-1-1-1-1-11-1-1-1-1111111-1-1-111-1-11-1−i−i−i−iiiii−i−iii1-1-1-11111-1-1ii−i−i−i−iii−iiii−i−i−i−iii−i−iii−i−iiiii−i−i-1-11111-1-1-1-111i−iii−i−i−i−iii1-1i−i-11
χ2911-1-1111-1-1-1111111-1-1-1-1-1-11-1-1-1-111-1-111-1-1-111111-1iiii−i−i−i−iii−i−i-11-1-111-1-111−i−iii−i−iiii−i−i−iiiii−i−i−i−iiiii−i−i−i−iii11-1-111-1-1-1-111−iiii−i−i−i−iii-11i−i1-1
χ3011-1-1111-1-1-1111111-1-1-1-1-1-11-1-1-1-111-1-111-1-1-111111-1iiii−i−i−i−i−i−iii-11-1-111-1-111−i−iii−i−iii−iiii−i−iii−i−i−i−iii−i−iiiii−i−i11-1-1-1-11111-1-1−iiii−i−iii−i−i1-1−ii-11
χ3111-1-1111-1-1-1111111-1-1-1-1-1-11-1-1-1-111-1-111-1-1-111111-1−i−i−i−iiiiiii−i−i-11-1-111-1-111ii−i−iii−i−ii−i−i−iii−i−iiiii−i−iii−i−i−i−iii11-1-1-1-11111-1-1i−i−i−iii−i−iii1-1i−i-11
χ3211-1-1111-1-1-1111111-1-1-1-1-1-11-1-1-1-111-1-111-1-1-111111-1−i−i−i−iiiii−i−iii-11-1-111-1-111ii−i−iii−i−i−iiii−i−i−i−iiiii−i−i−i−iiiii−i−i11-1-111-1-1-1-111i−i−i−iiiii−i−i-11−ii1-1
χ3322222222222222-2-2-2-222222-2-22-22-222-2-2-22-22-222-22000000000000222-22-2-2-2-2-20000000000000000000000000000002-22-2000000000000000000000000
χ3422222222222222-2-2-2-222222-2-22-22-2-2-2-2-2-22-22-2-2-2-22000000000000-2-22-22-22222000000000000000000000000000000-22-22000000000000000000000000
χ3522222222222222-2-2-2-222222-2-2-22-2222-2-2-2-22-2222-2200000000000022-22-22-2-2-2-2000000000000000000000000000000-22-22000000000000000000000000
χ3622222222222222-2-2-2-222222-2-2-22-22-2-2-2-2-2-22-22-2-2-22000000000000-2-2-22-2222220000000000000000000000000000002-22-2000000000000000000000000
χ37222222222222-2-2222222-2-2-2-2-20000002-22000000-2-222-2-222-2-222220000000000000000002200002-22-20000-2-2-2-2000000002-22-200000000000000000000
χ38222222222222-2-2222222-2-2-2-2-20000002-22000000-2-222-2-222-2-2-2-2-2-2000000000000000000-2-200002-22-20000222200000000-22-2200000000000000000000
χ39222222222222-2-2222222-2-2-2-2-20000002-22000000-2-2-2-222-2-2222222000000000000000000220000-22-220000-2-2-2-200000000-22-2200000000000000000000
χ40222222222222-2-2222222-2-2-2-2-20000002-22000000-2-2-2-222-2-222-2-2-2-2000000000000000000-2-20000-22-2200002222000000002-22-200000000000000000000
χ412222222222-2-2222222-2-222-22-2222200-22-2222200-2-222222222000000-2-2-2-2000022220000000000-2-2-2-2000000000000000000000000-2-200000000000000
χ422222222222-2-2222222-2-222-22-2222200-22-2222200-2-2-2-2-2-2-2-2-2-2000000-2-2-2-20000-2-2-2-2000000000022220000000000000000000000002200000000000000
χ432222222222-2-2222222-2-222-22-2-2-2-2-200-22-2-2-2-2-200-2-22222222200000022220000-2-2-2-20000000000-2-2-2-20000000000000000000000002200000000000000
χ442222222222-2-2222222-2-222-22-2-2-2-2-200-22-2-2-2-2-200-2-2-2-2-2-2-2-2-2-200000022220000222200000000002222000000000000000000000000-2-200000000000000
χ452222222222-2-222-2-2-2-2-2-222-2-222-22-2002-222-22-2002-200000000000000-22-220000000022220000000000-2-2-2-200000000000000000000002-22-20000000000
χ462222222222-2-222-2-2-2-2-2-222-2-222-22-2002-222-22-2002-200000000000000-22-2200000000-2-2-2-2000000000022220000000000000000000000-22-220000000000
χ472222222222-2-222-2-2-2-2-2-222-2-22-22-22002-22-22-22002-2000000000000002-22-20000000022220000000000-2-2-2-20000000000000000000000-22-220000000000
χ482222222222-2-222-2-2-2-2-2-222-2-22-22-22002-22-22-22002-2000000000000002-22-200000000-2-2-2-20000000000222200000000000000000000002-22-20000000000
χ492222222222-2-2-2-22222-2-2-2-22-22000000-2-2-20000002222-2-222-2-20000000000000000000000002222-22-2200000000-2-2-2-2000000002-22-20000000000000000
χ502222222222-2-2-2-22222-2-2-2-22-22000000-2-2-20000002222-2-222-2-2000000000000000000000000-2-2-2-2-22-2200000000222200000000-22-220000000000000000
χ512222222222-2-2-2-22222-2-2-2-22-22000000-2-2-200000022-2-222-2-22200000000000000000000000022222-22-200000000-2-2-2-200000000-22-220000000000000000
χ522222222222-2-2-2-22222-2-2-2-22-22000000-2-2-200000022-2-222-2-222000000000000000000000000-2-2-2-22-22-2000000002222000000002-22-20000000000000000
χ5322-2-2222-2-2-22222-2-222-2-2-2-22222-2-2222-2-222-2-22-2-2-2-20000000000002-22-2-22-2-2220000000000000000000000000000002-2-22000000000000000000000000
χ5422-2-2222-2-2-22222-2-222-2-2-2-22222-2-22-2-2-2-222-2-2222-2-2000000000000-222-2-2222-2-2000000000000000000000000000000-222-2000000000000000000000000
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χ5722-2-2222-2-2-222-2-222-2-2-2-222-2220000002-2-2000000-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000002i−2i00002i−2i−2i2i0000−2i−2i2i2i000000002-2-2200000000000000000000
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χ6222-2-2222-2-2-2-2-22222-2-222-2-2-2-2222-2-200-22222-2-200-22−2i−2i−2i−2i2i2i2i2i000000-2-2220000−2i−2i2i2i00000000002i2i−2i−2i0000000000000000000000002i−2i00000000000000
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χ6422-2-2222-2-2-2-2-22222-2-222-2-2-2-22-2-22200-222-2-22200-22−2i−2i−2i−2i2i2i2i2i00000022-2-200002i2i−2i−2i00000000002i2i−2i−2i000000000000000000000000−2i2i00000000000000
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χ6722-2-2222-2-2-2-2-222-2-22222-2-2-22-2-222-2002-2-2-222-20022000000000000002-2-22000000002i2i−2i−2i0000000000−2i−2i2i2i0000000000000000000000−2i2i2i−2i0000000000
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χ6922-2-2222-2-2-2-2-2-2-222-2-2222222-2000000-2-220000002-22i2i−2i−2i−2i−2i2i2i0000000000000000000000002i2i−2i−2i−2i2i2i−2i00000000−2i−2i2i2i000000002-2-220000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.