Finite Group Databasebeta

← Group #72342848

Character table — Group #72342848

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122
size1111222222444444444444888888888888888888888888888888881616161616161616161616161616161616161616161616161616161616161616161616161616161632323232323232323232323232323232323232323232646464646464
order12442224442222224444442222222222224444444444448888888822444444444488888888888888888888888888884444448888888888888888444488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1111111111-1-1-1-1111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ71111111111111111111111111111-1-1-1-1111111111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-1111111-1-1-1-1
χ9111111111111111111111111-1-1-1-1111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111111111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ10111111111111111111111111-1-1-1-1111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-111
χ11111111111111111111111111-1-1-1-1111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111
χ12111111111111111111111111-1-1-1-1111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-1-1
χ13111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ14111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ15111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ16111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ1711-1-1111-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1111-1-111-1-111-1-11ii−i−iii−i−i1-11-111-1-111-1-1i−iii−i−ii−iii−i−iii−i−iii−i−iii−i−iii−i−i1-111-1-1ii−i−iii−i−iii−i−iii−i−i1-11-11-1
χ1811-1-1111-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1111-1-111-1-111-1-11ii−i−i−i−iii1-11-111-1-111-1-1i−iii−i−i−ii−i−iiiii−i−iii−i−i−i−iii−i−iii1-1-1-111ii−i−iii−i−i−i−iii−i−iii-11-11-11
χ1911-1-1111-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1111-1-111-1-111-1-11−i−iiiii−i−i1-11-111-1-111-1-1−ii−i−iiii−iii−i−i−i−iii−i−iiiii−i−iii−i−i1-1-1-111−i−iii−i−iiiii−i−iii−i−i-11-11-11
χ2011-1-1111-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1111-1-111-1-111-1-11−i−iii−i−iii1-11-111-1-111-1-1−ii−i−iii−ii−i−iii−i−iii−i−iii−i−iii−i−iii1-111-1-1−i−iii−i−iii−i−iii−i−iii1-11-11-1
χ2111-1-1111-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-111-1-1-1-1111ii−i−iii−i−i-11-1111-1-1-1-111i−iii−i−ii−i−i−iiiii−i−iii−i−iii−i−i−i−iii-1111-1-1−i−iii−i−iiiii−i−i−i−iii1-1-11-11
χ2211-1-1111-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-111-1-1-1-1111ii−i−i−i−iii-11-1111-1-1-1-111i−iii−i−i−iiii−i−iii−i−iii−i−i−i−iiiii−i−i-11-1-111−i−iii−i−iii−i−iiiii−i−i-111-11-1
χ2311-1-1111-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-111-1-1-1-1111−i−iiiii−i−i-11-1111-1-1-1-111−ii−i−iiii−i−i−iii−i−iii−i−iiiii−i−i−i−iii-11-1-111ii−i−iii−i−iii−i−i−i−iii-111-11-1
χ2411-1-1111-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-111-1-1-1-1111−i−iii−i−iii-11-1111-1-1-1-111−ii−i−iii−iiii−i−i−i−iii−i−iii−i−iiiii−i−i-1111-1-1ii−i−iii−i−i−i−iiiii−i−i1-1-11-11
χ2511-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1-11111-1-11ii−i−iii−i−i-11-11-1-11111-1-1i−i−i−iiii−iii−i−iii−i−i−i−iiiii−i−iii−i−i-1111-1-1ii−i−i−i−iii−i−iii−i−iii-111-1-11
χ2611-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1-11111-1-11ii−i−i−i−iii-11-11-1-11111-1-1i−i−i−iii−ii−i−iiiii−i−i−i−iii−i−iii−i−iii-11-1-111ii−i−i−i−iiiii−i−iii−i−i1-1-111-1
χ2711-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1-11111-1-11−i−iiiii−i−i-11-11-1-11111-1-1−iiii−i−ii−iii−i−i−i−iiiii−i−iii−i−iii−i−i-11-1-111−i−iiiii−i−i−i−iii−i−iii1-1-111-1
χ2811-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1-11111-1-11−i−iii−i−iii-11-11-1-11111-1-1−iiii−i−i−ii−i−iii−i−iiiii−i−i−i−iii−i−iii-1111-1-1−i−iiiii−i−iii−i−iii−i−i-111-1-11
χ2911-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-111-1-1111ii−i−iii−i−i1-11-1-1-111-1-111i−i−i−iiii−i−i−iiiii−i−i−i−iiiii−i−i−i−iii1-111-1-1−i−iiiii−i−i−i−iiiii−i−i-11-111-1
χ3011-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-111-1-1111ii−i−i−i−iii1-11-1-1-111-1-111i−i−i−iii−iiii−i−iii−i−i−i−iii−i−iiiii−i−i1-1-1-111−i−iiiii−i−iii−i−i−i−iii1-11-1-11
χ3111-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-111-1-1111−i−iiiii−i−i1-11-1-1-111-1-111−iiii−i−ii−i−i−iii−i−iiiii−i−iii−i−i−i−iii1-1-1-111ii−i−i−i−iii−i−iiiii−i−i1-11-1-11
χ3211-1-1111-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-111-1-1111−i−iii−i−iii1-11-1-1-111-1-111−iiii−i−i−iiii−i−i−i−iiiii−i−i−i−iiiii−i−i1-111-1-1ii−i−i−i−iiiii−i−i−i−iii-11-111-1
χ3322222222222222-2-2-2-222222-222222222-2-22-2-222222222-2000000002222-2-2-2-2-2-2-2-20000000000000000000000000000-2-200000000000000000000000000
χ3422222222222222-2-2-2-222222-22222-2-2-2-2-2-22-2-22222-2-2-2-2-200000000-2-2-2-2-2-2-2-2222200000000000000000000000000002200000000000000000000000000
χ3522222222222222-2-2-2-222222-2-2-2-2-22222-2-22-2-2-2-2-2-22222-200000000-2-2-2-22222-2-2-2-200000000000000000000000000002200000000000000000000000000
χ3622222222222222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2-22-2-2-2-2-2-2-2-2-2-2-2000000002222222222220000000000000000000000000000-2-200000000000000000000000000
χ37222222222222-2-2222222-2-2-2-200002-22-22-2-22-200002-22-2-222220000000000002-22-2220000000000-2-2-2-20000000000000000002-22-2000000000000000000
χ38222222222222-2-2222222-2-2-2-200002-22-22-2-22-200002-22-2-2-2-2-2-20000000000002-22-2-2-200000000002222000000000000000000-22-22000000000000000000
χ39222222222222-2-2222222-2-2-2-20000-22-222-2-22-20000-22-22-22222000000000000-22-22220000000000-2-2-2-2000000000000000000-22-22000000000000000000
χ40222222222222-2-2222222-2-2-2-20000-22-222-2-22-20000-22-22-2-2-2-2-2000000000000-22-22-2-2000000000022220000000000000000002-22-2000000000000000000
χ41222222222222-2-2-2-2-2-222-2-2-2200002-22-2-22-2-2200002-22-220000000000000000-22-220022220000000000-2-2-2-20000000000000000002-22-200000000000000
χ42222222222222-2-2-2-2-2-222-2-2-2200002-22-2-22-2-2200002-22-220000000000000000-22-2200-2-2-2-200000000002222000000000000000000-22-2200000000000000
χ43222222222222-2-2-2-2-2-222-2-2-220000-22-22-22-2-220000-22-22200000000000000002-22-20022220000000000-2-2-2-2000000000000000000-22-2200000000000000
χ44222222222222-2-2-2-2-2-222-2-2-220000-22-22-22-2-220000-22-22200000000000000002-22-200-2-2-2-2000000000022220000000000000000002-22-200000000000000
χ452222222222-2-2222222-2-222-2-22-22-20000-22-2-222-22-20000-20000222200002-22-2000000000022000000000000-2-2-2-20000000000000000002-22-20000000000
χ462222222222-2-2222222-2-222-2-22-22-20000-22-2-222-22-20000-20000-2-2-2-200002-22-20000000000-2-20000000000002222000000000000000000-22-220000000000
χ472222222222-2-2222222-2-222-2-2-22-220000-22-2-22-22-220000-2000022220000-22-22000000000022000000000000-2-2-2-2000000000000000000-22-220000000000
χ482222222222-2-2222222-2-222-2-2-22-220000-22-2-22-22-220000-20000-2-2-2-20000-22-220000000000-2-200000000000022220000000000000000002-22-20000000000
χ492222222222-2-222-2-2-2-2-2-222-222-22-200002-2-22-22-22-200002000000000000-22-220000000000002222000000000000-2-2-2-20000000000000000002-22-2000000
χ502222222222-2-222-2-2-2-2-2-222-222-22-200002-2-22-22-22-200002000000000000-22-22000000000000-2-2-2-20000000000002222000000000000000000-22-22000000
χ512222222222-2-222-2-2-2-2-2-222-22-22-2200002-2-22-2-22-22000020000000000002-22-20000000000002222000000000000-2-2-2-2000000000000000000-22-22000000
χ522222222222-2-222-2-2-2-2-2-222-22-22-2200002-2-22-2-22-22000020000000000002-22-2000000000000-2-2-2-200000000000022220000000000000000002-22-2000000
χ5322-2-2222-2-2-22222-2-222-2-2-2-2-2222-2-222-2-2-2-222222-2-222-2-2-2000000002-22-2-2-222-2-2220000000000000000000000000000-2200000000000000000000000000
χ5422-2-2222-2-2-22222-2-222-2-2-2-2-2222-2-2-2-222-2-222222-2-2-2-222-200000000-22-22-2-22222-2-200000000000000000000000000002-200000000000000000000000000
χ5522-2-2222-2-2-22222-2-222-2-2-2-2-22-2-22222-2-2-2-2222-2-22222-2-2-200000000-22-2222-2-2-2-22200000000000000000000000000002-200000000000000000000000000
χ5622-2-2222-2-2-22222-2-222-2-2-2-2-22-2-222-2-222-2-2222-2-222-2-222-2000000002-22-222-2-222-2-20000000000000000000000000000-2200000000000000000000000000
χ5722-2-2222-2-2-222-2-222-2-2-2-2222200002-2-222-2-2-2200002-2-22-22i2i−2i−2i0000000000002-2-222i−2i0000000000−2i−2i2i2i0000000000000000002i−2i−2i2i000000000000000000
χ5822-2-2222-2-2-222-2-222-2-2-2-2222200002-2-222-2-2-2200002-2-22-2−2i−2i2i2i0000000000002-2-22−2i2i00000000002i2i−2i−2i000000000000000000−2i2i2i−2i000000000000000000
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χ6222-2-2222-2-2-222-2-2-2-222-2-2222-200002-2-22-22-22-200002-2-2220000000000000000-222-200−2i−2i2i2i00000000002i2i−2i−2i000000000000000000−2i2i2i−2i00000000000000
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χ6922-2-2222-2-2-2-2-222-2-22222-2-22-22-2-2200002-2-2-222-2-2200002000000000000-222-20000000000002i2i−2i−2i000000000000−2i−2i2i2i0000000000000000002i−2i−2i2i000000
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χ844444-44-4-4-444-40000004-400000000040-40000000000-40400000-2-2-2-200000000000000000022-22-2200000000-22-22-22-220000000000000000000000000000
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χ11188-8-8-8-88-8880000000000000000000000000000000000000000000044-4-40000000000000000000000000000000000000000000000000000000000000000
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χ1148-88i−8i00000000004-44i−4i00000000000000000000000000004ζ−4ζ4ζ3−4ζ3−4ζ4ζ−4ζ34ζ3000000000000000000000000000000000000000000-22−2i2i0000000000000000000000
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χ1178-8−8i8i00000000004-4−4i4i00000000000000000000000000004ζ3−4ζ34ζ−4ζ4ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000000000002-2−2i2i0000000000000000000000
χ1188-8−8i8i00000000004-4−4i4i00000000000000000000000000004ζ3−4ζ34ζ−4ζ−4ζ34ζ3−4ζ4ζ000000000000000000000000000000000000000000-222i−2i0000000000000000000000
χ1198-8−8i8i00000000004-4−4i4i0000000000000000000000000000−4ζ34ζ3−4ζ4ζ4ζ3−4ζ34ζ−4ζ000000000000000000000000000000000000000000-222i−2i0000000000000000000000
χ1208-8−8i8i00000000004-4−4i4i0000000000000000000000000000−4ζ34ζ3−4ζ4ζ−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000000000002-2−2i2i0000000000000000000000
χ12116-1616i−16i0000000000-88−8i8i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ12216-16−16i16i0000000000-888i−8i00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.