Finite Group Databasebeta

← Group #72221623

Character table — Group #72221623

Order 6400.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136
size112224444444444555588888888888810101010101016161616161616161616161616161616202020202020202020202020202020202020202025254040404040404040404040404040404050505080808080808080808080808080808080100100100100100100100100100100100100100100100100100100200200200200200200200200
order1224444551010202020204444101020202020202020202020222244510101020202020202020202020202044448888888810101010202020202244441010202020202020202020202442020202020202020404040404040404044444444448888888844444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111-1-11111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111-1-111111111111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111-1-11111111111111-11-11-1111111111111111111-1-11111ii−i−i11-1-111-1-1-1-111i−i1-11-11111-1-1-1-1-1-1-11111ii−i−i1111ii−i−i-1-1iiii−i−i−i−i-1-1-1-1ii−i−i-1-1i−iii−i−i
χ611111111111111111-1-11111111111111-11-11-1111111111111111111-1-11111−i−iii11-1-111-1-1-1-111−ii1-11-11111-1-1-1-1-1-1-11111−i−iii1111−i−iii-1-1−i−i−i−iiiii-1-1-1-1−i−iii-1-1−ii−i−iii
χ711111111111111111-1-11111111111111-11-11-1111111111111111111-1-1-1-1-1-1ii−i−i11-1-111-1-1-1-1-1-1i−i1-11-11111-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1ii−i−i-1-1−i−i−i−iiiii1111ii−i−i11i−i−i−iii
χ811111111111111111-1-11111111111111-11-11-1111111111111111111-1-1-1-1-1-1−i−iii11-1-111-1-1-1-1-1-1−ii1-11-11111-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1−i−iii-1-1iiii−i−i−i−i1111−i−iii11−iiii−i−i
χ9111111111111111-1-111111111111111-11-11-111111111111111111-1-111ii−i−i1111-1-111-1-111-1-1i−i11-11-11-1-1-1-11111-1-1-1ii−i−i1111ii−i−i1111-1-1ii−i−iii−i−iii−i−i-1-1-1-1i−i-1-1i−ii−i
χ10111111111111111-1-111111111111111-11-11-111111111111111111-1-111ii−i−i-1-1-1-1-1-111-1-111-1-1i−i-1-1-11-11-1-1-1-11111-1-1-1ii−i−i-1-1-1-1ii−i−i-1-1-1-1-1-1−i−iii−i−iiiii−i−i1111i−i11−ii−ii
χ11111111111111111-1-111111111111111-11-11-111111111111111111-1-111−i−iii1111-1-111-1-111-1-1−ii11-11-11-1-1-1-11111-1-1-1−i−iii1111−i−iii1111-1-1−i−iii−i−iii−i−iii-1-1-1-1−ii-1-1−ii−ii
χ12111111111111111-1-111111111111111-11-11-111111111111111111-1-111−i−iii-1-1-1-1-1-111-1-111-1-1−ii-1-1-11-11-1-1-1-11111-1-1-1−i−iii-1-1-1-1−i−iii-1-1-1-1-1-1ii−i−iii−i−i−i−iii1111−ii11i−ii−i
χ13111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111111111111111-1-1-1-1ii−i−iii−i−i-1-1-1-1-1-1-1-111i−ii−i-1-1-1-1-1-1-1-1-1-1-1-1111ii−i−iii−i−iii−i−iii−i−i11-1-11111-1-1−i−iii−i−iii−ii−ii-111-1
χ14111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111111111111111-1-1-1-1ii−i−i−i−iii-1-1-1-1-1-1-1-111i−i−ii-1-1-1-1-1-1-1-1-1-1-1-1111ii−i−i−i−iiiii−i−i−i−iii1111-1-1-1-111−i−iiiii−i−i−iii−i1-1-11
χ15111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111111111111111-1-1-1-1−i−iiiii−i−i-1-1-1-1-1-1-1-111−iii−i-1-1-1-1-1-1-1-1-1-1-1-1111−i−iiiii−i−i−i−iiiii−i−i1111-1-1-1-111ii−i−i−i−iiii−i−ii1-1-11
χ16111111111111111-1-1-1-1111111111111-1-1-1-1-1-11111111111111111-1-1-1-1−i−iii−i−iii-1-1-1-1-1-1-1-111−ii−ii-1-1-1-1-1-1-1-1-1-1-1-1111−i−iii−i−iii−i−iii−i−iii11-1-11111-1-1ii−i−iii−i−ii−ii−i-111-1
χ1711111-1-11111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-11111111111111111-1-1-1-1-1-1-1-1
χ1811111-1-11111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111
χ1911111-1-11111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111
χ2011111-1-11111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ2111111-1-11111111111-1-11111-1-1-1-1-1-1-1-11-11-11-111111111-1-1-1-1-1-1-1-1-1-1111111ii−i−i11-1-111-1-1-1-1-1-1−ii1-11-1-1-1-1-11111-1-1-1-1-1-1-1−i−iii1111ii−i−i11iiii−i−i−i−i-1-1-1-1ii−i−i11−ii−i−iii
χ2211111-1-11111111111-1-11111-1-1-1-1-1-1-1-11-11-11-111111111-1-1-1-1-1-1-1-1-1-1111111−i−iii11-1-111-1-1-1-1-1-1i−i1-11-1-1-1-1-11111-1-1-1-1-1-1-1ii−i−i1111−i−iii11−i−i−i−iiiii-1-1-1-1−i−iii11i−iii−i−i
χ2311111-1-11111111111-1-11111-1-1-1-1-1-1-1-11-11-11-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i11-1-111-1-1-1-111−ii1-11-1-1-1-1-11111-1-1-11111−i−iii-1-1-1-1ii−i−i11−i−i−i−iiiii1111ii−i−i-1-1−iiii−i−i
χ2411111-1-11111111111-1-11111-1-1-1-1-1-1-1-11-11-11-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−iii11-1-111-1-1-1-111i−i1-11-1-1-1-1-11111-1-1-11111ii−i−i-1-1-1-1−i−iii11iiii−i−i−i−i1111−i−iii-1-1i−i−i−iii
χ2511111-1-111111111-1-1111111-1-1-1-1-1-1-1-1-11-11-1111111111-1-1-1-1-1-1-1-111-1-1ii−i−i1111-1-111-1-111-1-1−ii-1-1-11-111111-1-1-1-1-1-1-1−i−iii-1-1-1-1ii−i−i111111ii−i−iii−i−iii−i−i-1-1-1-1−ii11−ii−ii
χ2611111-1-111111111-1-1111111-1-1-1-1-1-1-1-1-11-11-1111111111-1-1-1-1-1-1-1-111-1-1ii−i−i-1-1-1-1-1-111-1-111-1-1−ii11-11-111111-1-1-1-1-1-1-1−i−iii1111ii−i−i-1-1-1-111−i−iii−i−iiiii−i−i1111−ii-1-1i−ii−i
χ2711111-1-111111111-1-1111111-1-1-1-1-1-1-1-1-11-11-1111111111-1-1-1-1-1-1-1-111-1-1−i−iii1111-1-111-1-111-1-1i−i-1-1-11-111111-1-1-1-1-1-1-1ii−i−i-1-1-1-1−i−iii111111−i−iii−i−iii−i−iii-1-1-1-1i−i11i−ii−i
χ2811111-1-111111111-1-1111111-1-1-1-1-1-1-1-1-11-11-1111111111-1-1-1-1-1-1-1-111-1-1−i−iii-1-1-1-1-1-111-1-111-1-1i−i11-11-111111-1-1-1-1-1-1-1ii−i−i1111−i−iii-1-1-1-111ii−i−iii−i−i−i−iii1111i−i-1-1−ii−ii
χ2911111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i-1-1-1-1-1-1-1-111−ii−ii-1-1-1-111111111111−i−iii−i−iiiii−i−iii−i−i-1-1-1-11111-1-1−i−iii−i−iiii−ii−i1-1-11
χ3011111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iii-1-1-1-1-1-1-1-111−iii−i-1-1-1-111111111111−i−iiiii−i−iii−i−i−i−iii-1-111-1-1-1-111−i−iiiii−i−ii−i−ii-111-1
χ3111111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i-1-1-1-1-1-1-1-111i−i−ii-1-1-1-111111111111ii−i−i−i−iii−i−iiiii−i−i-1-111-1-1-1-111ii−i−i−i−iii−iii−i-111-1
χ3211111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iii−i−iii-1-1-1-1-1-1-1-111i−ii−i-1-1-1-111111111111ii−i−iii−i−i−i−iii−i−iii-1-1-1-11111-1-1ii−i−iii−i−i−ii−ii1-1-11
χ33222-2-2002222-2-2-2-2222222-2-200000000-2-2-2-2222222-2-2-2-200000000000000000000-2-2-2-22222220000-2-222000000002-2-20000000000000000002-22-22-22-20000000000000000
χ34222-2-2002222-2-2-2-2222222-2-200000000-2-2-2-2222222-2-2-2-200000000000000000000-2-2-2-22222220000-2-222000000002-2-2000000000000000000-22-22-22-220000000000000000
χ35222-2-2002222-2-2-2-222-2-222-2-200000000-22-222-22222-2-2-2-200000000000000000000-2-22222-2-2-2-20000-222-200000000-2220000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ36222-2-2002222-2-2-2-222-2-222-2-200000000-22-222-22222-2-2-2-200000000000000000000-2-22222-2-2-2-20000-222-200000000-222000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ37222-2-2002222-2-2-2-2-2-22222-2-2000000002-22-2-222222-2-2-2-20000000000000000000022-2-2-2-222-2-200002-2-2200000000-2220000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ38222-2-2002222-2-2-2-2-2-22222-2-2000000002-22-2-222222-2-2-2-20000000000000000000022-2-2-2-222-2-200002-2-2200000000-222000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ39222-2-2002222-2-2-2-2-2-2-2-222-2-2000000002222-2-22222-2-2-2-2000000000000000000002222-2-2-2-222000022-2-2000000002-2-20000000000000000002-2-22-222-20000000000000000
χ40222-2-2002222-2-2-2-2-2-2-2-222-2-2000000002222-2-22222-2-2-2-2000000000000000000002222-2-2-2-222000022-2-2000000002-2-2000000000000000000-222-22-2-220000000000000000
χ4122-22-200222222-2-22222-2-22-2000000002-2-22-2-222-2-222-2-20000000000002-22-20000-2-22222222200002-2-2-200000000-22-2000000002-22-2000000000000002-22-2000000000000
χ4222-22-200222222-2-22222-2-22-2000000002-2-22-2-222-2-222-2-2000000000000-22-220000-2-22222222200002-2-2-200000000-22-200000000-22-2200000000000000-22-22000000000000
χ4322-22-200222222-2-222-2-2-2-22-20000000022-2-2-2222-2-222-2-20000000000002-22-20000-2-2-2-222-2-2-2-2000022-22000000002-22000000002-22-200000000000000-22-22000000000000
χ4422-22-200222222-2-222-2-2-2-22-20000000022-2-2-2222-2-222-2-2000000000000-22-220000-2-2-2-222-2-2-2-2000022-22000000002-2200000000-22-22000000000000002-22-2000000000000
χ4522-22-200222222-2-2-2-222-2-22-200000000-2-2222-222-2-222-2-20000000000002i−2i−2i2i00002222-2-222-2-20000-2-22-2000000002-22000000002i−2i−2i2i000000000000002i−2i−2i2i000000000000
χ4622-22-200222222-2-2-2-222-2-22-200000000-2-2222-222-2-222-2-2000000000000−2i2i2i−2i00002222-2-222-2-20000-2-22-2000000002-2200000000−2i2i2i−2i00000000000000−2i2i2i−2i000000000000
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χ4822-22-200222222-2-2-2-2-2-2-2-22-200000000-222-22222-2-222-2-2000000000000−2i2i2i−2i000022-2-2-2-2-2-2220000-222200000000-22-200000000−2i2i2i−2i000000000000002i−2i−2i2i000000000000
χ4922-2-22002222-2-2222222-2-2-2200000000-222-2-2-222-2-2-2-22200000000000000002-22-222-2-22222220000-22-2-200000000-2-220000000000002-22-2000000000000002-22-200000000
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χ5122-2-22002222-2-22222-2-2-2-2-2200000000-2-222-2222-2-2-2-22200000000000000002i−2i−2i2i222222-2-2-2-20000-2-2-220000000022-20000000000002i−2i−2i2i000000000000002i−2i−2i2i00000000
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χ5422-2-22002222-2-222-2-222-2-2-220000000022-2-22-222-2-2-2-2220000000000000000-22-22-2-2-2-2-2-222-2-20000222-20000000022-2000000000000-22-22000000000000002-22-200000000
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χ5944444444-14-144-1-1-4-4004-1-144444-1-1-1-1-40-40-40-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4004i4i−4i−4i000011001100004i−4i00101011110000000−i−iii0000−i−iii000000000000000000000000000000
χ6044444444-14-144-1-1-4-4004-1-144444-1-1-1-1-40-40-40-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-400−4i−4i4i4i00001100110000−4i4i00101011110000000ii−i−i0000ii−i−i000000000000000000000000000000
χ614444444-14-14-1-1440044-144-1-1-1-1-14444040404-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100440000444400-1-100-1-10000440-10-10000-1-1-1-10000000-1-1-1-10000-1-1-1-100000000000000000000000000
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χ634444444-14-14-1-14400-4-4-144-1-1-1-1-144440-40-40-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-4-400004i4i−4i−4i0011001100004i−4i0101000011110000000−i−iii0000−i−iii00000000000000000000000000
χ644444444-14-14-1-14400-4-4-144-1-1-1-1-144440-40-40-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-4-40000−4i−4i4i4i001100110000−4i4i0101000011110000000ii−i−i0000ii−i−i00000000000000000000000000
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χ6644444-4-44-14-144-1-144004-1-14-4-4-4-41111404040-1-1-1-1-1-1-1-111111111-4-400-4-4-4-40000-1-100-1-100004400-10-1011110000000-1-1-1-100001111000000000000000000000000000000
χ6744444-4-44-14-144-1-1-4-4004-1-14-4-4-4-41111-40-40-40-1-1-1-1-1-1-1-11111111144004i4i−4i−4i00001100110000−4i4i001010-1-1-1-10000000ii−i−i0000−i−iii000000000000000000000000000000
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Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.