Finite Group Databasebeta

← Group #72271750

Character table — Group #72271750

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222222244444444444444444444444444448888881616161616161616161616161616161616161616161616161616161616161616161616162424242424242424484848484848484848484848
order1222222222222236662244444444666666666612121212121212126612121212244444446688881212121212121212121212121212242424242424242422222222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ911111111-1-1-1-1-1-111111-1111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-11-1111-111-1-1ii−i−i11ii−i−i11-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i11-1-1
χ1011111111-1-1-1-1-1-111111-1111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-11-1111-111-1-1ii−i−i11ii−i−i11-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii-1-111
χ1111111111-1-1-1-1-1-111111-1111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-11-1111-111-1-1−i−iii11−i−iii11-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii11-1-1
χ1211111111-1-1-1-1-1-111111-1111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-11-1111-111-1-1−i−iii11−i−iii11-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i-1-111
χ1311111111-1-1-1-1-1-111111-1111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-11-1111-1-1-111ii−i−i-1-1−i−iii-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1ii−i−i−i−iii-1-111
χ1411111111-1-1-1-1-1-111111-1111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-11-1111-1-1-111ii−i−i-1-1−i−iii-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−iiiii−i−i11-1-1
χ1511111111-1-1-1-1-1-111111-1111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-11-1111-1-1-111−i−iii-1-1ii−i−i-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−i−iiiii−i−i-1-111
χ1611111111-1-1-1-1-1-111111-1111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-11-1111-1-1-111−i−iii-1-1ii−i−i-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111ii−i−i−i−iii11-1-1
χ1722222222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-222-2-2-2-2000000000000000000000000000000000000000000002-22-200000000
χ1822222222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-222-2-2-2-200000000000000000000000000000000000000000000-22-2200000000
χ1922222222222222-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
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χ2722222222-2-2-2-2-2-2-1-1-1-12-2222-2-2-2-22-1-1-1-1111111-1-1111111-11-1-1-11-2-2222i2i−2i−2i11−2i−2i2i2i11-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ2822222222-2-2-2-2-2-2-1-1-1-12-2222-2-2-2-22-1-1-1-1111111-1-1111111-11-1-1-11-2-222−2i−2i2i2i112i2i−2i−2i11-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000000000
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χ39222222-2-2-2-2-2-2222222-22-2-222-2-22222-2-2-2-222-2-22222-2-222-22-2-22-200000000000000000000000000000000000022-2-2-2-222000000000000
χ40222222-2-2-2-2-2-2222222-22-2-222-2-22222-2-2-2-222-2-22222-2-222-22-2-22-2000000000000000000000000000000000000-2-22222-2-2000000000000
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χ472222-2-22222-2-2-2-22222-22-22-2-2-2222-2-222-2-2-2-222-2-2-2-2-2-222-22-22222-22-20000220000-2-222-2-2000000000000000000000000000000000000
χ482222-2-22222-2-2-2-22222-22-22-2-2-2222-2-222-2-2-2-222-2-2-2-2-2-222-22-2222-22-220000-2-2000022-2-222000000000000000000000000000000000000
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χ884-4-44004-400-44-444-4-440000000000004-4-44-440000000000000000000000000000000000000000000000000000-22-222-22-2000000000000
χ894-4-4400-44004-4-444-4-44000000000000-444-4-4400000000000000000000000000000000000000000000000000002-2-222-2-22000000000000
χ904-4-4400-44004-4-444-4-44000000000000-444-4-440000000000000000000000000000000000000000000000000000-222-2-222-2000000000000
χ914-4-4400-4400-444-44-4-44000000000000-44-444-400000000000000000000000000000000000000000000000000002-2-22-222-2000000000000
χ924-4-4400-4400-444-44-4-44000000000000-44-444-40000000000000000000000000000000000000000000000000000-222-22-2-22000000000000
χ9388-8-800008-8000088-8-80000000000000000008-80000000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-800008-80000-4-444000000000000000000-4443−430043−430000000000000000000000000000000000000000000000000000000000000000
χ9588-8-800008-80000-4-444000000000000000000-44−434300−43430000000000000000000000000000000000000000000000000000000000000000
χ9688-8-80000-88000088-8-8000000000000000000-880000000000000000000000000000000000000000000000000000000000000000000000
χ9788-8-80000-880000-4-4440000000000000000004-443−4300−43430000000000000000000000000000000000000000000000000000000000000000
χ9888-8-80000-880000-4-4440000000000000000004-4−43430043−430000000000000000000000000000000000000000000000000000000000000000
χ998-88-88-8000000008-88-800000000008-8000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1008-88-88-800000000-44-440000000000-44000000000043−430043−4300000000000000000000000000000000000000000000000000000000000000
χ1018-88-88-800000000-44-440000000000-440000000000−434300−434300000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-88000000008-88-80000000000-88000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-8800000000-44-4400000000004-4000000000043−4300−434300000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-8800000000-44-4400000000004-40000000000−43430043−4300000000000000000000000000000000000000000000000000000000000000
χ1058-8-88008-8008-88-8-444-4000000000000-44-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88008-800-88-88-444-4000000000000-444-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-8800-88008-8-88-444-40000000000004-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-8800-8800-888-8-444-40000000000004-44-4-44000000000000000000000000000000000000000000000000000000000000000000000000

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