Finite Group Databasebeta

← Group #72255320

Character table — Group #72255320

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222222244444444444444448888888888888888888888881616161616161616161616161616161616161616161616161616161616162424242424242424484848484848484848484848
order1222223444466612121212222222444444661212444466666612121212121212121212121212124444444444121212121212121212121212121212121212121288888888222244444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1
χ61111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ71111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-111-1-1-1-1
χ81111111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111
χ91111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-11-11-1ii−i−i
χ101111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11-1ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11-11-11-11−i−iii
χ111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11-11-11-11ii−i−i
χ121111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11-1−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-11-11-11-1−i−iii
χ131111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-11ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-111-1-11−i−iii
χ141111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-11ii−i−i−i−iii-1-111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-111-1-111-1ii−i−i
χ151111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-11−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-111-1-111-1−i−iii
χ161111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-11−i−iiiii−i−i-1-111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-111-1-11ii−i−i
χ172222222222222222222-2-22-2-222-2-2-2-2222200002-2-2-22-222-2-2-2-200000000000000000000000000000000000000000000002200-2-2000000
χ182222222222222222222-2-22-2-222-2-2-2-2222200002-2-2-22-222-2-2-2-20000000000000000000000000000000000000000000000-2-20022000000
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χ272222222-2-2-2-2222-2-2-2-2-222-22222-2-2-2-222-2-20000-2222-2222-2-2-2-200000000000000000000000000000000000000000000002-200-22000000
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χ31222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111-2-22222-2-2-2-21111-1-1-1-1-1-1-1-11111111100000000000000000000
χ32222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-2-2-22222111111111111-1-1-1-1-1-1-1-100000000000000000000
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χ37222222-1-2-2-2-2-1-1-1111122-222-2-2-2-2-222-1-11122-2-2-1-111-1-11111-1-1-1-1-1-11111-220000000011-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000000000
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χ40222222-1-2-2-2-2-1-1-1111122-222-2-2-2-2-222-1-111-2-222-1-111-1-11111-1-11111-1-1-1-12-200000000-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ41222222-1-2-2-2-2-1-1-11111-2-2-2-2-2-2222222-1-11122-2-2111111-1-1-1-1-1-1-1-1-1-111112-22i2i−2i−2i2i2i−2i−2i-1-111−i−i−i−iiiii−i−i−i−iiiii00000000000000000000
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χ44222222-1-2-2-2-2-1-1-11111-2-2-2-2-2-2222222-1-111-2-222111111-1-1-1-1-1-11111-1-1-1-1-22−2i−2i2i2i2i2i−2i−2i11-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000000000
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χ9688-8-800800008-8-80000000000000000000000-440000000000000000-44-4400000000000000000000000000000000000000000000000000
χ9788-8-800-40000-44443−4343−430000000000000000004-400000000000023−2323−23-22-2200000000000000000000000000000000000000000000000000
χ9888-8-800-40000-44443−4343−43000000000000000000-44000000000000−2323−23232-22-200000000000000000000000000000000000000000000000000
χ9988-8-800-40000-444−4343−43430000000000000000004-4000000000000−2323−2323-22-2200000000000000000000000000000000000000000000000000
χ10088-8-800-40000-444−4343−4343000000000000000000-4400000000000023−2323−232-22-200000000000000000000000000000000000000000000000000
χ1018-88-80080000-88-8000000000000000000004-4000000000000004-4-44000000000000000000000000000000000000000000000000000000
χ1028-88-80080000-88-800000000000000000000-4400000000000000-444-4000000000000000000000000000000000000000000000000000000
χ1038-88-800-400004-4443−43−434300000000000000004-400000000000000-222-2−232323−2300000000000000000000000000000000000000000000000000
χ1048-88-800-400004-4443−43−43430000000000000000-44000000000000002-2-2223−23−232300000000000000000000000000000000000000000000000000
χ1058-88-800-400004-44−434343−4300000000000000004-400000000000000-222-223−23−232300000000000000000000000000000000000000000000000000
χ1068-88-800-400004-44−434343−430000000000000000-44000000000000002-2-22−232323−2300000000000000000000000000000000000000000000000000
χ1078-8-888-8-48-8-8844-4-4-4440000000000004-44-400000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-888-8-4-888-844-444-4-40000000000004-4-4400000000000000000000000000000000000000000000000000000000000000000000000000

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