Finite Group Databasebeta

← Group #13137445

Character table — Group #13137445

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222222222222222666666669999121212121212121212121212121212121212121212121212121212121818181818181818181818181818181818181818181836363636363636367272727272727272
order1244234444466612121212121212121212121233661212121222443666661212121212121212121212121212121212121212121224444466661212121212121212121212122244888866121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11-11-111-1-1
χ41111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-11-11-1-111
χ51111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111-1-1-1-11111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11-1-1-1111-11-1-1-111
χ81111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1111-1-1-11-1111-1-1
χ911-1-1-111ii−i−i1-1-111-1-1iiii−i−i−i−i1111-1-1-1-111-1-11-1-11-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-11ii−i−i11-1-111-1-1iiii−i−i−i−i11-1-1i−ii−i11-1-1i−ii−i
χ1011-1-1-111ii−i−i1-1-111-1-1iiii−i−i−i−i1111-1-1-1-111-1-11-1-11-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i-11ii−i−i11-1-111-1-1iiii−i−i−i−i-1-111−ii−ii-1-111−ii−ii
χ1111-1-1-111ii−i−i1-1-111-1-1iiii−i−i−i−i1111-1-1-1-1-1-1111-1-11-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1−i−iii-1-111-1-111−i−i−i−iiiii1-1-11i−i−ii1-1-11i−i−ii
χ1211-1-1-111ii−i−i1-1-111-1-1iiii−i−i−i−i1111-1-1-1-1-1-1111-1-11-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1−i−iii-1-111-1-111−i−i−i−iiiii-111-1−iii−i-111-1−iii−i
χ1311-1-1-111−i−iii1-1-111-1-1−i−i−i−iiiii1111-1-1-1-111-1-11-1-11-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-11−i−iii11-1-111-1-1−i−i−i−iiiii11-1-1−ii−ii11-1-1−ii−ii
χ1411-1-1-111−i−iii1-1-111-1-1−i−i−i−iiiii1111-1-1-1-111-1-11-1-11-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii-11−i−iii11-1-111-1-1−i−i−i−iiiii-1-111i−ii−i-1-111i−ii−i
χ1511-1-1-111−i−iii1-1-111-1-1−i−i−i−iiiii1111-1-1-1-1-1-1111-1-11-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1ii−i−i-1-111-1-111iiii−i−i−i−i1-1-11−iii−i1-1-11−iii−i
χ1611-1-1-111−i−iii1-1-111-1-1−i−i−i−iiiii1111-1-1-1-1-1-1111-1-11-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1ii−i−i-1-111-1-111iiii−i−i−i−i-111-1i−i−ii-111-1i−i−ii
χ17222222222222222222222222222-12-122-1-10000-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000000000000000000020200220-10-100-1-1
χ18222222222222222222222222222-12-122-1-10000-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100000000000000000000000-20-200-2-201010011
χ1922222222222222222222222222-12-12-1-1220000-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000000020202200-10-10-1-100
χ2022222222222222222222222222-12-12-1-1220000-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10000000000000000000000-20-20-2-20010101100
χ212222222-2-2-2-22222222-2-2-2-2-2-2-2-22-12-122-1-10000-12-1-1-1-12-1-1-1-1-1-2-2111111-2-21111110000000000000000000000020200-2-20-10-10011
χ222222222-2-2-2-22222222-2-2-2-2-2-2-2-22-12-122-1-10000-12-1-1-1-12-1-1-1-1-1-2-2111111-2-211111100000000000000000000000-20-20022010100-1-1
χ232222222-2-2-2-22222222-2-2-2-2-2-2-2-2-12-12-1-1220000-1-12-1-1-1-12-1-1-1-111-2-2111111-2-2111100000000000000000000002020-2-200-10-101100
χ242222222-2-2-2-22222222-2-2-2-2-2-2-2-2-12-12-1-1220000-1-12-1-1-1-12-1-1-1-111-2-2111111-2-211110000000000000000000000-20-2022001010-1-100
χ252222-22-200002-2-2-2-222000000002222222222222-2-22-2-2-2-2-2-2220000000000000000-2-2000022-2-2-2-222000000000000000000000000
χ262222-22-200002-2-2-2-2220000000022222222-2-2-2-22-2-22-2-2-2-2-2-2220000000000000000220000-2-22222-2-2000000000000000000000000
χ2722-2-222-20000222-2-2-2-2000000002222-2-2-2-222-2-2222222-2-2-2-2-2-200000000000000002-200002222-2-2-2-2000000000000000000000000
χ2822-2-222-20000222-2-2-2-2000000002222-2-2-2-2-2-222222222-2-2-2-2-2-20000000000000000-220000-2-2-2-22222000000000000000000000000
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χ3122-2-2-2222i2i−2i−2i2-2-222-2-22i2i2i2i−2i−2i−2i−2i-12-1211-2-20000-11-2-111-12-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii000000000000000000000020-202i−2i00-1010−ii00
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χ3522-2-2-222−2i−2i2i2i2-2-222-2-2−2i−2i−2i−2i2i2i2i2i-12-1211-2-20000-11-2-111-12-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i000000000000000000000020-20−2i2i00-1010i−i00
χ3622-2-2-222−2i−2i2i2i2-2-222-2-2−2i−2i−2i−2i2i2i2i2i-12-1211-2-20000-11-2-111-12-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i0000000000000000000000-20202i−2i0010-10−ii00
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χ464444444-4-4-4-44444444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-200001-2-2111-2-211112222-1-1-1-12222-1-1-1-100000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.