Finite Group Databasebeta

← Group #13137397

Character table — Group #13137397

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222222222222222666666669999121212121212121212121212121212121212121212121212121212121818181818181818181818181818181818181818181836363636363636367272727272727272
order12442344444666121212121212121212121212336612121212888836666612121212121212121212121212121212121212121212888888242424242424242424242424242424242244888866121224242424
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
χ5111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-1111-11-1-1-111
χ6111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1111-1-1-11-1111-1-1
χ7111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ8111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ911-1-1-11ii−i−i11-1-1iiii−i−i−i−i11-1-11111-1-1-1-1ii−i−i1-1-11-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−ii−i11-1-1iiii−i−i−i−i1111-1-1-1-111-1-1i−ii−i11-1-1i−ii−i
χ1011-1-1-11ii−i−i11-1-1iiii−i−i−i−i11-1-11111-1-1-1-1ii−i−i1-1-11-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−ii−i11-1-1iiii−i−i−i−i1111-1-1-1-1-1-111−ii−ii-1-111−ii−ii
χ1111-1-1-11ii−i−i11-1-1iiii−i−i−i−i11-1-11111-1-1-1-1−i−iii1-1-11-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−ii-1-111−i−i−i−iiiii-1-1-1-111111-1-11i−i−ii1-1-11i−i−ii
χ1211-1-1-11ii−i−i11-1-1iiii−i−i−i−i11-1-11111-1-1-1-1−i−iii1-1-11-1-11111-1-1iiiiiiii−i−i−i−i−i−i−i−i−ii-1-111−i−i−i−iiiii-1-1-1-11111-111-1−iii−i-111-1−iii−i
χ1311-1-1-11−i−iii11-1-1−i−i−i−iiiii11-1-11111-1-1-1-1ii−i−i1-1-11-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiii−i-1-111iiii−i−i−i−i-1-1-1-111111-1-11−iii−i1-1-11−iii−i
χ1411-1-1-11−i−iii11-1-1−i−i−i−iiiii11-1-11111-1-1-1-1ii−i−i1-1-11-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiiii−i-1-111iiii−i−i−i−i-1-1-1-11111-111-1i−i−ii-111-1i−i−ii
χ1511-1-1-11−i−iii11-1-1−i−i−i−iiiii11-1-11111-1-1-1-1−i−iii1-1-11-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−ii11-1-1−i−i−i−iiiii1111-1-1-1-111-1-1−ii−ii11-1-1−ii−ii
χ1611-1-1-11−i−iii11-1-1−i−i−i−iiiii11-1-11111-1-1-1-1−i−iii1-1-11-1-11111-1-1−i−i−i−i−i−i−i−iiiiiiiii−ii11-1-1−i−i−i−iiiii1111-1-1-1-1-1-111i−ii−i-1-111i−ii−i
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
χ21222222-2-2-2-22222-2-2-2-2-2-2-2-222222-12-122-1-10000-12-1-1-1-12-1-1-1-1-1-2-2111111-2-21111110000000000000000000000020200-2-20-10-10011
χ22222222-2-2-2-22222-2-2-2-2-2-2-2-222222-12-122-1-10000-12-1-1-1-12-1-1-1-1-1-2-2111111-2-211111100000000000000000000000-20-20022010100-1-1
χ23222222-2-2-2-22222-2-2-2-2-2-2-2-22222-12-12-1-1220000-1-12-1-1-1-12-1-1-1-111-2-2111111-2-2111100000000000000000000002020-2-200-10-101100
χ24222222-2-2-2-22222-2-2-2-2-2-2-2-22222-12-12-1-1220000-1-12-1-1-1-12-1-1-1-111-2-2111111-2-211110000000000000000000000-20-2022001010-1-100
χ252222-220000-22-2-200000000-2-2222222222222222-2-22-2-2-2-2-2-2220000000000000000-2-2000022-2-222-2-2000000000000000000000000
χ262222-220000-22-2-200000000-2-22222222222-2-2-2-22-2-22-2-2-2-2-2-2220000000000000000220000-2-222-2-222000000000000000000000000
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χ2822-2-2220000-222200000000-2-2-2-22222-2-2-2-2−2i−2i2i2i222222-2-2-2-2-2-200000000000000002i−2i0000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
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χ3022-2-2-222i2i−2i−2i22-2-22i2i2i2i−2i−2i−2i−2i22-2-22-12-1-2-2110000-1-21-1112-1-1-1112i2i−i−i−i−i−i−i−2i−2iiiiiii00000000000000000000000-20200−2i2i010-100i−i
χ3122-2-2-222i2i−2i−2i22-2-22i2i2i2i−2i−2i−2i−2i22-2-2-12-1211-2-20000-11-2-111-12-1-111−i−i2i2i−i−i−i−iii−2i−2iiiii000000000000000000000020-202i−2i00-1010−ii00
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χ3422-2-2-22−2i−2i2i2i22-2-2−2i−2i−2i−2i2i2i2i2i22-2-22-12-1-2-2110000-1-21-1112-1-1-111−2i−2iiiiiii2i2i−i−i−i−i−i−i00000000000000000000000-202002i−2i010-100−ii
χ3522-2-2-22−2i−2i2i2i22-2-2−2i−2i−2i−2i2i2i2i2i22-2-2-12-1211-2-20000-11-2-111-12-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i000000000000000000000020-20−2i2i00-1010i−i00
χ3622-2-2-22−2i−2i2i2i22-2-2−2i−2i−2i−2i2i2i2i2i22-2-2-12-1211-2-20000-11-2-111-12-1-111ii−2i−2iiiii−i−i2i2i−i−i−i−i0000000000000000000000-20202i−2i0010-10−ii00
χ372-22i−2i021+i−1−i1−i−1+i0-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i002i−2i22-2-22i−2i2i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13200-20000002i−2i1+i−1−i1+i−1−i1+i1+i−1−i−1−i1−i−1+i1−i−1+i1−i1−i−1+i−1+i002−2−i2i22ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ130022−2−2−i2−i2i2i20000000000000000
χ382-22i−2i021+i−1−i1−i−1+i0-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i002i−2i22-2-22i−2i2i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13200-20000002i−2i1+i−1−i1+i−1−i1+i1+i−1−i−1−i1−i−1+i1−i−1+i1−i1−i−1+i−1+i00−22i2−i2−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ1300−2−222i2i2−i2−i20000000000000000
χ392-22i−2i02−1−i1+i−1+i1−i0-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i002i−2i22-2-22i−2i2i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13200-20000002i−2i−1−i1+i−1−i1+i−1−i−1−i1+i1+i−1+i1−i−1+i1−i−1+i−1+i1−i1−i00−22i2−i22ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ1300−2−222i2i2−i2−i20000000000000000
χ402-22i−2i02−1−i1+i−1+i1−i0-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i002i−2i22-2-22i−2i2i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13200-20000002i−2i−1−i1+i−1−i1+i−1−i−1−i1+i1+i−1+i1−i−1+i1−i−1+i−1+i1−i1−i002−2−i2i2−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ130022−2−2−i2−i2i2i20000000000000000
χ412-2−2i2i021−i−1+i1+i−1−i0-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i00−2i2i22-2-2−2i2i−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23200-2000000−2i2i1−i−1+i1−i−1+i1−i1−i−1+i−1+i1+i−1−i1+i−1−i1+i1+i−1−i−1−i002−2i2−i2−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ230022−2−2i2i2−i2−i20000000000000000
χ422-2−2i2i021−i−1+i1+i−1−i0-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i00−2i2i22-2-2−2i2i−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23200-2000000−2i2i1−i−1+i1−i−1+i1−i1−i−1+i−1+i1+i−1−i1+i−1−i1+i1+i−1−i−1−i00−22−i2i22ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ2300−2−222−i2−i2i2i20000000000000000
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χ46444444-4-4-4-44444-4-4-4-4-4-4-4-44444-2-2-2-2-2-2-2-200001-2-2111-2-211112222-1-1-1-12222-1-1-1-100000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.