Finite Group Databasebeta

← Group #13138862

Character table — Group #13138862

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222222222222222666666669999121212121212121212121212121212121212121212121212121212121818181818181818181818181818181818181818181836363636363636367272727272727272
order12442346668888121212122424242424242424336612121212888836666612121212121224242424242424242424242424242424444488121212121212121224242424242424242244888866121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11-111-1-11-11-111-1-1
χ61111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-11-11-1-111-11-11-1-111
χ71111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-11-11-1-1-1111-11-1-1-111
χ81111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-11-1111-1-1-11-1111-1-1
χ911-1-1-1111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−i1-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1ii−i−ii−iiiii−i−i−i−iiiii−i−i−i−i11-1-1i−ii−i11-1-1i−ii−i
χ1011-1-1-1111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−i1-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1ii−i−ii−iiiii−i−i−i−iiiii−i−i−i−i-1-111−ii−ii-1-111−ii−ii
χ1111-1-1-1111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii1-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1−i−iii−ii−i−i−i−iiiii−i−i−i−iiiii11-1-1−ii−ii11-1-1−ii−ii
χ1211-1-1-1111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii1-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1−i−iii−ii−i−i−i−iiiii−i−i−i−iiiii-1-111i−ii−i-1-111i−ii−i
χ1311-1-1-1111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−i1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111−i−iiii−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11i−i−ii1-1-11i−i−ii
χ1411-1-1-1111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−i1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111−i−iiii−i−i−i−i−iiiiiiiii−i−i−i−i-111-1−iii−i-111-1−iii−i
χ1511-1-1-1111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iii1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111ii−i−i−iiiiii−i−i−i−i−i−i−i−iiiii1-1-11−iii−i1-1-11−iii−i
χ1611-1-1-1111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iii1-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111ii−i−i−iiiiii−i−i−i−i−i−i−i−iiiii-111-1i−i−ii-111-1i−i−ii
χ17222222222222222222222222222-12-1-1-1220000-12-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000000022220000-1-1-1-10000
χ18222222222222222222222222222-12-1-1-1220000-12-1-1-1-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-10000000000000000000000-2-2-2-2000011110000
χ1922222222222222222222222222-12-1222-1-10000-1-12-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-10000000000000000000000000022220000-1-1-1-1
χ2022222222222222222222222222-12-1222-1-10000-1-12-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-100000000000000000000000000-2-2-2-200001111
χ212222222222-2-2-2-22222-2-2-2-2-2-2-2-22-12-1-1-1220000-12-1-1-1-1-1-12-1-1-1-2-2111111-2-211111100000000000000000000002-22-20000-11-110000
χ222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-12-1-1-1220000-12-1-1-1-1-1-12-1-1-1-2-2111111-2-21111110000000000000000000000-22-2200001-11-10000
χ232222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1222-1-10000-1-12-1-1-1-1-1-12-1-111-2-2111111-2-211110000000000000000000000000022-2-20000-1-111
χ242222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1222-1-10000-1-12-1-1-1-1-1-12-1-111-2-2111111-2-2111100000000000000000000000000-2-222000011-1-1
χ252222-22-22-2-20000-2-222000000002222222222222-2-2-2-2222-2-2-2-200000000000000000000-2-20000000022-2-222-2-20000000000000000
χ262222-22-22-2-20000-2-2220000000022222222-2-2-2-22-2-2-2-2222-2-2-2-2000000000000000000002200000000-2-222-2-2220000000000000000
χ2722-2-222-22220000-2-2-2-2000000002222-2-2-2-22i2i−2i−2i222222-2-2-2-2-2-200000000000000000000−2i2i000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822-2-222-22220000-2-2-2-2000000002222-2-2-2-2−2i−2i2i2i222222-2-2-2-2-2-2000000000000000000002i−2i00000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2922-2-2-2222-2-222-2-222-2-22222-2-2-2-22-12-111-2-20000-1-2111-1112-1-1-122-1-1-1-1-1-1-2-2111111000000000000000000000022-2-20000-1-1110000
χ3022-2-2-2222-2-222-2-222-2-22222-2-2-2-22-12-111-2-20000-1-2111-1112-1-1-122-1-1-1-1-1-1-2-21111110000000000000000000000-2-222000011-1-10000
χ3122-2-2-2222-2-222-2-222-2-22222-2-2-2-2-12-12-2-2110000-11-211-111-12-1-1-1-122-1-1-1-111-2-21111000000000000000000000000002i−2i2i−2i0000−ii−ii
χ3222-2-2-2222-2-222-2-222-2-22222-2-2-2-2-12-12-2-2110000-11-211-111-12-1-1-1-122-1-1-1-111-2-2111100000000000000000000000000−2i2i−2i2i0000i−ii−i
χ3322-2-2-2222-2-2-2-22222-2-2-2-2-2-222222-12-111-2-20000-1-2111-1112-1-1-1-2-211111122-1-1-1-1-1-100000000000000000000002-2-220000-111-10000
χ3422-2-2-2222-2-2-2-22222-2-2-2-2-2-222222-12-111-2-20000-1-2111-1112-1-1-1-2-211111122-1-1-1-1-1-10000000000000000000000-222-200001-1-110000
χ3522-2-2-2222-2-2-2-22222-2-2-2-2-2-22222-12-12-2-2110000-11-211-111-12-1-111-2-21111-1-122-1-1-1-1000000000000000000000000002i−2i−2i2i0000−iii−i
χ3622-2-2-2222-2-2-2-22222-2-2-2-2-2-22222-12-12-2-2110000-11-211-111-12-1-111-2-21111-1-122-1-1-1-100000000000000000000000000−2i2i2i−2i0000i−i−ii
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χ382-22i−2i020-2002−2−i2i2002i−2i22−2−2−i2−i2i2i222-2-22i−2i2i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1320000-22i−2i00002−22−222−2−2−i2i2−i2i2−i2−i2i2i2−1−i1+i−1+i1−i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ392-22i−2i020-200−22i2−i2002i−2i−2−222i2i2−i2−i222-2-22i−2i2i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1320000-22i−2i0000−22−22−2−222i2−i2i2−i2i2i2−i2−i2−1−i1+i−1+i1−i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i2ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13000000000000000000
χ402-22i−2i020-200−22i2−i2002i−2i−2−222i2i2−i2−i222-2-22i−2i2i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1320000-22i−2i0000−22−22−2−222i2−i2i2−i2i2i2−i2−i21+i−1−i1−i−1+i001+i1+i−1−i−1−i1−i1−i−1+i−1+i−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ13000000000000000000
χ412-2−2i2i020-2002−2i2−i200−2i2i22−2−2i2i2−i2−i222-2-2−2i2i−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2320000-2−2i2i00002−22−222−2−2i2−i2i2−i2i2i2−i2−i21−i−1+i1+i−1−i001−i1−i−1+i−1+i1+i1+i−1−i−1−i−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ422-2−2i2i020-2002−2i2−i200−2i2i22−2−2i2i2−i2−i222-2-2−2i2i−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2320000-2−2i2i00002−22−222−2−2i2−i2i2−i2i2i2−i2−i2−1+i1−i−1−i1+i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i2ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ432-2−2i2i020-200−22−i2i200−2i2i−2−222−i2−i2i2i222-2-2−2i2i−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2320000-2−2i2i0000−22−22−2−222−i2i2−i2i2−i2−i2i2i2−1+i1−i−1−i1+i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ23000000000000000000
χ442-2−2i2i020-200−22−i2i200−2i2i−2−222−i2−i2i2i222-2-2−2i2i−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2320000-2−2i2i0000−22−22−2−222−i2i2−i2i2−i2−i2i2i21−i−1+i1+i−1−i001−i1−i−1+i−1+i1+i1+i−1−i−1−i2ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23000000000000000000
χ4544444444444444444444444444-2-2-2-2-2-2-2-200001-2-211111-2-211-2-2-2-21111-2-2-2-2111100000000000000000000000000000000000000
χ464444444444-4-4-4-44444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-200001-2-211111-2-2112222-1-1-1-12222-1-1-1-100000000000000000000000000000000000000
χ474444-44-44-4-40000-4-444000000004-24-2-2-2440000-2-4222-2-2-2-4222000000000000000000000000000000000000000000000000000000
χ484444-44-44-4-40000-4-44400000000-24-2444-2-20000-22-422-2-2-22-422000000000000000000000000000000000000000000000000000000
χ494444-44-44-4-40000-4-44400000000-2-2-2-2-2-2-2-20000122-1-111122-1-100003i−3i3i−3i00003i−3i3i−3i00000000000000000000000000000000000000
χ504444-44-44-4-40000-4-44400000000-2-2-2-2-2-2-2-20000122-1-111122-1-10000−3i3i−3i3i0000−3i3i−3i3i00000000000000000000000000000000000000
χ5144-4-444-44440000-4-4-4-4000000004-24-222-4-40000-24-2-2-2-222-4222000000000000000000000000000000000000000000000000000000
χ5244-4-444-44440000-4-4-4-400000000-24-24-4-4220000-2-24-2-2-2222-422000000000000000000000000000000000000000000000000000000
χ5344-4-444-44440000-4-4-4-400000000-2-2-2-2222200001-2-2111-1-122-1-100003i−3i3i−3i0000−3i3i−3i3i00000000000000000000000000000000000000
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χ5544-4-4-4444-4-444-4-444-4-44444-4-4-4-4-2-2-2-222220000122-1-11-1-1-2-211-2-2-2-211112222-1-1-1-100000000000000000000000000000000000000
χ5644-4-4-4444-4-4-4-44444-4-4-4-4-4-44444-2-2-2-222220000122-1-11-1-1-2-2112222-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.