Finite Group Databasebeta

← Group #14301169

Character table — Group #14301169

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1122222444444444445588888888888888888101010101016161616161616161616161616161616161620202020204040404040404040606060606060606060606060120120
order1223446245610121215153030444681012121220202424303060606060224121210202020303040406060606060601201201201202466122666812242488888888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-11-111-1-111-1-11111111111111-1-111-1-111-1-1-1-1-1-1-1-111111-11-1-1-11-1-111111111-1-1-1-1-1-1
χ411111111111111111111-11-111-1-111-1-11111111111111-1-111-1-111-1-1-1-1-1-1-1-111111-11-1-1-11-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-111111111111111111-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−ii−i
χ6111111111111111111-1-111111111111111111-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii−ii
χ7111111111111111111-1-1-11-111-1-111-1-1111111-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-111iiii−i−i−i−i−i−iii−ii
χ8111111111111111111-1-1-11-111-1-111-1-1111111-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-111−i−i−i−iiiiiii−i−ii−i
χ91111111-1-1111111111111-1-11-11111-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-111-1-1-1-111-1-111-1-11111-1-1
χ101111111-1-1111111111111-1-11-11111-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-111-1-1-1-1-1-111-1-111-1-1-1-111
χ111111111-1-111111111111-1-111-1-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111-1-1-1-11-11111-1-111-1-1-1-1-1-111
χ121111111-1-111111111111-1-111-1-1-1111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111-1-1-1-11-111-1-111-1-1111111-1-1
χ131111111-1-1111111111-1-11-1-11-11111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11-1-11111ii−i−i−i−iiiii−i−i−ii
χ141111111-1-1111111111-1-11-1-11-11111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-11-1-11111−i−iiiii−i−i−i−iiii−i
χ151111111-1-1111111111-1-1-1-111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-11111-11-1-1ii−i−i−i−iii−i−iiii−i
χ161111111-1-1111111111-1-1-1-111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-11111-11-1-1−i−iiiii−i−iii−i−i−ii
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χ182222-2-2200222-2-22222220002000-2-20022-2-2-2-2-2-222200000000000000000000-2-2200000000-2200-2200000000
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χ24222-122-1222-12-1-1-1-1-1-1-2-2-2-1-22-1112211-1-1-1-1-1-1-2-2-21122-2-2-1-1-2-2-1-111111111-2-211121-1-121-1-100000000000000
χ25222-122-1-2-22-12-1-1-1-1-1-12221-221-1-12211-1-1-1-1-1-1222-1-1-2-22211-2-211-1-1-1-11111-2-2-1-1-121-1-1-211100000000000000
χ26222-122-1-2-22-12-1-1-1-1-1-122-212211122-1-1-1-1-1-1-1-1222-1-1-2-2-2-21122111111-1-1-1-1-2-2-1-1-1-211121-1-100000000000000
χ27222-122-1-2-22-12-1-1-1-1-1-1-2-221-221-1-12211-1-1-1-1-1-1-2-2-211-2-22211-2-211-1-1-1-1111122111-2-1112-1-1-100000000000000
χ28222-122-1-2-22-12-1-1-1-1-1-1-2-2-212211122-1-1-1-1-1-1-1-1-2-2-211-2-2-2-21122111111-1-1-1-1221112-1-1-1-2-11100000000000000
χ2922-222-22002-222-2222222000-20002-200-2-222-2-2-22-222000000000000000000002-2-200000000002-2002-2000000
χ3022-222-22002-222-2222222000-20002-200-2-222-2-2-22-222000000000000000000002-2-20000000000-2200-22000000
χ3122-222-22002-222-22222-2-2000-20002-200-2-222-2-22-22-2-200000000000000000000-22200000000002i−2i00−2i2i000000
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χ3422-22-2222-22-22-222222-2-2020-2-200-2200-2-2-2-222-222-2-22-2002200-2-2000000002-22-2202000-20000000000000000
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χ3622-22-222-222-22-222222-2-20-20-2200-2200-2-2-2-222-222-2-2-2200-2-2002200000000-222-220-200020000000000000000
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χ3922-2-1-22-12-22121-1-1-1-1-1-2-20-10-21−i3i3-22−i3i31111-1-1-222112-200-1-10011−i3−i3i3i3−i3−i3i3i32-2-11-10-1i3−i301i3−i300000000000000
χ4022-2-1-22-12-22121-1-1-1-1-1-2-20-10-21i3−i3-22i3−i31111-1-1-222112-200-1-10011i3i3−i3−i3i3i3−i3−i32-2-11-10-1−i3i301−i3i300000000000000
χ4122-2-1-22-1-222121-1-1-1-1-122010-2-1−i3i3-22i3−i31111-1-12-2-2-1-1-22001100-1-1−i3−i3i3i3i3i3−i3−i32-21-110-1−i3i301i3−i300000000000000
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χ4422-2-1-22-1-222121-1-1-1-1-1-2-2010-2-1i3−i3-22−i3i31111-1-1-22211-22001100-1-1i3i3−i3−i3−i3−i3i3i3-22-11-101−i3i30-1i3−i300000000000000
χ45444444444-14-144-1-1-1-100444-1444-1-144-1-1-1-1-1-100000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000
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χ474444444-4-4-14-144-1-1-1-1004-4-4-1-444-1-1-4-4-1-1-1-1-1-10000011-1-1111111-1-1-1-11111000000000000000000000000000
χ484444444-4-4-14-144-1-1-1-100-4-44-1-4-4-4-1-144-1-1-1-1-1-100000111111-1-1111111-1-1-1-1000000000000000000000000000
χ49444-244-244-1-2-1-2-21−i1521+i1521−i1521+i152004-24-1-2-2-2-1-1-2-21−i1521+i1521−i1521+i1521−i1521+i15200000-1-1-1-11−i1521+i152-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152000000000000000000000000000
χ50444-244-244-1-2-1-2-21−i1521+i1521−i1521+i15200-4-2-4-1-222-1-1221−i1521+i1521−i1521+i1521−i1521+i15200000-1-1111−i1521+i152111−i1521+i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152000000000000000000000000000
χ51444-244-244-1-2-1-2-21+i1521−i1521+i1521−i152004-24-1-2-2-2-1-1-2-21+i1521−i1521+i1521−i1521+i1521−i15200000-1-1-1-11+i1521−i152-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152000000000000000000000000000
χ52444-244-244-1-2-1-2-21+i1521−i1521+i1521−i15200-4-2-4-1-222-1-1221+i1521−i1521+i1521−i1521+i1521−i15200000-1-1111+i1521−i152111+i1521−i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152000000000000000000000000000
χ53444-244-2-4-4-1-2-1-2-21−i1521+i1521−i1521+i1520042-4-12-2-2-1-1221−i1521+i1521−i1521+i1521−i1521+i1520000011-1-1−1+i152−1−i15211−1+i152−1−i1521−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152000000000000000000000000000
χ54444-244-2-4-4-1-2-1-2-21−i1521+i1521−i1521+i15200-424-1222-1-1-2-21−i1521+i1521−i1521+i1521−i1521+i152000001111−1+i152−1−i152-1-1−1+i152−1−i152−1+i152−1−i152−1+i152−1−i1521−i1521+i1521−i1521+i152000000000000000000000000000
χ55444-244-2-4-4-1-2-1-2-21+i1521−i1521+i1521−i1520042-4-12-2-2-1-1221+i1521−i1521+i1521−i1521+i1521−i1520000011-1-1−1−i152−1+i15211−1−i152−1+i1521+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152000000000000000000000000000
χ56444-244-2-4-4-1-2-1-2-21+i1521−i1521+i1521−i15200-424-1222-1-1-2-21+i1521−i1521+i1521−i1521+i1521−i152000001111−1−i152−1+i152-1-1−1−i152−1+i152−1−i152−1+i152−1−i152−1+i1521+i1521−i1521+i1521−i152000000000000000000000000000
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χ8288-8-48-8-400-24-2-441+i151−i151+i151−i15000002000-2200−1−i15−1+i151+i151−i15−1−i15−1+i1500000000000000000000000000000000000000000000000000
χ838-80-40040080-800-4-4448i−8i00000000000000000000−4i4i000000000000000000000000000000000000000000000
χ848-80-40040080-800-4-444−8i8i000000000000000000004i−4i000000000000000000000000000000000000000000000
χ8516-1601600-1600-40400-4-444000000000000000000000000000000000000000000000000000000000000000000000
χ8616-160-800800-404002−2i152+2i15−2+2i15−2−2i15000000000000000000000000000000000000000000000000000000000000000000000
χ8716-160-800800-404002+2i152−2i15−2−2i15−2+2i15000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.