Finite Group Databasebeta

← Group #14300368

Character table — Group #14300368

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1122222444444444445588888888888888888101010101016161616161616161616161616161616161620202020204040404040404040606060606060606060606060120120
order12222362456661015153030444461010101212121212303030303030444121210202020202030306060606060606060606024121212446121212121288888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111-1-111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
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
χ7111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i−i−iii−ii
χ8111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiiiii−i−ii−i
χ91111111-1-1111111111111-1-1111-111-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-111-1-111-1-111-1-11111-1-1
χ101111111-1-1111111111111-1-1111-111-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-111-1-1-1-111-1-111-1-1-1-111
χ111111111-1-111111111111-11-1111-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111-11-1-1-1-11111-1-111-1-1-1-1-1-111
χ121111111-1-111111111111-11-1111-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111-11-1-1-1-111-1-111-1-1111111-1-1
χ131111111-1-1111111111-1-11-1-1111-111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111-1-111ii−i−i−i−iiiii−i−i−ii
χ141111111-1-1111111111-1-11-1-1111-111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111-1-111−i−iiiii−i−i−i−iiii−i
χ151111111-1-1111111111-1-1-11-1111-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-11-11111-1-1ii−i−i−i−iii−i−iiii−i
χ161111111-1-1111111111-1-1-11-1111-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-11-11111-1-1−i−iiiii−i−iii−i−i−ii
χ1722222-1-1222-1-1-12-1-1-1-12222-1222-1-1-1-1-1-1-1-1-1-1-1222-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-122-1-1-1-1-1-100000000000000
χ1822222-1-1222-1-1-12-1-1-1-122-2-2-1222-11111-1-1-1-1-1-1222-1-122-2-2-2-2-1-1-1-11111111122-1-1-1-2-2-1-1111100000000000000
χ1922222-1-1222-1-1-12-1-1-1-1-2-222-1222-1-1-1-1-1-1-1-1-1-1-1-2-2-211222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2111-2-211111100000000000000
χ2022222-1-1222-1-1-12-1-1-1-1-2-2-2-2-1222-11111-1-1-1-1-1-1-2-2-21122-2-2-2-2-1-1-1-111111111-2-21112211-1-1-1-100000000000000
χ2122222-1-1-2-22-1-1-12-1-1-1-1222-212221-1-111-1-1-1-1-1-1222-1-1-2-222-2-21111-1-1-1-11111-2-2-1-1-12-211-1-11100000000000000
χ2222222-1-1-2-22-1-1-12-1-1-1-122-221222111-1-1-1-1-1-1-1-1222-1-1-2-2-2-22211111111-1-1-1-1-2-2-1-1-1-221111-1-100000000000000
χ2322222-1-1-2-22-1-1-12-1-1-1-1-2-22-212221-1-111-1-1-1-1-1-1-2-2-211-2-222-2-21111-1-1-1-1111122111-22-1-111-1-100000000000000
χ2422222-1-1-2-22-1-1-12-1-1-1-1-2-2-221222111-1-1-1-1-1-1-1-1-2-2-211-2-2-2-22211111111-1-1-1-1221112-2-1-1-1-11100000000000000
χ25222-2-2222-222-2-222222220022-2-2-2000022-2-2-2-2-2-22222-2000022-2-200000000-222-2-200-22000000000000000000
χ26222-2-2222-222-2-222222-2-20022-2-2-2000022-2-2-2-222-2-2-22-2000022-2-2000000002-2-222002-2000000000000000000
χ27222-2-222-2222-2-2222222200-22-2-22000022-2-2-2-2-2-2222-220000-2-222000000002-22-2-2002-2000000000000000000
χ28222-2-222-2222-2-222222-2-200-22-2-22000022-2-2-2-222-2-2-2-220000-2-22200000000-22-22200-22000000000000000000
χ29222-2-2-1-12-22-1112-1-1-1-12200-12-2-213−33−3-1-11111-2-22-1-12-20000-1-11133−3−333−3−3-22-111001-13−33−300000000000000
χ30222-2-2-1-12-22-1112-1-1-1-12200-12-2-21−33−33-1-11111-2-22-1-12-20000-1-111−3−333−3−333-22-111001-1−33−3300000000000000
χ31222-2-2-1-12-22-1112-1-1-1-1-2-200-12-2-213−33−3-1-1111122-2112-20000-1-11133−3−333−3−32-21-1-100-11−33−3300000000000000
χ32222-2-2-1-12-22-1112-1-1-1-1-2-200-12-2-21−33−33-1-1111122-2112-20000-1-111−3−333−3−3332-21-1-100-113−33−300000000000000
χ33222-2-2-1-1-222-1112-1-1-1-1220012-2-2-13−3−33-1-11111-2-22-1-1-22000011-1-133−3−3−3−3332-2-11100-113−3−3300000000000000
χ34222-2-2-1-1-222-1112-1-1-1-1220012-2-2-1−333−3-1-11111-2-22-1-1-22000011-1-1−3−33333−3−32-2-11100-11−333−300000000000000
χ35222-2-2-1-1-222-1112-1-1-1-1-2-20012-2-2-13−3−33-1-1111122-211-22000011-1-133−3−3−3−333-221-1-1001-1−333−300000000000000
χ36222-2-2-1-1-222-1112-1-1-1-1-2-20012-2-2-1−333−3-1-1111122-211-22000011-1-1−3−33333−3−3-221-1-1001-13−3−3300000000000000
χ3722-22-222002-22-22222222000-22-200000-2-222-2-22-2-22200000000000000000000-22-2000000002-2002-200000000
χ3822-22-222002-22-22222222000-22-200000-2-222-2-22-2-22200000000000000000000-22-200000000-2200-2200000000
χ3922-22-222002-22-222222-2-2000-22-200000-2-222-2-2-222-2-2000000000000000000002-22000000002i−2i00−2i2i00000000
χ4022-22-222002-22-222222-2-2000-22-200000-2-222-2-2-222-2-2000000000000000000002-2200000000−2i2i002i−2i00000000
χ4122-2-2222002-2-222222222000-2-2200000-2-2-2-222-22-22200000000000000000000-2-2200000000002-2002-2000000
χ4222-2-2222002-2-222222222000-2-2200000-2-2-2-222-22-22200000000000000000000-2-220000000000-2200-22000000
χ4322-2-2222002-2-2222222-2-2000-2-2200000-2-2-2-2222-22-2-20000000000000000000022-200000000002i−2i00−2i2i000000
χ4422-2-2222002-2-2222222-2-2000-2-2200000-2-2-2-2222-22-2-20000000000000000000022-20000000000−2i2i002i−2i000000
χ45444444444-1444-1-1-1-1-100444-1-1-144444-1-1-1-1-1-100000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000
χ46444444444-1444-1-1-1-1-100-4-44-1-1-14-4-4-4-4-1-1-1-1-1-100000-1-11111-1-1-1-111111111000000000000000000000000000
χ474444444-4-4-1444-1-1-1-1-1004-4-4-1-1-1-444-4-4-1-1-1-1-1-10000011-1-1111111-1-1-1-11111000000000000000000000000000
χ484444444-4-4-1444-1-1-1-1-100-44-4-1-1-1-4-4-444-1-1-1-1-1-1000001111-1-111111111-1-1-1-1000000000000000000000000000
χ4944444-2-244-1-2-2-2-11−i1521+i1521−i1521+i1520044-2-1-1-1-2-2-2-2-21−i1521+i1521−i1521+i1521−i1521+i15200000-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i152000000000000000000000000000
χ5044444-2-244-1-2-2-2-11−i1521+i1521−i1521+i15200-4-4-2-1-1-1-222221−i1521+i1521−i1521+i1521−i1521+i15200000-1-111111−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152000000000000000000000000000
χ5144444-2-244-1-2-2-2-11+i1521−i1521+i1521−i1520044-2-1-1-1-2-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i15200000-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i1521+i1521−i152000000000000000000000000000
χ5244444-2-244-1-2-2-2-11+i1521−i1521+i1521−i15200-4-4-2-1-1-1-222221+i1521−i1521+i1521−i1521+i1521−i15200000-1-111111+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152000000000000000000000000000
χ5344444-2-2-4-4-1-2-2-2-11−i1521+i1521−i1521+i152004-42-1-1-12-2-2221−i1521+i1521−i1521+i1521−i1521+i1520000011-1-111−1+i152−1−i152−1+i152−1−i1521−i1521+i1521−i1521+i152−1+i152−1−i152−1+i152−1−i152000000000000000000000000000
χ5444444-2-2-4-4-1-2-2-2-11−i1521+i1521−i1521+i15200-442-1-1-1222-2-21−i1521+i1521−i1521+i1521−i1521+i152000001111-1-1−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i1521−i1521+i1521−i1521+i152000000000000000000000000000
χ5544444-2-2-4-4-1-2-2-2-11+i1521−i1521+i1521−i152004-42-1-1-12-2-2221+i1521−i1521+i1521−i1521+i1521−i1520000011-1-111−1−i152−1+i152−1−i152−1+i1521+i1521−i1521+i1521−i152−1−i152−1+i152−1−i152−1+i152000000000000000000000000000
χ5644444-2-2-4-4-1-2-2-2-11+i1521−i1521+i1521−i15200-442-1-1-1222-2-21+i1521−i1521+i1521−i1521+i1521−i152000001111-1-1−1−i152−1+i152−1−i152−1+i152−1−i152−1+i152−1−i152−1+i1521+i1521−i1521+i1521−i152000000000000000000000000000
χ57444-4-4444-4-14-4-4-1-1-1-1-100004-111-40000-1-1111100000-11−i5i5−i5i5-1-111−i5i5i5−i5−i5i5i5−i5000000000000000000000000000
χ58444-4-4444-4-14-4-4-1-1-1-1-100004-111-40000-1-1111100000-11i5−i5i5−i5-1-111i5−i5−i5i5i5−i5−i5i5000000000000000000000000000
χ59444-4-444-44-14-4-4-1-1-1-1-10000-4-11140000-1-11111000001-1−i5i5i5−i511-1-1−i5i5i5−i5i5−i5−i5i5000000000000000000000000000
χ60444-4-444-44-14-4-4-1-1-1-1-10000-4-11140000-1-11111000001-1i5−i5−i5i511-1-1i5−i5−i5i5−i5i5i5−i5000000000000000000000000000
χ61444-4-4-2-24-4-1-222-11−i1521+i1521−i1521+i1520000-2-111223−2323−231−i1521+i152−1+i152−1−i152−1+i152−1−i15200000-11i5−i5i5−i51−i1521+i152−1+i152−1−i152ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94000000000000000000000000000
χ62444-4-4-2-24-4-1-222-11−i1521+i1521−i1521+i1520000-2-1112−2323−23231−i1521+i152−1+i152−1−i152−1+i152−1−i15200000-11−i5i5−i5i51−i1521+i152−1+i152−1−i152−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94000000000000000000000000000
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χ66444-4-4-2-2-44-1-222-11−i1521+i1521−i1521+i15200002-111-2−232323−231−i1521+i152−1+i152−1−i152−1+i152−1−i152000001-1−i5i5i5−i5−1+i152−1−i1521−i1521+i152−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94000000000000000000000000000
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χ8516-1600016-1600-40004-4-444000000000000000000000000000000000000000000000000000000000000000000000
χ8616-16000-8800-400042−2i152+2i15−2+2i15−2−2i15000000000000000000000000000000000000000000000000000000000000000000000
χ8716-16000-8800-400042+2i152−2i15−2−2i15−2+2i15000000000000000000000000000000000000000000000000000000000000000000000

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