Finite Group Databasebeta

← Group #14299672

Character table — Group #14299672

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1122222444444444445588888888888888888101010101016161616161616161616161616161616161620202020204040404040404040606060606060606060606060120120
order1223446225610121215153030446688102020242424243030606060602241212101030303030404040401201201201201201201201204466128812122424242488888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111-1-1111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
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
χ7111111111111111111-1-111-1-1111-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111iiii−i−i−i−i−i−iii−ii
χ8111111111111111111-1-111-1-1111-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−iiiiiii−i−ii−i
χ91111111-1-111111111111-1-11-111111-1-111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-111-1-111-1-111-1-11111-1-1
χ101111111-1-111111111111-1-11-111111-1-111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-111-1-1-1-111-1-111-1-1-1-111
χ111111111-1-111111111111-1-1-11111-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111-11-1-1-1-11111-1-111-1-1-1-1-1-111
χ121111111-1-111111111111-1-1-11111-1-11111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111-11-1-1-1-111-1-111-1-1111111-1-1
χ131111111-1-1111111111-1-1-1-11-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111-1-111ii−i−i−i−iiiii−i−i−ii
χ141111111-1-1111111111-1-1-1-11-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111-1-111−i−iiiii−i−i−i−iiii−i
χ151111111-1-1111111111-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-11-11111-1-1ii−i−i−i−iii−i−iiii−i
χ161111111-1-1111111111-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-11-11111-1-1−i−iiiii−i−iii−i−i−ii
χ172222-2-222-2222-2-22222222-2002-2-2000022-2-2-2-2-2-22222-222-2-20000000000002-2-2-22002-2000000000000000000
χ182222-2-222-2222-2-22222-2-22-2002-2-2000022-2-2-2-222-2-2-22-222-2-2000000000000-2222-200-22000000000000000000
χ192222-2-22-22222-2-2222222-22002-2-2000022-2-2-2-2-2-2222-22-2-222000000000000-22-2-2200-22000000000000000000
χ202222-2-22-22222-2-22222-2-2-22002-2-2000022-2-2-2-222-2-2-2-22-2-2220000000000002-222-2002-2000000000000000000
χ21222-122-1222-12-1-1-1-1-1-122-1-122222-1-1-1-1-1-1-1-1-1-1222-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-122-1-1-1-1-1-100000000000000
χ22222-122-1222-12-1-1-1-1-1-122-1-1-2-22221111-1-1-1-1-1-1222-1-122-1-1-1-1-2-2-2-21111111122-1-1-1-2-2-1-1111100000000000000
χ23222-122-1222-12-1-1-1-1-1-1-2-2-1-122222-1-1-1-1-1-1-1-1-1-1-2-2-21122-1-1-1-12222-1-1-1-1-1-1-1-1-2-2111-2-211111100000000000000
χ24222-122-1222-12-1-1-1-1-1-1-2-2-1-1-2-22221111-1-1-1-1-1-1-2-2-21122-1-1-1-1-2-2-2-211111111-2-21112211-1-1-1-100000000000000
χ25222-122-1-2-22-12-1-1-1-1-1-122112-2222-1-111-1-1-1-1-1-1222-1-1-2-2111122-2-2-1-1-1-11111-2-2-1-1-12-211-1-11100000000000000
χ26222-122-1-2-22-12-1-1-1-1-1-12211-2222211-1-1-1-1-1-1-1-1222-1-1-2-21111-2-2221111-1-1-1-1-2-2-1-1-1-221111-1-100000000000000
χ27222-122-1-2-22-12-1-1-1-1-1-1-2-2112-2222-1-111-1-1-1-1-1-1-2-2-211-2-2111122-2-2-1-1-1-1111122111-22-1-111-1-100000000000000
χ28222-122-1-2-22-12-1-1-1-1-1-1-2-211-2222211-1-1-1-1-1-1-1-1-2-2-211-2-21111-2-2221111-1-1-1-1221112-2-1-1-1-11100000000000000
χ29222-1-2-2-12-22-1211-1-1-1-122-11002-2-23−33−3-1-11111-2-22-1-12-2-1-111000033−3−333−3−32-211-100-113−33−300000000000000
χ30222-1-2-2-12-22-1211-1-1-1-122-11002-2-2−33−33-1-11111-2-22-1-12-2-1-1110000−3−333−3−3332-211-100-11−33−3300000000000000
χ31222-1-2-2-12-22-1211-1-1-1-1-2-2-11002-2-23−33−3-1-1111122-2112-2-1-111000033−3−333−3−3-22-1-11001-1−33−3300000000000000
χ32222-1-2-2-12-22-1211-1-1-1-1-2-2-11002-2-2−33−33-1-1111122-2112-2-1-1110000−3−333−3−333-22-1-11001-13−33−300000000000000
χ33222-1-2-2-1-222-1211-1-1-1-1221-1002-2-23−3−33-1-11111-2-22-1-1-2211-1-1000033−3−3−3−333-2211-1001-13−3−3300000000000000
χ34222-1-2-2-1-222-1211-1-1-1-1221-1002-2-2−333−3-1-11111-2-22-1-1-2211-1-10000−3−33333−3−3-2211-1001-1−333−300000000000000
χ35222-1-2-2-1-222-1211-1-1-1-1-2-21-1002-2-23−3−33-1-1111122-211-2211-1-1000033−3−3−3−3332-2-1-1100-11−333−300000000000000
χ36222-1-2-2-1-222-1211-1-1-1-1-2-21-1002-2-2−333−3-1-1111122-211-2211-1-10000−3−33333−3−32-2-1-1100-113−3−3300000000000000
χ3722-222-22002-222-22222220000-22-20000-2-222-2-22-2-222000000000000000000002-2-200000000002-2002-2000000
χ3822-222-22002-222-22222220000-22-20000-2-222-2-22-2-222000000000000000000002-2-20000000000-2200-22000000
χ3922-222-22002-222-22222-2-20000-22-20000-2-222-2-2-222-2-200000000000000000000-22200000000002i−2i00−2i2i000000
χ4022-222-22002-222-22222-2-20000-22-20000-2-222-2-2-222-2-200000000000000000000-2220000000000−2i2i002i−2i000000
χ4122-22-222002-22-222222220000-2-220000-2-2-2-222-22-22200000000000000000000-22-2000000002-2002-200000000
χ4222-22-222002-22-222222220000-2-220000-2-2-2-222-22-22200000000000000000000-22-200000000-2200-2200000000
χ4322-22-222002-22-222222-2-20000-2-220000-2-2-2-2222-22-2-2000000000000000000002-22000000002i−2i00−2i2i00000000
χ4422-22-222002-22-222222-2-20000-2-220000-2-2-2-2222-22-2-2000000000000000000002-2200000000−2i2i002i−2i00000000
χ45444444444-14-144-1-1-1-1004444-1-1-14444-1-1-1-1-1-100000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000
χ46444444444-14-144-1-1-1-10044-4-4-1-1-1-4-4-4-4-1-1-1-1-1-100000-1-1-1-1-1-1111111111111000000000000000000000000000
χ474444444-4-4-14-144-1-1-1-100-4-44-4-1-1-144-4-4-1-1-1-1-1-100000111111-1-111-1-1-1-11111000000000000000000000000000
χ484444444-4-4-14-144-1-1-1-100-4-4-44-1-1-1-4-444-1-1-1-1-1-10000011111111-1-11111-1-1-1-1000000000000000000000000000
χ494444-4-444-4-14-1-4-4-1-1-1-1004-400-1110000-1-1111100000-11-1-111−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5000000000000000000000000000
χ504444-4-444-4-14-1-4-4-1-1-1-1004-400-1110000-1-1111100000-11-1-111i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5000000000000000000000000000
χ514444-4-44-44-14-1-4-4-1-1-1-100-4400-1110000-1-11111000001-111-1-1−i5i5i5−i5−i5i5−i5i5i5−i5i5−i5000000000000000000000000000
χ524444-4-44-44-14-1-4-4-1-1-1-100-4400-1110000-1-11111000001-111-1-1i5−i5−i5i5i5−i5i5−i5−i5i5−i5i5000000000000000000000000000
χ53444-244-244-1-2-1-2-21−i1521+i1521−i1521+i15200-2-244-1-1-1-2-2-2-21−i1521+i1521−i1521+i1521−i1521+i15200000-1-11−i1521+i1521−i1521+i152-1-1-1-11−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i152000000000000000000000000000
χ54444-244-244-1-2-1-2-21−i1521+i1521−i1521+i15200-2-2-4-4-1-1-122221−i1521+i1521−i1521+i1521−i1521+i15200000-1-11−i1521+i1521−i1521+i1521111−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152000000000000000000000000000
χ55444-244-244-1-2-1-2-21+i1521−i1521+i1521−i15200-2-244-1-1-1-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i15200000-1-11+i1521−i1521+i1521−i152-1-1-1-11+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i152000000000000000000000000000
χ56444-244-244-1-2-1-2-21+i1521−i1521+i1521−i15200-2-2-4-4-1-1-122221+i1521−i1521+i1521−i1521+i1521−i15200000-1-11+i1521−i1521+i1521−i1521111−1−i152−1+i152−1+i152−1−i152−1−i152−1+i152−1+i152−1−i152000000000000000000000000000
χ57444-244-2-4-4-1-2-1-2-21−i1521+i1521−i1521+i15200224-4-1-1-1-2-2221−i1521+i1521−i1521+i1521−i1521+i1520000011−1+i152−1−i152−1+i152−1−i152-1-1111−i1521+i1521+i1521−i152−1+i152−1−i152−1−i152−1+i152000000000000000000000000000
χ58444-244-2-4-4-1-2-1-2-21−i1521+i1521−i1521+i1520022-44-1-1-122-2-21−i1521+i1521−i1521+i1521−i1521+i1520000011−1+i152−1−i152−1+i152−1−i15211-1-1−1+i152−1−i152−1−i152−1+i1521−i1521+i1521+i1521−i152000000000000000000000000000
χ59444-244-2-4-4-1-2-1-2-21+i1521−i1521+i1521−i15200224-4-1-1-1-2-2221+i1521−i1521+i1521−i1521+i1521−i1520000011−1−i152−1+i152−1−i152−1+i152-1-1111+i1521−i1521−i1521+i152−1−i152−1+i152−1+i152−1−i152000000000000000000000000000
χ60444-244-2-4-4-1-2-1-2-21+i1521−i1521+i1521−i1520022-44-1-1-122-2-21+i1521−i1521+i1521−i1521+i1521−i1520000011−1−i152−1+i152−1−i152−1+i15211-1-1−1−i152−1+i152−1+i152−1−i1521+i1521−i1521−i1521+i152000000000000000000000000000
χ61444-2-4-4-24-4-1-2-1221−i1521+i1521−i1521+i15200-2200-11123−2323−231−i1521+i152−1+i152−1−i152−1+i152−1−i15200000-111−i1521+i152−1+i152−1−i152i5−i5i5−i5ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118000000000000000000000000000
χ62444-2-4-4-24-4-1-2-1221−i1521+i1521−i1521+i15200-2200-111−2323−23231−i1521+i152−1+i152−1−i152−1+i152−1−i15200000-111−i1521+i152−1+i152−1−i152−i5i5−i5i5−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118000000000000000000000000000
χ63444-2-4-4-24-4-1-2-1221+i1521−i1521+i1521−i15200-2200-11123−2323−231+i1521−i152−1−i152−1+i152−1−i152−1+i15200000-111+i1521−i152−1−i152−1+i152−i5i5−i5i5ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94000000000000000000000000000
χ64444-2-4-4-24-4-1-2-1221+i1521−i1521+i1521−i15200-2200-111−2323−23231+i1521−i152−1−i152−1+i152−1−i152−1+i15200000-111+i1521−i152−1−i152−1+i152i5−i5i5−i5−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94000000000000000000000000000
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χ66444-2-4-4-2-44-1-2-1221−i1521+i1521−i1521+i152002-200-111−232323−231−i1521+i152−1+i152−1−i152−1+i152−1−i152000001-1−1+i152−1−i1521−i1521+i152−i5i5i5−i5−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118000000000000000000000000000
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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.