Finite Group Databasebeta

← Group #14299674

Character table — Group #14299674

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1122222444444444445588888888888888888101010101016161616161616161616161616161616161620202020204040404040404040606060606060606060606060120120
order1223446445610121215153030448810121220202424242430306060606022412122020404040406060606012012012012012012012012022661266882424242488888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111-1-111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
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
χ7111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−iii−ii
χ8111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiii−i−ii−i
χ91111111-1-1111111111111-11-1-11111-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111-1-11-111-1-111-1-111-1-11111-1-1
χ101111111-1-1111111111111-11-1-11111-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111-1-11-111-1-1-1-111-1-111-1-1-1-111
χ111111111-1-111111111111-111-1-111-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111-1-1-11-1-11111-1-111-1-1-1-1-1-111
χ121111111-1-111111111111-111-1-111-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1111-1-1-11-1-111-1-111-1-1111111-1-1
χ131111111-1-1111111111-1-11-11-1-11111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-111-11-1-111ii−i−i−i−iiiii−i−i−ii
χ141111111-1-1111111111-1-11-11-1-11111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-111-11-1-111−i−iiiii−i−i−i−iiii−i
χ151111111-1-1111111111-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1111-111-1-1ii−i−i−i−iii−i−iiii−i
χ161111111-1-1111111111-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1111-111-1-1−i−iiiii−i−iii−i−i−ii
χ172222-2-222-2222-2-22222220022-2-2-2000022-2-2-2-2-2-22222-2000022-2-2000000002-2-2-222-200000000000000000000
χ182222-2-222-2222-2-22222-2-20022-2-2-2000022-2-2-2-222-2-2-22-2000022-2-200000000-2222-2-2200000000000000000000
χ192222-2-22-22222-2-2222222002-22-2-2000022-2-2-2-2-2-2222-220000-2-22200000000-22-2-22-2200000000000000000000
χ202222-2-22-22222-2-22222-2-2002-22-2-2000022-2-2-2-222-2-2-2-220000-2-222000000002-222-22-200000000000000000000
χ21222-122-1222-12-1-1-1-1-1-122222-1-122-1-1-1-1-1-1-1-1-1-1222-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-122-1-1-1-100000000000000
χ22222-122-1222-12-1-1-1-1-1-122-2-22-1-1221111-1-1-1-1-1-1222-1-122-2-2-2-2-1-1-1-11111111122-1-1-1-1-1-2-2111100000000000000
χ23222-122-1222-12-1-1-1-1-1-1-2-2222-1-122-1-1-1-1-1-1-1-1-1-1-2-2-211222222-1-1-1-1-1-1-1-1-1-1-1-1-2-211111-2-2111100000000000000
χ24222-122-1222-12-1-1-1-1-1-1-2-2-2-22-1-1221111-1-1-1-1-1-1-2-2-21122-2-2-2-2-1-1-1-111111111-2-21111122-1-1-1-100000000000000
χ25222-122-1-2-22-12-1-1-1-1-1-1222-221122-1-111-1-1-1-1-1-1222-1-1-2-222-2-21111-1-1-1-11111-2-2-1-1-1112-2-1-11100000000000000
χ26222-122-1-2-22-12-1-1-1-1-1-122-222112211-1-1-1-1-1-1-1-1222-1-1-2-2-2-22211111111-1-1-1-1-2-2-1-1-111-2211-1-100000000000000
χ27222-122-1-2-22-12-1-1-1-1-1-1-2-22-221122-1-111-1-1-1-1-1-1-2-2-211-2-222-2-21111-1-1-1-1111122111-1-1-2211-1-100000000000000
χ28222-122-1-2-22-12-1-1-1-1-1-1-2-2-222112211-1-1-1-1-1-1-1-1-2-2-211-2-2-2-22211111111-1-1-1-122111-1-12-2-1-11100000000000000
χ29222-1-2-2-12-22-1211-1-1-1-122002-11-2-23−33−3-1-11111-2-22-1-12-20000-1-11133−3−333−3−32-211-1-11003−33−300000000000000
χ30222-1-2-2-12-22-1211-1-1-1-122002-11-2-2−33−33-1-11111-2-22-1-12-20000-1-111−3−333−3−3332-211-1-1100−33−3300000000000000
χ31222-1-2-2-12-22-1211-1-1-1-1-2-2002-11-2-23−33−3-1-1111122-2112-20000-1-11133−3−333−3−3-22-1-111-100−33−3300000000000000
χ32222-1-2-2-12-22-1211-1-1-1-1-2-2002-11-2-2−33−33-1-1111122-2112-20000-1-111−3−333−3−333-22-1-111-1003−33−300000000000000
χ33222-1-2-2-1-222-1211-1-1-1-1220021-1-2-23−3−33-1-11111-2-22-1-1-22000011-1-133−3−3−3−333-2211-11-1003−3−3300000000000000
χ34222-1-2-2-1-222-1211-1-1-1-1220021-1-2-2−333−3-1-11111-2-22-1-1-22000011-1-1−3−33333−3−3-2211-11-100−333−300000000000000
χ35222-1-2-2-1-222-1211-1-1-1-1-2-20021-1-2-23−3−33-1-1111122-211-22000011-1-133−3−3−3−3332-2-1-11-1100−333−300000000000000
χ36222-1-2-2-1-222-1211-1-1-1-1-2-20021-1-2-2−333−3-1-1111122-211-22000011-1-1−3−33333−3−32-2-1-11-11003−3−3300000000000000
χ3722-222-22002-222-222222200-2002-20000-2-222-2-22-2-222000000000000000000002-2-200000000002-2002-2000000
χ3822-222-22002-222-222222200-2002-20000-2-222-2-22-2-222000000000000000000002-2-20000000000-2200-22000000
χ3922-222-22002-222-22222-2-200-2002-20000-2-222-2-2-222-2-200000000000000000000-22200000000002i−2i00−2i2i000000
χ4022-222-22002-222-22222-2-200-2002-20000-2-222-2-2-222-2-200000000000000000000-2220000000000−2i2i002i−2i000000
χ4122-22-222002-22-2222222200-200-220000-2-2-2-222-22-22200000000000000000000-22-2000000002-2002-200000000
χ4222-22-222002-22-2222222200-200-220000-2-2-2-222-22-22200000000000000000000-22-200000000-2200-2200000000
χ4322-22-222002-22-222222-2-200-200-220000-2-2-2-2222-22-2-2000000000000000000002-22000000002i−2i00−2i2i00000000
χ4422-22-222002-22-222222-2-200-200-220000-2-2-2-2222-22-2-2000000000000000000002-2200000000−2i2i002i−2i00000000
χ45444444444-14-144-1-1-1-10044-144-1-14444-1-1-1-1-1-100000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000
χ46444444444-14-144-1-1-1-100-4-4-144-1-1-4-4-4-4-1-1-1-1-1-100000-1-11111-1-1-1-111111111000000000000000000000000000
χ474444444-4-4-14-144-1-1-1-1004-4-1-4-4-1-144-4-4-1-1-1-1-1-10000011-1-1111111-1-1-1-11111000000000000000000000000000
χ484444444-4-4-14-144-1-1-1-100-44-1-4-4-1-1-4-444-1-1-1-1-1-1000001111-1-111111111-1-1-1-1000000000000000000000000000
χ494444-4-444-4-14-1-4-4-1-1-1-10000-14-4110000-1-1111100000-11−i5i5−i5i5-1-111−i5i5−i5i5−i5i5−i5i5000000000000000000000000000
χ504444-4-444-4-14-1-4-4-1-1-1-10000-14-4110000-1-1111100000-11i5−i5i5−i5-1-111i5−i5i5−i5i5−i5i5−i5000000000000000000000000000
χ514444-4-44-44-14-1-4-4-1-1-1-10000-1-44110000-1-11111000001-1−i5i5i5−i511-1-1−i5i5−i5i5i5−i5i5−i5000000000000000000000000000
χ524444-4-44-44-14-1-4-4-1-1-1-10000-1-44110000-1-11111000001-1i5−i5−i5i511-1-1i5−i5i5−i5−i5i5−i5i5000000000000000000000000000
χ53444-244-244-1-2-1-2-21−i1521+i1521−i1521+i1520044-1-2-2-1-1-2-2-2-21−i1521+i1521−i1521+i1521−i1521+i15200000-1-1-1-1-1-11−i1521+i1521−i1521+i1521−i1521+i1521+i1521−i1521−i1521+i1521+i1521−i152000000000000000000000000000
χ54444-244-244-1-2-1-2-21−i1521+i1521−i1521+i15200-4-4-1-2-2-1-122221−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
χ55444-244-244-1-2-1-2-21+i1521−i1521+i1521−i1520044-1-2-2-1-1-2-2-2-21+i1521−i1521+i1521−i1521+i1521−i15200000-1-1-1-1-1-11+i1521−i1521+i1521−i1521+i1521−i1521−i1521+i1521+i1521−i1521−i1521+i152000000000000000000000000000
χ56444-244-244-1-2-1-2-21+i1521−i1521+i1521−i15200-4-4-1-2-2-1-122221+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
χ57444-244-2-4-4-1-2-1-2-21−i1521+i1521−i1521+i152004-4-122-1-1-2-2221−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
χ58444-244-2-4-4-1-2-1-2-21−i1521+i1521−i1521+i15200-44-122-1-122-2-21−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
χ59444-244-2-4-4-1-2-1-2-21+i1521−i1521+i1521−i152004-4-122-1-1-2-2221+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
χ60444-244-2-4-4-1-2-1-2-21+i1521−i1521+i1521−i15200-44-122-1-122-2-21+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
χ61444-2-4-4-24-4-1-2-1221−i1521+i1521−i1521+i1520000-1-221123−2323−231−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−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+i1520000-1-2211−2323−23231−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+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−i1520000-1-221123−2323−231+i1521−i152−1−i152−1+i152−1−i152−1+i15200000-11−i5i5−i5i51+i1521−i152−1−i152−1+i152ζ38−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−i1520000-1-2211−2323−23231+i1521−i152−1−i152−1+i152−1−i152−1+i15200000-11i5−i5i5−i51+i1521−i152−1−i152−1+i152−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
χ65444-2-4-4-2-44-1-2-1221−i1521+i1521−i1521+i1520000-12-21123−23−23231−i1521+i152−1+i152−1−i152−1+i152−1−i152000001-1i5−i5−i5i5−1+i152−1−i1521−i1521+i152ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118000000000000000000000000000
χ66444-2-4-4-2-44-1-2-1221−i1521+i1521−i1521+i1520000-12-211−232323−231−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+ζ94ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118000000000000000000000000000
χ67444-2-4-4-2-44-1-2-1221+i1521−i1521+i1521−i1520000-12-21123−23−23231+i1521−i152−1−i152−1+i152−1−i152−1+i152000001-1−i5i5i5−i5−1−i152−1+i1521+i1521−i152ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94000000000000000000000000000
χ68444-2-4-4-2-44-1-2-1221+i1521−i1521+i1521−i1520000-12-211−232323−231+i1521−i152−1−i152−1+i152−1−i152−1+i152000001-1i5−i5−i5i5−1−i152−1+i1521+i1521−i152−ζ38+ζ46−ζ62+ζ94−ζ14+ζ22−ζ86+ζ118ζ14−ζ22+ζ86−ζ118ζ38−ζ46+ζ62−ζ94ζ38−ζ46+ζ62−ζ94ζ14−ζ22+ζ86−ζ118−ζ14+ζ22−ζ86+ζ118−ζ38+ζ46−ζ62+ζ94000000000000000000000000000
χ6944-4-24-4-200424-22-2-2-2-24400-4004-4000022-2-2224-4-4-2-200000000000000000000-2220000000000000000000000
χ7044-4-24-4-200424-22-2-2-2-2-4-400-4004-4000022-2-222-44422000000000000000000002-2-20000000000000000000000
χ7144-4-2-44-2004242-2-2-2-2-24400-400-4400002222-2-2-44-4-2-2000000000000000000002-220000000000000000000000
χ7244-4-2-44-2004242-2-2-2-2-2-4-400-400-4400002222-2-24-442200000000000000000000-22-20000000000000000000000
χ734-40400-40040-40044-4-44i−4i000000000000000000004i−4i0000000000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ10900
χ744-40400-40040-40044-4-44i−4i000000000000000000004i−4i000000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900
χ754-40400-40040-40044-4-4−4i4i00000000000000000000−4i4i000000000000000000000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900
χ764-40400-40040-40044-4-4−4i4i00000000000000000000−4i4i0000000000000000000000000000000000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ11900
χ7788-888-8800-2-8-28-8-2-2-2-20000200-22000022-2-22200000000000000000000000000000000000000000000000000
χ7888-88-88800-2-8-2-88-2-2-2-200002002-200002222-2-200000000000000000000000000000000000000000000000000
χ7988-8-48-8-400-24-2-441−i151+i151−i151+i150000200-220000−1+i15−1−i151−i151+i15−1+i15−1−i1500000000000000000000000000000000000000000000000000
χ8088-8-48-8-400-24-2-441+i151−i151+i151−i150000200-220000−1−i15−1+i151+i151−i15−1−i15−1+i1500000000000000000000000000000000000000000000000000
χ8188-8-4-88-400-24-24-41−i151+i151−i151+i1500002002-20000−1+i15−1−i15−1+i15−1−i151−i151+i1500000000000000000000000000000000000000000000000000
χ8288-8-4-88-400-24-24-41+i151−i151+i151−i1500002002-20000−1−i15−1+i15−1−i15−1+i151+i151−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.