Finite Group Databasebeta

← Group #14297308

Character table — Group #14297308

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112222244444445588888888888881010101010121212121616161616162020202020242424242424242440404040404040404040404040406060606060606060120120
order12234462456101212446101010121520202020306060224121224443030306060602466121010202020202020446881212121212242424242224888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-11-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111-1-11111111111111-1-1-1-1-11111111111-1-1-1-1-111111111i−i-1i−i-1ii−i−iii−i−i-1-1-1-1ii−i−ii−i
χ611111111111111-1-11111111111111-1-1-1-1-11111111111-1-1-1-1-111111111−ii-1−ii-1−i−iii−i−iii-1-1-1-1−i−iii−ii
χ711111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1i−i-1i−i-1ii−i−iii−i−i1111−i−iii−ii
χ811111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1−ii-1−ii-1−i−iii−i−iii1111ii−i−ii−i
χ91111111-1-11111111-11-1-1-1111-1-11111111111-1-11-1-11-1-1-1-11111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-111111-1-1
χ101111111-1-11111111-11-1-1-1111-1-11111111111-1-11-1-11-1-1-1-11111111-1-1-1-1-1-1-111-1-1-1-1-111111-1-11-1-1-1-111
χ111111111-1-11111111-11-1-1-1111-1-111111111-1-1111-1-11-1-1-1-1111-1-1-1-1111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-111
χ121111111-1-11111111-11-1-1-1111-1-111111111-1-1111-1-11-1-1-1-1111-1-1-1-11111-1-1-111-1-1-1-1-11111-111-11111-1-1
χ131111111-1-111111-1-1-11-1-1-1111-1-1111-1-1-1-1-111-1-11-1-11-1-111-1-1-11111-1-1-1-1i−i1−ii1ii−i−i−i−iii-111-1ii−i−i−ii
χ141111111-1-111111-1-1-11-1-1-1111-1-1111-1-1-1-1-111-1-11-1-11-1-111-1-1-11111-1-1-1-1−ii1i−i1−i−iiiii−i−i-111-1−i−iiii−i
χ151111111-1-111111-1-1-11-1-1-1111-1-1111-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-1-1-1-11111i−i1−ii1ii−i−i−i−iii1-1-11−i−iiii−i
χ161111111-1-111111-1-1-11-1-1-1111-1-1111-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-1-1-1-11111−ii1i−i1−i−iiiii−i−i1-1-11ii−i−i−ii
χ172222-2-2200222-2-222020002-2-2002-2-2-2-2222002-2200-20000-2-22000022-2-20000000000000002-20000000
χ182222-2-2200222-2-222020002-2-2002-2-2-2-222200-22200-20000-2-220000-2-222000000000000000-220000000
χ192222-2-2200222-2-2-2-2020002-2-2002-2-222-2-2-2002-2200-2000022-2000022-2-2000000000000000-220000000
χ202222-2-2200222-2-2-2-2020002-2-2002-2-222-2-2-200-22200-2000022-20000-2-2220000000000000002-20000000
χ21222-122-1222-12-1-122-1222-1-12222-1-1-1222-1-10000-1-1-1-1-1-122-1-1-10000000022-122-1-1-1-1-1-1-1-1-10000000000
χ22222-122-1222-12-1-122-1222-1-12222-1-1-1222-1-10000-1-1-1-1-1-122-1-1-100000000-2-2-1-2-2-1111111110000000000
χ23222-122-1222-12-1-1-2-2-1222-1-12222-1-1-1-2-2-2110000-1-1-1-1-1-1-2-2111000000002i−2i12i−2i1−i−iii−i−iii0000000000
χ24222-122-1222-12-1-1-2-2-1222-1-12222-1-1-1-2-2-2110000-1-1-1-1-1-1-2-211100000000−2i2i1−2i2i1ii−i−iii−i−i0000000000
χ25222-122-1-2-22-12-1-12212-2-21-122-2-2-1-1-1222-1-10000-111-111-2-2-1-1-100000000221-2-21-1-1-1-111110000000000
χ26222-122-1-2-22-12-1-12212-2-21-122-2-2-1-1-1222-1-10000-111-111-2-2-1-1-100000000-2-212211111-1-1-1-10000000000
χ27222-122-1-2-22-12-1-1-2-212-2-21-122-2-2-1-1-1-2-2-2110000-111-11122111000000002i−2i-1−2i2i-1−i−iiiii−i−i0000000000
χ28222-122-1-2-22-12-1-1-2-212-2-21-122-2-2-1-1-1-2-2-2110000-111-1112211100000000−2i2i-12i−2i-1ii−i−i−i−iii0000000000
χ2922-222-22002-222-2220-200022-200222-22-2222-200-200-200002-2-222-2-2000000000000000000-2002000000
χ3022-222-22002-222-2220-200022-200222-22-222-2200-200-200002-2-2-2-222000000000000000000200-2000000
χ3122-222-22002-222-2-2-20-200022-2002222-22-2-22-200-200-20000-22222-2-2000000000000000000200-2000000
χ3222-222-22002-222-2-2-20-200022-2002222-22-2-2-2200-200-20000-222-2-222000000000000000000-2002000000
χ3322-22-2222-22-22-22222-222-22-22-2-22-2-22-2-2220000-2222-2-2-22-22-20000000000-2002000000000000000000
χ3422-22-2222-22-22-22-2-22-222-22-22-2-22-2-2-222-2-20000-2222-2-22-22-220000000000200-2000000000000000000
χ3522-22-222-222-22-2222-2-2-2-222-22222-2-22-2-2220000-2-2-22222-2-22-20000000000200-2000000000000000000
χ3622-22-222-222-22-22-2-2-2-2-2-222-22222-2-2-222-2-20000-2-2-2222-222-220000000000-2002000000000000000000
χ3722-2-1-22-12-22121-122-1-2221-1-22-2-2-1112-2-2-1-100001-1-1-111-221-110000000000100-1−i3i3−i3i3−i3i3−i3i30000000000
χ3822-2-1-22-12-22121-122-1-2221-1-22-2-2-1112-2-2-1-100001-1-1-111-221-110000000000100-1i3−i3i3−i3i3−i3i3−i30000000000
χ3922-2-1-22-12-22121-1-2-2-1-2221-1-22-2-2-111-2221100001-1-1-1112-2-11-10000000000-10013−3−333−3−330000000000
χ4022-2-1-22-12-22121-1-2-2-1-2221-1-22-2-2-111-2221100001-1-1-1112-2-11-10000000000-1001−333−3−333−30000000000
χ4122-2-1-22-1-222121-1221-2-2-2-1-1-2222-1112-2-2-1-10000111-1-1-12-21-110000000000-1001−i3i3−i3i3i3−i3i3−i30000000000
χ4222-2-1-22-1-222121-1221-2-2-2-1-1-2222-1112-2-2-1-10000111-1-1-12-21-110000000000-1001i3−i3i3−i3−i3i3−i3i30000000000
χ4322-2-1-22-1-222121-1-2-21-2-2-2-1-1-2222-111-222110000111-1-1-1-22-11-10000000000100-13−3−33−333−30000000000
χ4422-2-1-22-1-222121-1-2-21-2-2-2-1-1-2222-111-222110000111-1-1-1-22-11-10000000000100-1−333−33−3−330000000000
χ45444444444-14-144004-1-1-14-1-1-1-1-1-1-1-1000004444-1-1-1-1-1-100000-1-1-1-1-1-1-1-1000000000000000000000000
χ46444444444-14-144004-1-1-14-1-1-1-1-1-1-1-100000-4-4-4-4-1-1-1-1-1-10000011111111000000000000000000000000
χ474444444-4-4-14-14400-4-111-4-1-1-111-1-1-10000044-4-4-111-11100000-1-1-1-11111000000000000000000000000
χ484444444-4-4-14-14400-4-111-4-1-1-111-1-1-100000-4-444-111-111000001111-1-1-1-1000000000000000000000000
χ494444-4-4400-14-1-4-4000-1−550-111−55-11100000004-4-1−551−5500000−55−55-1-111000000000000000000000000
χ504444-4-4400-14-1-4-4000-1−550-111−55-1110000000-44-1−551−55000005−55−511-1-1000000000000000000000000
χ514444-4-4400-14-1-4-4000-15−50-1115−5-11100000004-4-15−515−5000005−55−5-1-111000000000000000000000000
χ524444-4-4400-14-1-4-4000-15−50-1115−5-1110000000-44-15−515−500000−55−5511-1-1000000000000000000000000
χ53444-2-4-4-2004-24224404000-2-4-400-222-4-44-2-20000-2002000022-200000000000000000000000000000000
χ54444-2-4-4-2004-2422-4-404000-2-4-400-22244-4220000-20020000-2-2200000000000000000000000000000000
χ5544-444-4400-1-4-14-40001−550-1-115−5-1-1-1000004-4001−5515−500000-1-111−55−55000000000000000000000000
χ5644-444-4400-1-4-14-40001−550-1-115−5-1-1-100000-44001−5515−50000011-1-15−55−5000000000000000000000000
χ5744-444-4400-1-4-14-400015−50-1-11−55-1-1-1000004-40015−51−5500000-1-1115−55−5000000000000000000000000
χ5844-444-4400-1-4-14-400015−50-1-11−55-1-1-100000-440015−51−550000011-1-1−55−55000000000000000000000000
χ5944-44-4444-4-1-4-1-440041-1-1-4-11-111-1110000000001-1-1-11100000−555−5−555−5000000000000000000000000
χ6044-44-4444-4-1-4-1-440041-1-1-4-11-111-1110000000001-1-1-111000005−5−555−5−55000000000000000000000000
χ6144-44-444-44-1-4-1-4400-41114-11-1-1-1-111000000000111-1-1-100000−555−55−5−55000000000000000000000000
χ6244-44-444-44-1-4-1-4400-41114-11-1-1-1-111000000000111-1-1-1000005−5−55−555−5000000000000000000000000
χ6344-4-24-4-200424-22440-4000-24-400-2-2-2-44-4-2-2000020020000-22200000000000000000000000000000000
χ6444-4-24-4-200424-22-4-40-4000-24-400-2-2-24-44220000200200002-2-200000000000000000000000000000000
χ654-40400-40040-4004i−4i0000040000-4000004i−4i00000000000000000000000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900
χ664-40400-40040-4004i−4i0000040000-4000004i−4i000000000000000000000000000000000000000002ζ13+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
χ674-40400-40040-400−4i4i0000040000-400000−4i4i000000000000000000000000000000000000000002ζ7+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
χ684-40400-40040-400−4i4i0000040000-400000−4i4i00000000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900
χ69888-488-488-2-4-2-4-400-4-2-2-2-41-2-2-2-21110000000001111110000000000000000000000000000000000000
χ70888-488-4-8-8-2-4-2-4-4004-22241-2-2221110000000001-1-11-1-10000000000000000000000000000000000000
χ71888-4-8-8-400-2-4-244000-2−25250122−25251-1-100000000015−5-15−50000000000000000000000000000000000000
χ72888-4-8-8-400-2-4-244000-225−25012225−251-1-10000000001−55-1−550000000000000000000000000000000000000
χ7388-8-48-8-400-24-2-440002−252501-2225−25111000000000-15−5-1−550000000000000000000000000000000000000
χ7488-8-48-8-400-24-2-44000225−2501-22−2525111000000000-1−55-15−50000000000000000000000000000000000000
χ7588-8-4-88-48-8-24-24-400-42-2-2412-2221-1-1000000000-1111-1-10000000000000000000000000000000000000
χ7688-8-4-88-4-88-24-24-4004222-412-2-2-21-1-1000000000-1-1-11110000000000000000000000000000000000000
χ778-80-40040080-8008i−8i00000-40000400000−4i4i00000000000000000000000000000000000000000000000
χ788-80-40040080-800−8i8i00000-400004000004i−4i00000000000000000000000000000000000000000000000
χ7916-1601600-1600-404000000000-400004000000000000000000000000000000000000000000000000000000
χ8016-160-800800-40400000000020000-2−2152150000000000000000000000000000000000000000000000000000
χ8116-160-800800-40400000000020000-2215−2150000000000000000000000000000000000000000000000000000

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