Finite Group Databasebeta

← Group #14297312

Character table — Group #14297312

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112222244444445588888888888881010101010121212121616161616162020202020242424242424242440404040404040404040404040406060606060606060120120
order12234462256101212446610101010101520203030302241212224430303030606044661210101010202020204444121212121212121212122244888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111-1-11111111111111-1-1-1-1-11111111111-1-1-1-1-111111111ii−i−i-1-1iiii−i−i−i−i-1-1-1-1ii−i−ii−i
χ611111111111111-1-11111111111111-1-1-1-1-11111111111-1-1-1-1-111111111−i−iii-1-1−i−i−i−iiiii-1-1-1-1−i−iii−ii
χ711111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1iiii−i−i−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−i−iii-1-1−i−i−i−iiiii1111ii−i−ii−i
χ91111111-1-11111111-1-11-1-1-1-1111111111111-11-1-1-1-1-111-1-111111-1-111-1-11-11-1-1-111-1-111-1-11-11-11111-1-1
χ101111111-1-11111111-1-11-1-1-1-1111111111111-11-1-1-1-1-111-1-111111-1-111-1-1-11-11-1-1-1-111-1-1111-11-1-1-1-1-111
χ111111111-1-11111111-1-11-1-1-1-111111111111-11-11-1-1-1-111-1-1111-1-111-1-1111-11-1-1-111-1-111-1-1-11-11-1-1-1-111
χ121111111-1-11111111-1-11-1-1-1-111111111111-11-11-1-1-1-111-1-1111-1-111-1-111-11-11-1-1-1-111-1-111-11-111111-1-1
χ131111111-1-111111-1-1-1-11-1-1-1-1111111-1-1-1-1-11-11-1-1-1-1-11111-1-1-111-1-111-1-1i−i−ii11ii−i−i−i−iii-11-11ii−i−i−ii
χ141111111-1-111111-1-1-1-11-1-1-1-1111111-1-1-1-1-11-11-1-1-1-1-11111-1-1-111-1-111-1-1−iii−i11−i−iiiii−i−i-11-11−i−iiii−i
χ151111111-1-111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-1-111-1-111i−i−ii11ii−i−i−i−iii1-11-1−i−iiii−i
χ161111111-1-111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-1-111-1-111−iii−i11−i−iiiii−i−i1-11-1ii−i−i−ii
χ172222-2-222-2222-2-2222-2222-2-22-2-2222-2-2222000022-2-2-2-22-2-2-220000000000002-2000000000000000000
χ182222-2-222-2222-2-2-2-22-2222-2-22-2-222222-2-2-2000022-2-2-2-2-2222-2000000000000-22000000000000000000
χ192222-2-22-22222-2-222-222-2-2222-2-2222-2-22220000-2-222-2-2-22-2-22000000000000-22000000000000000000
χ202222-2-22-22222-2-2-2-2-222-2-2222-2-222222-2-2-20000-2-222-2-22-222-20000000000002-2000000000000000000
χ21222-122-1222-12-1-122-1-122222-122-1-1-1222-1-10000-1-1-1-1-1-122-1-1-1000000002222-1-1-1-1-1-1-1-1-1-10000000000
χ22222-122-1222-12-1-122-1-122222-122-1-1-1222-1-10000-1-1-1-1-1-122-1-1-100000000-2-2-2-2-1-1111111110000000000
χ23222-122-1222-12-1-1-2-2-1-122222-122-1-1-1-2-2-2110000-1-1-1-1-1-1-2-2111000000002i2i−2i−2i11−i−i−i−iiiii0000000000
χ24222-122-1222-12-1-1-2-2-1-122222-122-1-1-1-2-2-2110000-1-1-1-1-1-1-2-211100000000−2i−2i2i2i11iiii−i−i−i−i0000000000
χ25222-122-1-2-22-12-1-122112-2-2-2-2-122-1-1-1222-1-100001111-1-1-2-2-1-1-1000000002-22-211-1-111-1-1110000000000
χ26222-122-1-2-22-12-1-122112-2-2-2-2-122-1-1-1222-1-100001111-1-1-2-2-1-1-100000000-22-221111-1-111-1-10000000000
χ27222-122-1-2-22-12-1-1-2-2112-2-2-2-2-122-1-1-1-2-2-21100001111-1-122111000000002i−2i−2i2i-1-1−i−iiiii−i−i0000000000
χ28222-122-1-2-22-12-1-1-2-2112-2-2-2-2-122-1-1-1-2-2-21100001111-1-12211100000000−2i2i2i−2i-1-1ii−i−i−i−iii0000000000
χ29222-1-2-2-12-22-121122-11222-2-2-1-2-2-1-1-1-2-22-1-10000-1-111112-211-1000000000000-113−33−33−33−30000000000
χ30222-1-2-2-12-22-121122-11222-2-2-1-2-2-1-1-1-2-22-1-10000-1-111112-211-1000000000000-11−33−33−33−330000000000
χ31222-1-2-2-12-22-1211-2-2-11222-2-2-1-2-2-1-1-122-2110000-1-11111-22-1-110000000000001-1−i3i3−i3i3i3−i3i3−i30000000000
χ32222-1-2-2-12-22-1211-2-2-11222-2-2-1-2-2-1-1-122-2110000-1-11111-22-1-110000000000001-1i3−i3i3−i3−i3i3−i3i30000000000
χ33222-1-2-2-1-222-1211221-12-2-222-1-2-2-1-1-1-2-22-1-1000011-1-111-2211-10000000000001-13−3−333−3−330000000000
χ34222-1-2-2-1-222-1211221-12-2-222-1-2-2-1-1-1-2-22-1-1000011-1-111-2211-10000000000001-1−333−3−333−30000000000
χ35222-1-2-2-1-222-1211-2-21-12-2-222-1-2-2-1-1-122-211000011-1-1112-2-1-11000000000000-11−i3i3i3−i3i3−i3−i3i30000000000
χ36222-1-2-2-1-222-1211-2-21-12-2-222-1-2-2-1-1-122-211000011-1-1112-2-1-11000000000000-11i3−i3−i3i3−i3i3i3−i30000000000
χ3722-222-22002-222-22200-2000022-2-2-222-2-222020-200002-2002-2-2002200-2-2000000000000000-202000000
χ3822-222-22002-222-22200-2000022-2-2-222-2-2220-20200002-2002-2-200-2-2002200000000000000020-2000000
χ3922-222-22002-222-2-2-200-2000022-2-2-22-222-2-2020-200002-200-222002200-2-200000000000000020-2000000
χ4022-222-22002-222-2-2-200-2000022-2-2-22-222-2-20-20200002-200-22200-2-20022000000000000000-202000000
χ4122-22-222002-22-222200-200002-22-2-22-22-22220-200000-2200-22-22200-2-20000000000000000-2020000000
χ4222-22-222002-22-222200-200002-22-2-22-22-222-20200000-2200-22-2-2-20022000000000000000020-20000000
χ4322-22-222002-22-22-2-200-200002-22-2-222-22-2-220-200000-22002-222200-2-2000000000000000020-20000000
χ4422-22-222002-22-22-2-200-200002-22-2-222-22-2-2-20200000-22002-22-2-200220000000000000000-2020000000
χ45444444444-14-1440044-1-1-1-1-1-1-1-1-1-1-1000004444-1-1-1-1-1-100000-1-1-1-1-1-1-1-1000000000000000000000000
χ46444444444-14-1440044-1-1-1-1-1-1-1-1-1-1-100000-4-4-4-4-1-1-1-1-1-10000011111111000000000000000000000000
χ474444444-4-4-14-14400-4-4-11111-1-1-1-1-1-1000004-44-41111-1-100000-1-111-1-111000000000000000000000000
χ484444444-4-4-14-14400-4-4-11111-1-1-1-1-1-100000-44-441111-1-10000011-1-111-1-1000000000000000000000000
χ494444-4-444-4-14-1-4-4004-4-1-1-111-111-1-1-1000000000-1-1111100000−55−55−55−55000000000000000000000000
χ504444-4-444-4-14-1-4-4004-4-1-1-111-111-1-1-1000000000-1-11111000005−55−55−55−5000000000000000000000000
χ514444-4-44-44-14-1-4-400-44-111-1-1-111-1-1-100000000011-1-11100000−555−5−555−5000000000000000000000000
χ524444-4-44-44-14-1-4-400-44-111-1-1-111-1-1-100000000011-1-111000005−5−555−5−55000000000000000000000000
χ5344-444-4400-1-4-14-400001−55−55-1-1111-100000040-4−55−55-1100000−55-1-15−511000000000000000000000000
χ5444-444-4400-1-4-14-400001−55−55-1-1111-1000000-404−55−55-11000005−511−55-1-1000000000000000000000000
χ5544-444-4400-1-4-14-4000015−55−5-1-1111-100000040-45−55−5-11000005−5-1-1−5511000000000000000000000000
χ5644-444-4400-1-4-14-4000015−55−5-1-1111-1000000-4045−55−5-1100000−55115−5-1-1000000000000000000000000
χ5744-44-44400-1-4-1-4400001−555−5-11-111-10000040-40−555−51-100000-1-1−55115−5000000000000000000000000
χ5844-44-44400-1-4-1-4400001−555−5-11-111-100000-4040−555−51-100000115−5-1-1−55000000000000000000000000
χ5944-44-44400-1-4-1-44000015−5−55-11-111-10000040-405−5−551-100000-1-15−511−55000000000000000000000000
χ6044-44-44400-1-4-1-44000015−5−55-11-111-100000-40405−5−551-10000011−55-1-15−5000000000000000000000000
χ6144-4-24-4-200424-224400-40000-24-422-24-4-4-2-200000000-2200-22200000000000000000000000000000000
χ6244-4-24-4-200424-22-4-400-40000-24-422-2-4442200000000-22002-2-200000000000000000000000000000000
χ6344-4-2-44-2004242-24400-40000-2-4422-2-44-4-2-2000000002-2002-2200000000000000000000000000000000
χ6444-4-2-44-2004242-2-4-400-40000-2-4422-24-4422000000002-200-22-200000000000000000000000000000000
χ654-40400-40040-4004i−4i000000040000-40004i−4i000000000000000000000000000000000000000002ζ7+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
χ664-40400-40040-4004i−4i000000040000-40004i−4i00000000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900
χ674-40400-40040-400−4i4i000000040000-4000−4i4i00000000000000000000000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900
χ684-40400-40040-400−4i4i000000040000-4000−4i4i000000000000000000000000000000000000000002ζ13+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
χ69888-488-488-2-4-2-4-400-4-4-2-2-2-2-21-2-21110000000001111110000000000000000000000000000000000000
χ70888-488-4-8-8-2-4-2-4-40044-222221-2-2111000000000-1-1-1-1110000000000000000000000000000000000000
χ71888-4-8-8-48-8-2-4-24400-44-2-2-22212211100000000011-1-1-1-10000000000000000000000000000000000000
χ72888-4-8-8-4-88-2-4-244004-4-222-2-2122111000000000-1-111-1-10000000000000000000000000000000000000
χ7388-8-48-8-400-24-2-4400002−2525−25251-22-1-110000000005−55−51-10000000000000000000000000000000000000
χ7488-8-48-8-400-24-2-440000225−2525−251-22-1-11000000000−55−551-10000000000000000000000000000000000000
χ7588-8-4-88-400-24-24-400002−252525−2512-2-1-110000000005−5−55-110000000000000000000000000000000000000
χ7688-8-4-88-400-24-24-40000225−25−252512-2-1-11000000000−555−5-110000000000000000000000000000000000000
χ778-80-40040080-8008i−8i0000000-400004000−4i4i00000000000000000000000000000000000000000000000
χ788-80-40040080-800−8i8i0000000-4000040004i−4i00000000000000000000000000000000000000000000000
χ7916-1601600-1600-40400000000000-4000040000000000000000000000000000000000000000000000000000
χ8016-160-800800-40400000000000200−2i152i15-20000000000000000000000000000000000000000000000000000
χ8116-160-800800-404000000000002002i15−2i15-20000000000000000000000000000000000000000000000000000

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