Finite Group Databasebeta

← Group #14301214

Character table — Group #14301214

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1122222444444444445588888881010101010161616161616161620202020202020202020202020202020202020202020202020202020202020202024244848484860606060120120120120
order122344624566610121212124410152020306060224121210203030306060602466668888888812121224242424242424242424242424242424281010404088884448
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-11
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1
χ5111111111111111111-1-11111111-1-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1-1iiiiiiii−i−i−i−i−i−i−i−i111111ii−i−i-1i−i-1
χ6111111111111111111-1-11111111-1-1-1-1-111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1−i−iii1−ii1
χ7111111111111111111-1-11111111-1-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1-1−i−i−i−i−i−i−i−iiiiiiiii111111−i−iii-1−ii-1
χ8111111111111111111-1-11111111-1-1-1-1-111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1ii−i−i1i−i1
χ91111111-1-111-1-1111-1-111111111111111-1-11-1-11-1-1-1-111-1-111-1-111-1-11-1-11111-1-1-1-11111-1-1-1-11-111-1-111111-1-1-1
χ101111111-1-111-1-1111-1-111111111111111-1-11-1-11-1-1-1-111-1-111-1-111-1-11-1-11111-1-1-1-11111-1-1-1-1-11-1-111-1-1-1-1-1111
χ111111111-1-111-1-1111-1-111111111111111-1-11-1-11-1-1-1-111-1-1-1-111-1-1111-1-1-1-1-1-11111-1-1-1-111111-111-1-1-1-1-1-1111-1
χ121111111-1-111-1-1111-1-111111111111111-1-11-1-11-1-1-1-111-1-1-1-111-1-1111-1-1-1-1-1-11111-1-1-1-11111-11-1-1111111-1-1-11
χ131111111-1-111-1-1111-1-1-1-11111111-1-1-1-1-1-1-11-1-11-1-111-1-111ii−i−i−i−iii-111iiii−i−i−i−i−i−i−i−iiiii1-111-1-1ii−i−i-1−ii1
χ141111111-1-111-1-1111-1-1-1-11111111-1-1-1-1-1-1-11-1-11-1-111-1-111ii−i−i−i−iii-111iiii−i−i−i−i−i−i−i−iiiii-11-1-111−i−iii1i−i-1
χ151111111-1-111-1-1111-1-1-1-11111111-1-1-1-1-1-1-11-1-11-1-111-1-111−i−iiiii−i−i-111−i−i−i−iiiiiiiii−i−i−i−i1-111-1-1−i−iii-1i−i1
χ161111111-1-111-1-1111-1-1-1-11111111-1-1-1-1-1-1-11-1-11-1-111-1-111−i−iiiii−i−i-111−i−i−i−iiiiiiiii−i−i−i−i-11-1-111ii−i−i1−ii-1
χ172222-2-220022002-2-2002222-2-22-2-2-2-222200200-20000-2-2002-2002-20020022-2-2000022-2-2000000000000000000
χ182222-2-220022002-2-2002222-2-22-2-2-2-222200200-20000-2-200-2200-2200200-2-2220000-2-222000000000000000000
χ192222-2-220022002-2-200-2-222-2-22-2-222-2-2-200200-2000022002i−2i00−2i2i00-2002i2i−2i−2i0000−2i−2i2i2i000000000000000000
χ202222-2-220022002-2-200-2-222-2-22-2-222-2-2-200200-200002200−2i2i002i−2i00-200−2i−2i2i2i00002i2i−2i−2i000000000000000000
χ21222-122-1222-1-1-12-1-1-1-1222-122-1-1-1222-1-122-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ22222-122-1222-1-1-12-1-1-1-1222-122-1-1-1222-1-122-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1111111111111111100000000000000
χ23222-122-1222-1-1-12-1-1-1-1-2-22-122-1-1-1-2-2-21122-1-1-1-1-1-1-2-211112i2i2i2i−2i−2i−2i−2i111−i−i−i−i−i−i−i−iiiiiiiii00000000000000
χ24222-122-1222-1-1-12-1-1-1-1-2-22-122-1-1-1-2-2-21122-1-1-1-1-1-1-2-21111−2i−2i−2i−2i2i2i2i2i111iiiiiiii−i−i−i−i−i−i−i−i00000000000000
χ25222-122-1-2-22-1112-1-111222-122-1-1-1222-1-1-2-2-111-111-2-2-1-11122-2-222-2-2-111-1-1-1-11111-1-1-1-1111100000000000000
χ26222-122-1-2-22-1112-1-111222-122-1-1-1222-1-1-2-2-111-111-2-2-1-111-2-222-2-222-1111111-1-1-1-11111-1-1-1-100000000000000
χ27222-122-1-2-22-1112-1-111-2-22-122-1-1-1-2-2-211-2-2-111-1112211-1-12i2i−2i−2i−2i−2i2i2i1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000
χ28222-122-1-2-22-1112-1-111-2-22-122-1-1-1-2-2-211-2-2-111-1112211-1-1−2i−2i2i2i2i2i−2i−2i1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000
χ29222-1-2-2-1002-1−i3i3211−i3i3222-1-2-2-111-2-22-1-100-1−i3i31−i3i30011−i3i32-2002-200-1−i3i3-1-111−i3−i3i3i3-1-111−i3−i3i3i300000000000000
χ30222-1-2-2-1002-1−i3i3211−i3i3222-1-2-2-111-2-22-1-100-1−i3i31−i3i30011−i3i3-2200-2200-1−i3i311-1-1i3i3−i3−i311-1-1i3i3−i3−i300000000000000
χ31222-1-2-2-1002-1−i3i3211−i3i3-2-22-1-2-2-11122-21100-1−i3i31−i3i300-1-1i3−i32i−2i00−2i2i001i3−i3−i−iii33−3−3ii−i−i−3−33300000000000000
χ32222-1-2-2-1002-1−i3i3211−i3i3-2-22-1-2-2-11122-21100-1−i3i31−i3i300-1-1i3−i3−2i2i002i−2i001i3−i3ii−i−i−3−333−i−iii33−3−300000000000000
χ33222-1-2-2-1002-1i3−i3211i3−i3222-1-2-2-111-2-22-1-100-1i3−i31i3−i30011i3−i32-2002-200-1i3−i3-1-111i3i3−i3−i3-1-111i3i3−i3−i300000000000000
χ34222-1-2-2-1002-1i3−i3211i3−i3222-1-2-2-111-2-22-1-100-1i3−i31i3−i30011i3−i3-2200-2200-1i3−i311-1-1−i3−i3i3i311-1-1−i3−i3i3i300000000000000
χ35222-1-2-2-1002-1i3−i3211i3−i3-2-22-1-2-2-11122-21100-1i3−i31i3−i300-1-1−i3i32i−2i00−2i2i001−i3i3−i−iii−3−333ii−i−i33−3−300000000000000
χ36222-1-2-2-1002-1i3−i3211i3−i3-2-22-1-2-2-11122-21100-1i3−i31i3−i300-1-1−i3i3−2i2i002i−2i001−i3i3ii−i−i33−3−3−i−iii−3−33300000000000000
χ3722-222-22002-20022-20022-222-2222-22-22200-200-200002-200002-2002-2-20000002-22-200002-22-200000000000000
χ3822-222-22002-20022-20022-222-2222-22-22200-200-200002-20000-2200-22-2000000-22-220000-22-2200000000000000
χ3922-222-22002-20022-200-2-2-222-22222-22-2-200-200-20000-2200002i−2i00−2i2i20000002i−2i2i−2i0000−2i2i−2i2i00000000000000
χ4022-222-22002-20022-200-2-2-222-22222-22-2-200-200-20000-220000−2i2i002i−2i2000000−2i2i−2i2i00002i−2i2i−2i00000000000000
χ4122-22-2222-22-2222-22-2-222-22-222-2-22-2-2222-2-2222-2-2-22-22-2-200000000-222000000000000000000000000000000
χ4222-22-2222-22-2222-22-2-2-2-2-22-222-2-2-222-2-22-2-2222-2-22-22-222000000002-2-2000000000000000000000000000000
χ4322-22-222-222-2-2-22-222222-22-222-2-22-2-222-22-2-2-22222-2-222200000000-2-2-2000000000000000000000000000000
χ4422-22-222-222-2-2-22-2222-2-2-22-222-2-2-222-2-2-22-2-2-2222-222-2-2-200000000222000000000000000000000000000000
χ4522-2-12-2-10021−i3i32-11i3−i322-2-12-2-1-1-1-22-2-1-1001−i3i31i3−i300-11i3−i3002-2002-21−i3i3−i3i3−i3i3-11-11−i3i3−i3i3-11-1100000000000000
χ4622-2-12-2-10021−i3i32-11i3−i322-2-12-2-1-1-1-22-2-1-1001−i3i31i3−i300-11i3−i300-2200-221−i3i3i3−i3i3−i31-11-1i3−i3i3−i31-11-100000000000000
χ4722-2-12-2-10021−i3i32-11i3−i3-2-2-2-12-2-1-1-12-2211001−i3i31i3−i3001-1−i3i3002i−2i00−2i2i-1i3−i33−33−3−ii−ii−33−33i−ii−i00000000000000
χ4822-2-12-2-10021−i3i32-11i3−i3-2-2-2-12-2-1-1-12-2211001−i3i31i3−i3001-1−i3i300−2i2i002i−2i-1i3−i3−33−33i−ii−i3−33−3−ii−ii00000000000000
χ4922-2-12-2-10021i3−i32-11−i3i322-2-12-2-1-1-1-22-2-1-1001i3−i31−i3i300-11−i3i3002-2002-21i3−i3i3−i3i3−i3-11-11i3−i3i3−i3-11-1100000000000000
χ5022-2-12-2-10021i3−i32-11−i3i322-2-12-2-1-1-1-22-2-1-1001i3−i31−i3i300-11−i3i300-2200-221i3−i3−i3i3−i3i31-11-1−i3i3−i3i31-11-100000000000000
χ5122-2-12-2-10021i3−i32-11−i3i3-2-2-2-12-2-1-1-12-2211001i3−i31−i3i3001-1i3−i3002i−2i00−2i2i-1−i3i3−33−33−ii−ii3−33−3i−ii−i00000000000000
χ5222-2-12-2-10021i3−i32-11−i3i3-2-2-2-12-2-1-1-12-2211001i3−i31−i3i3001-1i3−i300−2i2i002i−2i-1−i3i33−33−3i−ii−i−33−33−ii−ii00000000000000
χ5322-2-1-22-12-221-1-121-11122-2-1-22-1112-2-2-1-12-21-1-1-111-221-111000000001-1-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i300000000000000
χ5422-2-1-22-12-221-1-121-11122-2-1-22-1112-2-2-1-12-21-1-1-111-221-111000000001-1-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i300000000000000
χ5522-2-1-22-12-221-1-121-111-2-2-2-1-22-111-222112-21-1-1-1112-2-11-1-100000000-1113−3−333−3−33−333−3−333−300000000000000
χ5622-2-1-22-12-221-1-121-111-2-2-2-1-22-111-222112-21-1-1-1112-2-11-1-100000000-111−333−3−333−33−3−333−3−3300000000000000
χ5722-2-1-22-1-22211121-1-1-122-2-1-22-1112-2-2-1-1-22111-1-1-12-21-1-1-100000000111−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i300000000000000
χ5822-2-1-22-1-22211121-1-1-122-2-1-22-1112-2-2-1-1-22111-1-1-12-21-1-1-100000000111i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i300000000000000
χ5922-2-1-22-1-22211121-1-1-1-2-2-2-1-22-111-22211-22111-1-1-1-22-111100000000-1-1-13−3−33−333−3−333−33−3−3300000000000000
χ6022-2-1-22-1-22211121-1-1-1-2-2-2-1-22-111-22211-22111-1-1-1-22-111100000000-1-1-1−333−33−3−333−3−33−333−300000000000000
χ61444444444-1444-1444400-1-1-1-1-1-1-100000-1-1-1-1-1-1-1-100000000000000000000000000000000044-1-1-1-100000000
χ62444444444-1444-1444400-1-1-1-1-1-1-100000-1-1-1-1-1-1-1-1000000000000000000000000000000000-4-4111100000000
χ634444444-4-4-14-4-4-144-4-400-1-1-1-1-1-1-10000011-111-1110000000000000000000000000000000004-4-1-11100000000
χ644444444-4-4-14-4-4-144-4-400-1-1-1-1-1-1-10000011-111-111000000000000000000000000000000000-4411-1-100000000
χ6544-44-4444-4-1-444-1-44-4-4001-11-1-11100000-111-1-1-11100000000000000000000000000000000000−55−5500000000
χ6644-44-4444-4-1-444-1-44-4-4001-11-1-11100000-111-1-1-111000000000000000000000000000000000005−55−500000000
χ6744-44-444-44-1-4-4-4-1-4444001-11-1-111000001-1111-1-1-100000000000000000000000000000000000−555−500000000
χ6844-44-444-44-1-4-4-4-1-4444001-11-1-111000001-1111-1-1-1000000000000000000000000000000000005−5−5500000000
χ694-40400-4004000-400004i−4i0400-4000004i−4i000000000000000000000000000000000000000000000002ζ7+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+2ζ1090000
χ704-40400-4004000-400004i−4i0400-4000004i−4i00000000000000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090000
χ714-40400-4004000-40000−4i4i0400-400000−4i4i00000000000000000000000000000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190000
χ724-40400-4004000-40000−4i4i0400-400000−4i4i000000000000000000000000000000000000000000000002ζ13+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+2ζ1190000
χ738888-8-8800-2800-2-8-80000-2-222-2220000000-20020000000000000000000000000000000000000000000000000
χ74888-488-488-2-4-4-4-2-4-4-4-400-21-2-211100000-2-211111100000000000000000000000000000000000000000000000
χ75888-488-4-8-8-2-444-2-4-44400-21-2-211100000221-1-11-1-100000000000000000000000000000000000000000000000
χ76888-4-8-8-400-2-4−4i34i3-244−4i34i300-21221-1-100000001i3−i3-1i3−i300000000000000000000000000000000000000000000000
χ77888-4-8-8-400-2-44i3−4i3-2444i3−4i300-21221-1-100000001−i3i3-1−i3i300000000000000000000000000000000000000000000000
χ7888-888-8800-2-800-28-800002-2-22-2-2-2000000020020000000000000000000000000000000000000000000000000
χ7988-8-48-8-400-24−4i34i3-2-444i3−4i30021-221110000000-1i3−i3-1−i3i300000000000000000000000000000000000000000000000
χ8088-8-48-8-400-244i3−4i3-2-44−4i34i30021-221110000000-1−i3i3-1i3−i300000000000000000000000000000000000000000000000
χ8188-8-4-88-48-8-24-4-4-24-44400212-21-1-100000-22-1111-1-100000000000000000000000000000000000000000000000
χ8288-8-4-88-4-88-2444-24-4-4-400212-21-1-1000002-2-1-1-111100000000000000000000000000000000000000000000000
χ838-80-4004008000-800008i−8i0-400400000−4i4i0000000000000000000000000000000000000000000000000000000
χ848-80-4004008000-80000−8i8i0-4004000004i−4i0000000000000000000000000000000000000000000000000000000
χ8516-1601600-1600-400040000000-400400000000000000000000000000000000000000000000000000000000000000
χ8616-160-800800-400040000000200-2−215215000000000000000000000000000000000000000000000000000000000000
χ8716-160-800800-400040000000200-2215−215000000000000000000000000000000000000000000000000000000000000

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