Finite Group Databasebeta

← Group #14297311

Character table — Group #14297311

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1122222224444445588888888888881010101010101012121212161616161616202020202020202020202020202020202424242424242424404040404040404060606060120120120120
order1223446662251012124466101010101015202030303022412121212224430303030606044668888242424242424242410101010202020208812122424242422444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ5111111111111111-1-11111111111111-1-1-1-1-1-1-11111111111-1-1-1-1ii−i−iiiii−i−i−i−i11111111i−i-1-1ii−i−i-1-1-1-1ii−i−i
χ6111111111111111-1-11111111111111-1-1-1-1-1-1-11111111111-1-1-1-1−i−iii−i−i−i−iiiii11111111−ii-1-1−i−iii-1-1-1-1−i−iii
χ7111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1ii−i−iiiii−i−i−i−i-1-1-1-1-1-1-1-1i−i-1-1ii−i−i1111−i−iii
χ8111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1−i−iii−i−i−i−iiiii-1-1-1-1-1-1-1-1−ii-1-1−i−iii1111ii−i−i
χ9111111111-1-1111111-1-11-1-1-1-111111111111111-11-1-1-1-1-111-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-11-11-11-11-1
χ10111111111-1-1111111-1-11-1-1-1-111111111111111-11-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111111-11-1-11-11
χ11111111111-1-1111111-1-11-1-1-1-11111111111111-11-11-1-1-1-111-1-111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-11-11-11-11
χ12111111111-1-1111111-1-11-1-1-1-11111111111111-11-11-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-11-111-11-1
χ13111111111-1-11111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-11-11-1-1-1-1-11111-1-1ii−i−iiiii−i−i−i−i11-1-111-1-1−ii11−i−iii-11-11i−i−ii
χ14111111111-1-11111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-11-11-1-1-1-1-11111-1-1−i−iii−i−i−i−iiiii11-1-111-1-1i−i11ii−i−i-11-11−iii−i
χ15111111111-1-11111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1ii−i−iiiii−i−i−i−i-1-111-1-111−ii11−i−iii1-11-1−iii−i
χ16111111111-1-11111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1−i−iii−i−i−i−iiiii-1-111-1-111i−i11ii−i−i1-11-1i−i−ii
χ172222-2-22222-222-2-2222-2222-2-22-2-2222-2-222222000022-2-2-2-22-2-2-200000000000000000000002-2000000000000
χ182222-2-22222-222-2-2-2-22-2222-2-22-2-222222-2-2-2-2-2000022-2-2-2-2-22220000000000000000000000-22000000000000
χ192222-2-2222-2222-2-222-222-2-2222-2-2222-2-2222220000-2-222-2-2-22-2-20000000000000000000000-22000000000000
χ202222-2-2222-2222-2-2-2-2-222-2-2222-2-222222-2-2-2-2-20000-2-222-2-22-22200000000000000000000002-2000000000000
χ21222-122-1-1-12222-1-122-1-122222-122-1-1-1222-1-1-1-10000-1-1-1-1-1-122-1-12222-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-100000000
χ22222-122-1-1-12222-1-122-1-122222-122-1-1-1222-1-1-1-10000-1-1-1-1-1-122-1-1-2-2-2-21111111100000000-2-2-1-1111100000000
χ23222-122-1-1-12222-1-1-2-2-1-122222-122-1-1-1-2-2-211110000-1-1-1-1-1-1-2-2112i2i−2i−2i−i−i−i−iiiii000000002i−2i11−i−iii00000000
χ24222-122-1-1-12222-1-1-2-2-1-122222-122-1-1-1-2-2-211110000-1-1-1-1-1-1-2-211−2i−2i2i2iiiii−i−i−i−i00000000−2i2i11ii−i−i00000000
χ25222-122-1-1-1-2-222-1-122112-2-2-2-2-122-1-1-1222-1-1-1-100001111-1-1-2-2-1-12222-1-1-1-1-1-1-1-100000000-2-211111100000000
χ26222-122-1-1-1-2-222-1-122112-2-2-2-2-122-1-1-1222-1-1-1-100001111-1-1-2-2-1-1-2-2-2-211111111000000002211-1-1-1-100000000
χ27222-122-1-1-1-2-222-1-1-2-2112-2-2-2-2-122-1-1-1-2-2-2111100001111-1-122112i2i−2i−2i−i−i−i−iiiii00000000−2i2i-1-1ii−i−i00000000
χ28222-122-1-1-1-2-222-1-1-2-2112-2-2-2-2-122-1-1-1-2-2-2111100001111-1-12211−2i−2i2i2iiiii−i−i−i−i000000002i−2i-1-1−i−iii00000000
χ29222-1-2-2-1-1-12-2221122-11222-2-2-1-2-2-1-1-1-2-22-1-1-1-10000-1-111112-2110000−i3−i3i3i3−i3−i3i3i30000000000-11−i3i3−i3i300000000
χ30222-1-2-2-1-1-12-2221122-11222-2-2-1-2-2-1-1-1-2-22-1-1-1-10000-1-111112-2110000i3i3−i3−i3i3i3−i3−i30000000000-11i3−i3i3−i300000000
χ31222-1-2-2-1-1-12-22211-2-2-11222-2-2-1-2-2-1-1-122-211110000-1-11111-22-1-1000033−3−3−3−33300000000001-13−3−3300000000
χ32222-1-2-2-1-1-12-22211-2-2-11222-2-2-1-2-2-1-1-122-211110000-1-11111-22-1-10000−3−33333−3−300000000001-1−333−300000000
χ33222-1-2-2-1-1-1-222211221-12-2-222-1-2-2-1-1-1-2-22-1-1-1-1000011-1-111-22110000−i3−i3i3i3−i3−i3i3i300000000001-1i3−i3i3−i300000000
χ34222-1-2-2-1-1-1-222211221-12-2-222-1-2-2-1-1-1-2-22-1-1-1-1000011-1-111-22110000i3i3−i3−i3i3i3−i3−i300000000001-1−i3i3−i3i300000000
χ35222-1-2-2-1-1-1-222211-2-21-12-2-222-1-2-2-1-1-122-21111000011-1-1112-2-1-1000033−3−3−3−3330000000000-11−333−300000000
χ36222-1-2-2-1-1-1-222211-2-21-12-2-222-1-2-2-1-1-122-21111000011-1-1112-2-1-10000−3−33333−3−30000000000-113−3−3300000000
χ3722-222-2-2-2200222-22200-2000022-2-2-222-2-222-2-2020-200002-2002-2000000000000002200-2-2000000000-2020000
χ3822-222-2-2-2200222-22200-2000022-2-2-222-2-222-2-20-20200002-2002-200000000000000-2-2002200000000020-20000
χ3922-222-2-2-2200222-2-2-200-2000022-2-2-22-222-2-222020-200002-200-22000000000000002200-2-200000000020-20000
χ4022-222-2-2-2200222-2-2-200-2000022-2-2-22-222-2-2220-20200002-200-2200000000000000-2-20022000000000-2020000
χ4122-22-22-2-220022-222200-200002-22-2-22-22-222-2-220-200000-2200-220000000000002200-2-20000000000-20200000
χ4222-22-22-2-220022-222200-200002-22-2-22-22-222-2-2-20200000-2200-22000000000000-2-20022000000000020-200000
χ4322-22-22-2-220022-22-2-200-200002-22-2-222-22-2-22220-200000-22002-20000000000002200-2-2000000000020-200000
χ4422-22-22-2-220022-22-2-200-200002-22-2-222-22-2-222-20200000-22002-2000000000000-2-200220000000000-20200000
χ4544444444444-1-1440044-1-1-1-1-1-1-1-1-1-1-100000004444-1-1-1-1-1-10000000000000000-1-1-1-1-1-1-1-10000000000000000
χ4644444444444-1-1440044-1-1-1-1-1-1-1-1-1-1-10000000-4-4-4-4-1-1-1-1-1-10000000000000000111111110000000000000000
χ47444444444-4-4-1-14400-4-4-11111-1-1-1-1-1-100000004-44-41111-1-10000000000000000-1-111-1-1110000000000000000
χ48444444444-4-4-1-14400-4-4-11111-1-1-1-1-1-10000000-44-441111-1-1000000000000000011-1-111-1-10000000000000000
χ494444-4-44444-4-1-1-4-4004-4-1-1-111-111-1-1-100000000000-1-111110000000000000000−55−55−55−550000000000000000
χ504444-4-44444-4-1-1-4-4004-4-1-1-111-111-1-1-100000000000-1-1111100000000000000005−55−55−55−50000000000000000
χ514444-4-4444-44-1-1-4-400-44-111-1-1-111-1-1-10000000000011-1-1110000000000000000−555−5−555−50000000000000000
χ524444-4-4444-44-1-1-4-400-44-111-1-1-111-1-1-10000000000011-1-11100000000000000005−5−555−5−550000000000000000
χ5344-444-4-4-4400-1-14-400001−55−55-1-1111-10000000040-4−55−55-110000000000000000−55-1-15−5110000000000000000
χ5444-444-4-4-4400-1-14-400001−55−55-1-1111-100000000-404−55−55-1100000000000000005−511−55-1-10000000000000000
χ5544-444-4-4-4400-1-14-4000015−55−5-1-1111-10000000040-45−55−5-1100000000000000005−5-1-1−55110000000000000000
χ5644-444-4-4-4400-1-14-4000015−55−5-1-1111-100000000-4045−55−5-110000000000000000−55115−5-1-10000000000000000
χ5744-44-44-4-4400-1-1-4400001−555−5-11-111-1000000040-40−555−51-10000000000000000-1-1−55115−50000000000000000
χ5844-44-44-4-4400-1-1-4400001−555−5-11-111-10000000-4040−555−51-10000000000000000115−5-1-1−550000000000000000
χ5944-44-44-4-4400-1-1-44000015−5−55-11-111-1000000040-405−5−551-10000000000000000-1-15−511−550000000000000000
χ6044-44-44-4-4400-1-1-44000015−5−55-11-111-10000000-40405−5−551-1000000000000000011−55-1-15−50000000000000000
χ6144-4-24-422-20044-224400-40000-24-422-24-4-4-2-22200000000-2200-22000000000000000000000000000000000000
χ6244-4-24-422-20044-22-4-400-40000-24-422-2-44422-2-200000000-22002-2000000000000000000000000000000000000
χ6344-4-2-4422-200442-24400-40000-2-4422-2-44-4-2-222000000002-2002-2000000000000000000000000000000000000
χ6444-4-2-4422-200442-2-4-400-40000-2-4422-24-4422-2-2000000002-200-22000000000000000000000000000000000000
χ654-4040000-4004-4004i−4i000000040000-40004i−4i00000000000000002ζ7+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+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+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+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109000000000000000000000000
χ664-4040000-4004-4004i−4i000000040000-40004i−4i0000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109000000000000000000000000
χ674-4040000-4004-400−4i4i000000040000-4000−4i4i0000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119000000000000000000000000
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χ724-40-200−2i32i32004-400−4i4i0000000-200−2i32i320002i−2i−2323000000000000002ζ13+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+2ζ119−2ζ13−2ζ37−2ζ61−2ζ1092ζ13+2ζ37+2ζ61+2ζ109−2ζ29−2ζ53−2ζ77−2ζ1012ζ29+2ζ53+2ζ77+2ζ1012ζ7+2ζ31+2ζ79+2ζ103−2ζ7−2ζ31−2ζ79−2ζ1032ζ23+2ζ47+2ζ71+2ζ119−2ζ23−2ζ47−2ζ71−2ζ119000000000000000000000000
χ734-40-2002i3−2i32004-4004i−4i0000000-2002i3−2i32000−2i2i−2323000000000000002ζ7+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+2ζ109−2ζ23−2ζ47−2ζ71−2ζ1192ζ23+2ζ47+2ζ71+2ζ119−2ζ7−2ζ31−2ζ79−2ζ1032ζ7+2ζ31+2ζ79+2ζ1032ζ29+2ζ53+2ζ77+2ζ101−2ζ29−2ζ53−2ζ77−2ζ1012ζ13+2ζ37+2ζ61+2ζ109−2ζ13−2ζ37−2ζ61−2ζ109000000000000000000000000
χ744-40-2002i3−2i32004-4004i−4i0000000-2002i3−2i32000−2i2i−232300000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ23+2ζ47+2ζ71+2ζ119−2ζ23−2ζ47−2ζ71−2ζ1192ζ7+2ζ31+2ζ79+2ζ103−2ζ7−2ζ31−2ζ79−2ζ103−2ζ29−2ζ53−2ζ77−2ζ1012ζ29+2ζ53+2ζ77+2ζ101−2ζ13−2ζ37−2ζ61−2ζ1092ζ13+2ζ37+2ζ61+2ζ109000000000000000000000000
χ754-40-2002i3−2i32004-400−4i4i0000000-2002i3−2i320002i−2i23−2300000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ29+2ζ53+2ζ77+2ζ101−2ζ29−2ζ53−2ζ77−2ζ1012ζ13+2ζ37+2ζ61+2ζ109−2ζ13−2ζ37−2ζ61−2ζ109−2ζ23−2ζ47−2ζ71−2ζ1192ζ23+2ζ47+2ζ71+2ζ119−2ζ7−2ζ31−2ζ79−2ζ1032ζ7+2ζ31+2ζ79+2ζ103000000000000000000000000
χ764-40-2002i3−2i32004-400−4i4i0000000-2002i3−2i320002i−2i23−23000000000000002ζ13+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+2ζ119−2ζ29−2ζ53−2ζ77−2ζ1012ζ29+2ζ53+2ζ77+2ζ101−2ζ13−2ζ37−2ζ61−2ζ1092ζ13+2ζ37+2ζ61+2ζ1092ζ23+2ζ47+2ζ71+2ζ119−2ζ23−2ζ47−2ζ71−2ζ1192ζ7+2ζ31+2ζ79+2ζ103−2ζ7−2ζ31−2ζ79−2ζ103000000000000000000000000
χ77888-488-4-4-488-2-2-4-400-4-4-2-2-2-2-21-2-2111000000000001111110000000000000000000000000000000000000000
χ78888-488-4-4-4-8-8-2-2-4-40044-222221-2-211100000000000-1-1-1-1110000000000000000000000000000000000000000
χ79888-4-8-8-4-4-48-8-2-24400-44-2-2-2221221110000000000011-1-1-1-10000000000000000000000000000000000000000
χ80888-4-8-8-4-4-4-88-2-244004-4-222-2-212211100000000000-1-111-1-10000000000000000000000000000000000000000
χ8188-8-48-844-400-2-2-4400002−2525−25251-22-1-11000000000005−55−51-10000000000000000000000000000000000000000
χ8288-8-48-844-400-2-2-440000225−2525−251-22-1-1100000000000−55−551-10000000000000000000000000000000000000000
χ8388-8-4-8844-400-2-24-400002−252525−2512-2-1-11000000000005−5−55-110000000000000000000000000000000000000000
χ8488-8-4-8844-400-2-24-40000225−25−252512-2-1-1100000000000−555−5-110000000000000000000000000000000000000000
χ8516-160160000-1600-4400000000000-400004000000000000000000000000000000000000000000000000000000000
χ8616-160-800−8i38i3800-44000000000002002i3−2i3-2000000000000000000000000000000000000000000000000000000000
χ8716-160-8008i3−8i3800-4400000000000200−2i32i3-2000000000000000000000000000000000000000000000000000000000

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