Finite Group Databasebeta

← Group #14297173

Character table — Group #14297173

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1122222224444445588888888888881010101010101012121212161616161616202020202020202020202020202020202424242424242424404040404040404060606060120120120120
order1222236662456610446101010101012152020303030444121212122244303030306060248888121224242424242424241010101020202020688122424242422448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-11111-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111
χ5111111111111111-1-11111111111111-1-1-1-1-1-1-11111111111-1-1ii−i−i-1-1iiii−i−i−i−i11111111-1i−i-1ii−i−i-1-1-1-1ii−i−i
χ6111111111111111-1-11111111111111-1-1-1-1-1-1-11111111111-1-1−i−iii-1-1−i−i−i−iiiii11111111-1−ii-1−i−iii-1-1-1-1−i−iii
χ7111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1ii−i−i-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1-1i−i-1ii−i−i1111−i−iii
χ8111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−iii-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1-1−ii-1−i−iii1111ii−i−i
χ9111111111-1-1111111-1111-1-1-11-1-111111111111-11-111-1-1-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-11-11-11-11-1
χ10111111111-1-1111111-1111-1-1-11-1-111111111111-11-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-1-111-111111-11-1-11-11
χ11111111111-1-1111111-1111-1-1-11-1-11111111111-11-1111-1-1-1-1-1-111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-11-11-11-11
χ12111111111-1-1111111-1111-1-1-11-1-11111111111-11-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-111-11111-11-111-11-1
χ13111111111-1-11111-1-1-1111-1-1-11-1-1111-1-1-1-1-1-1-11-11-111-1-1-1-111ii−i−i-1-1iiii−i−i−i−i11-1-111-1-11−ii1−i−iii-11-11i−i−ii
χ14111111111-1-11111-1-1-1111-1-1-11-1-1111-1-1-1-1-1-1-11-11-111-1-1-1-111−i−iii-1-1−i−i−i−iiiii11-1-111-1-11i−i1ii−i−i-11-11−iii−i
χ15111111111-1-11111-1-1-1111-1-1-11-1-1111-1-1-1-1-1-1-1-11-1111-1-1-1-111ii−i−i-1-1iiii−i−i−i−i-1-111-1-1111−ii1−i−iii1-11-1−iii−i
χ16111111111-1-11111-1-1-1111-1-1-11-1-1111-1-1-1-1-1-1-1-11-1111-1-1-1-111−i−iii-1-1−i−i−i−iiiii-1-111-1-1111i−i1ii−i−i1-11-1i−i−ii
χ1722222-1-1-1-1222-1-1222-122222-1-122-1-1-1222-1-1-1-10000-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-100000000-122-1-1-1-1-100000000
χ1822222-1-1-1-1222-1-1222-122222-1-122-1-1-1222-1-1-1-10000-1-1-1-1-1-122-2-2-2-2-1-11111111100000000-1-2-2-1111100000000
χ1922222-1-1-1-1222-1-12-2-2-122222-1-122-1-1-1-2-2-211110000-1-1-1-1-1-1-2-22i2i−2i−2i11−i−i−i−iiiii0000000012i−2i1−i−iii00000000
χ2022222-1-1-1-1222-1-12-2-2-122222-1-122-1-1-1-2-2-211110000-1-1-1-1-1-1-2-2−2i−2i2i2i11iiii−i−i−i−i000000001−2i2i1ii−i−i00000000
χ2122222-1-1-1-1-2-22-1-12221222-2-21-1-2-2-1-1-1222-1-1-1-10000-1-11111-2-22222-1-1-1-1-1-1-1-1-1-1000000001-2-21111100000000
χ2222222-1-1-1-1-2-22-1-12221222-2-21-1-2-2-1-1-1222-1-1-1-10000-1-11111-2-2-2-2-2-2-1-111111111000000001221-1-1-1-100000000
χ2322222-1-1-1-1-2-22-1-12-2-21222-2-21-1-2-2-1-1-1-2-2-211110000-1-11111222i2i−2i−2i11−i−i−i−iiiii00000000-1−2i2i-1ii−i−i00000000
χ2422222-1-1-1-1-2-22-1-12-2-21222-2-21-1-2-2-1-1-1-2-2-211110000-1-1111122−2i−2i2i2i11iiii−i−i−i−i00000000-12i−2i-1−i−iii00000000
χ25222-2-222222-22-2-222222-2-222-22-2-22222-2-222220000-2-222-2-2-220000-2-20000000000000000-2002000000000000
χ26222-2-222222-22-2-22-2-222-2-222-22-2-2222-222-2-2-2-20000-2-222-2-22-20000220000000000000000200-2000000000000
χ27222-2-22222-222-2-2222-22-2-2-2-222222222-2-222220000-2-2-2-2222-20000-2-20000000000000000200-2000000000000
χ28222-2-22222-222-2-22-2-2-22-2-2-2-22222222-222-2-2-2-20000-2-2-2-222-220000220000000000000000-2002000000000000
χ29222-2-2-1-1-1-12-2211222-12-2-2221-1-2-2-1-1-12-2-2-1-1-1-1000011-1-111-22000011−i3−i3i3i3−i3−i3i3i300000000100-1−i3i3−i3i300000000
χ30222-2-2-1-1-1-12-2211222-12-2-2221-1-2-2-1-1-12-2-2-1-1-1-1000011-1-111-22000011i3i3−i3−i3i3i3−i3−i300000000100-1i3−i3i3−i300000000
χ31222-2-2-1-1-1-12-22112-2-2-12-2-2221-1-2-2-1-1-1-2221111000011-1-1112-20000-1-133−3−3−3−33300000000-10013−3−3300000000
χ32222-2-2-1-1-1-12-22112-2-2-12-2-2221-1-2-2-1-1-1-2221111000011-1-1112-20000-1-1−3−33333−3−300000000-1001−333−300000000
χ33222-2-2-1-1-1-1-2221122212-2-2-2-2-1-122-1-1-12-2-2-1-1-1-100001111-1-12-2000011−i3−i3i3i3−i3−i3i3i300000000-1001i3−i3i3−i300000000
χ34222-2-2-1-1-1-1-2221122212-2-2-2-2-1-122-1-1-12-2-2-1-1-1-100001111-1-12-2000011i3i3−i3−i3i3i3−i3−i300000000-1001−i3i3−i3i300000000
χ35222-2-2-1-1-1-1-222112-2-212-2-2-2-2-1-122-1-1-1-222111100001111-1-1-220000-1-133−3−3−3−33300000000100-1−333−300000000
χ36222-2-2-1-1-1-1-222112-2-212-2-2-2-2-1-122-1-1-1-222111100001111-1-1-220000-1-1−3−33333−3−300000000100-13−3−3300000000
χ3722-22-22-2-220022-22220-22-2000200-2-22-22-222-2-2020-22-200000000002-200000000002200-2-2000000000-2020000
χ3822-22-22-2-220022-22220-22-2000200-2-22-22-222-2-20-2022-200000000002-20000000000-2-2002200000000020-20000
χ3922-22-22-2-220022-22-2-20-22-2000200-2-222-22-2-222020-22-20000000000-2200000000002200-2-200000000020-20000
χ4022-22-22-2-220022-22-2-20-22-2000200-2-222-22-2-2220-2022-20000000000-220000000000-2-20022000000000-2020000
χ4122-2-222-2-22002-222220-2-22000200-2-22-2-2222-2-220-20-220000000000-22000000002200-2-20000000000-20200000
χ4222-2-222-2-22002-222220-2-22000200-2-22-2-2222-2-2-2020-220000000000-2200000000-2-20022000000000020-200000
χ4322-2-222-2-22002-222-2-20-2-22000200-2-2222-2-2-22220-20-2200000000002-2000000002200-2-2000000000020-200000
χ4422-2-222-2-22002-222-2-20-2-22000200-2-2222-2-2-222-2020-2200000000002-200000000-2-200220000000000-20200000
χ4544444444444-144-1004-1-1-1-1-14-1-1-1-1-1-100000004444-1-1-1-1-1-10000000000000000-1-1-1-1-1-1-1-10000000000000000
χ4644444444444-144-1004-1-1-1-1-14-1-1-1-1-1-10000000-4-4-4-4-1-1-1-1-1-10000000000000000111111110000000000000000
χ47444444444-4-4-144-100-4-1-1-111-4-111-1-1-100000004-44-4-1-111110000000000000000-1-111-1-1110000000000000000
χ48444444444-4-4-144-100-4-1-1-111-4-111-1-1-10000000-44-44-1-11111000000000000000011-1-111-1-10000000000000000
χ49444-4-444444-4-1-4-4-1004-111-1-1-4-111-1-1-10000000000011-1-1110000000000000000−55−55−55−550000000000000000
χ50444-4-444444-4-1-4-4-1004-111-1-1-4-111-1-1-10000000000011-1-11100000000000000005−55−55−55−50000000000000000
χ51444-4-44444-44-1-4-4-100-4-111114-1-1-1-1-1-1000000000001111-1-10000000000000000−555−5−555−50000000000000000
χ52444-4-44444-44-1-4-4-100-4-111114-1-1-1-1-1-1000000000001111-1-100000000000000005−5−555−5−550000000000000000
χ5344-44-44-4-4400-14-4-10001-11−550-1−5511-10000000040-4-11−55−550000000000000000−55-1-15−5110000000000000000
χ5444-44-44-4-4400-14-4-10001-11−550-1−5511-100000000-404-11−55−5500000000000000005−511−55-1-10000000000000000
χ5544-44-44-4-4400-14-4-10001-115−50-15−511-10000000040-4-115−55−500000000000000005−5-1-1−55110000000000000000
χ5644-44-44-4-4400-14-4-10001-115−50-15−511-100000000-404-115−55−50000000000000000−55115−5-1-10000000000000000
χ5744-44-4-222-2004-224440-44-4000-20022-2-44-4-2-2220000-220000000000-2200000000000000000000000000000000
χ5844-44-4-222-2004-224-4-40-44-4000-20022-24-4422-2-20000-2200000000002-200000000000000000000000000000000
χ5944-4-444-4-4400-1-44-100011-1−550-15−511-1000000040-401-1−555−50000000000000000-1-1−55115−50000000000000000
χ6044-4-444-4-4400-1-44-100011-1−550-15−511-10000000-40401-1−555−50000000000000000115−5-1-1−550000000000000000
χ6144-4-444-4-4400-1-44-100011-15−50-1−5511-1000000040-401-15−5−550000000000000000-1-15−511−550000000000000000
χ6244-4-444-4-4400-1-44-100011-15−50-1−5511-10000000-40401-15−5−55000000000000000011−55-1-15−50000000000000000
χ6344-4-44-222-20042-24440-4-44000-20022-2-4-44-2-22200002-200000000002-200000000000000000000000000000000
χ6444-4-44-222-20042-24-4-40-4-44000-20022-244-422-2-200002-20000000000-2200000000000000000000000000000000
χ654-4000400-400400-44i−4i000000040000-40004i−4i000000000000002ζ7+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+2ζ109002ζ7+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
χ664-4000400-400400-44i−4i000000040000-40004i−4i00000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+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
χ674-4000400-400400-4−4i4i000000040000-4000−4i4i00000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+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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χ724-4000-2−2i32i3200400-4−4i4i0000000-200−2i32i320002i−2i−23230000000000002ζ13+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+2ζ11900−2ζ13−2ζ37−2ζ61−2ζ1092ζ13+2ζ37+2ζ61+2ζ109−2ζ29−2ζ53−2ζ77−2ζ1012ζ29+2ζ53+2ζ77+2ζ1012ζ7+2ζ31+2ζ79+2ζ103−2ζ7−2ζ31−2ζ79−2ζ1032ζ23+2ζ47+2ζ71+2ζ119−2ζ23−2ζ47−2ζ71−2ζ119000000000000000000000000
χ734-4000-22i3−2i3200400-44i−4i0000000-2002i3−2i32000−2i2i−23230000000000002ζ7+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+2ζ10900−2ζ23−2ζ47−2ζ71−2ζ1192ζ23+2ζ47+2ζ71+2ζ119−2ζ7−2ζ31−2ζ79−2ζ1032ζ7+2ζ31+2ζ79+2ζ1032ζ29+2ζ53+2ζ77+2ζ101−2ζ29−2ζ53−2ζ77−2ζ1012ζ13+2ζ37+2ζ61+2ζ109−2ζ13−2ζ37−2ζ61−2ζ109000000000000000000000000
χ744-4000-22i3−2i3200400-44i−4i0000000-2002i3−2i32000−2i2i−2323000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109002ζ23+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
χ754-4000-22i3−2i3200400-4−4i4i0000000-2002i3−2i320002i−2i23−23000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119002ζ29+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
χ764-4000-22i3−2i3200400-4−4i4i0000000-2002i3−2i320002i−2i23−230000000000002ζ13+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+2ζ11900−2ζ29−2ζ53−2ζ77−2ζ1012ζ29+2ζ53+2ζ77+2ζ101−2ζ13−2ζ37−2ζ61−2ζ1092ζ13+2ζ37+2ζ61+2ζ1092ζ23+2ζ47+2ζ71+2ζ119−2ζ23−2ζ47−2ζ71−2ζ1192ζ7+2ζ31+2ζ79+2ζ103−2ζ7−2ζ31−2ζ79−2ζ103000000000000000000000000
χ7788888-4-4-4-488-2-4-4-200-4-2-2-2-2-2-41-2-2111000000000001111110000000000000000000000000000000000000000
χ7888888-4-4-4-4-8-8-2-4-4-2004-2-2-22241221110000000000011-1-1-1-10000000000000000000000000000000000000000
χ79888-8-8-4-4-4-48-8-244-200-4-222-2-2412211100000000000-1-111-1-10000000000000000000000000000000000000000
χ80888-8-8-4-4-4-4-88-244-2004-22222-41-2-211100000000000-1-1-1-1110000000000000000000000000000000000000000
χ8188-88-8-444-400-2-44-20002-22−252501−2525-1-11000000000001-15−55−50000000000000000000000000000000000000000
χ8288-88-8-444-400-2-44-20002-2225−250125−25-1-11000000000001-1−55−550000000000000000000000000000000000000000
χ8388-8-88-444-400-24-4-200022-2−25250125−25-1-1100000000000-115−5−550000000000000000000000000000000000000000
χ8488-8-88-444-400-24-4-200022-225−2501−2525-1-1100000000000-11−555−50000000000000000000000000000000000000000
χ8516-160001600-1600-4004000000000-400004000000000000000000000000000000000000000000000000000000000
χ8616-16000-8−8i38i3800-40040000000002002i3−2i3-2000000000000000000000000000000000000000000000000000000000
χ8716-16000-88i3−8i3800-4004000000000200−2i32i3-2000000000000000000000000000000000000000000000000000000000

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