Finite Group Databasebeta

← Group #14305025

Character table — Group #14305025

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size11111111222222224444444444444455555555888888888888888888881010101010101010121212122020202020202020202020202020202020202020202020202020202020202424242424242424606060606060606060606060
order1222222236666666445101010101010101212121244444444152020202030303030303030606060606060606012121212121212124444448888888812121212242424242424242424242424242424242020202020202020444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1ii−i−iii−i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111-1-1-1-1iiii−i−i−i−i
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111-1-1−i−iii−i−iii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111-1-1-1-1−i−i−i−iiiii
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-11111−i−i−i−iiiii
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-11111iiii−i−i−i−i
χ91111111111111111-1-111111111-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-111111111-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ111111111111111111-1-111111111-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ121111111111111111-1-111111111-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ131111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-111ii−i−i−i−iii
χ141111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-111−i−iiiii−i−i
χ151111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii1111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1−i−iiiii−i−i
χ161111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i1111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111111-1-1ii−i−i−i−iii
χ1722222222-1-1-1-1-1-1-1-12222222222-1-1-1-122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100002222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ1822222222-1-1-1-1-1-1-1-12222222222-1-1-1-122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-2-2-2-2-2-2-2-2-1-1-1-1111111111111111100000000000000000000
χ1922222222-1-1-1-1-1-1-1-12222222222-1-1-1-1-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111110000-2-22i2i−2i−2i2i2i−2i−2i1111−i−i−i−i−i−i−i−iiiiiiiii00000000000000000000
χ2022222222-1-1-1-1-1-1-1-12222222222-1-1-1-1-2-2-2-2-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111110000-2-2−2i−2i2i2i−2i−2i2i2i1111iiiiiiii−i−i−i−i−i−i−i−i00000000000000000000
χ2122222222-1-1-1-1-1-1-1-1-2-222222222111122222222-1-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-10000-2-22222-2-2-2-21111-1-1-1-11111-1-1-1-1111100000000000000000000
χ2222222222-1-1-1-1-1-1-1-1-2-222222222111122222222-1-2-2-2-2-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-10000-2-2-2-2-2-2222211111111-1-1-1-11111-1-1-1-100000000000000000000
χ2322222222-1-1-1-1-1-1-1-1-2-2222222221111-2-2-2-2-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-111111111111111110000222i2i−2i−2i−2i−2i2i2i-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000
χ2422222222-1-1-1-1-1-1-1-1-2-2222222221111-2-2-2-2-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-11111111111111111000022−2i−2i2i2i2i2i−2i−2i-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii00000000000000000000
χ25222-22-2-2-2222-2-2-22-2002222-2-2-2-2000022-2-222-2-220000222-2-2-2-20000000022-2-222-2-20000002-22-20000000022-2-2000022-2-2000000000000000000000000
χ26222-22-2-2-2222-2-2-22-2002222-2-2-2-2000022-2-222-2-220000222-2-2-2-20000000022-2-222-2-2000000-22-2200000000-2-2220000-2-222000000000000000000000000
χ27222-22-2-2-2222-2-2-22-2002222-2-2-2-20000-2-222-2-22220000222-2-2-2-200000000-2-222-2-2220000002i−2i−2i2i000000002i2i−2i−2i0000−2i−2i2i2i000000000000000000000000
χ28222-22-2-2-2222-2-2-22-2002222-2-2-2-20000-2-222-2-22220000222-2-2-2-200000000-2-222-2-222000000−2i2i2i−2i00000000−2i−2i2i2i00002i2i−2i−2i000000000000000000000000
χ29222-22-2-2-2-1-1-1111-11002222-2-2-2-233−3−322-2-222-2-2-10000-1-1-111113333−3−3−3−3-1-111-1-1110000002-22-2000033−3−3-1-11133−3−3-1-11133−3−300000000000000000000
χ30222-22-2-2-2-1-1-1111-11002222-2-2-2-233−3−322-2-222-2-2-10000-1-1-111113333−3−3−3−3-1-111-1-111000000-22-22000033−3−311-1-1−3−33311-1-1−3−33300000000000000000000
χ31222-22-2-2-2-1-1-1111-11002222-2-2-2-233−3−3-2-222-2-222-10000-1-1-111113333−3−3−3−311-1-111-1-10000002i−2i−2i2i0000−3−333−i−iiii3i3−i3−i3ii−i−i−i3−i3i3i300000000000000000000
χ32222-22-2-2-2-1-1-1111-11002222-2-2-2-233−3−3-2-222-2-222-10000-1-1-111113333−3−3−3−311-1-111-1-1000000−2i2i2i−2i0000−3−333ii−i−i−i3−i3i3i3−i−iiii3i3−i3−i300000000000000000000
χ33222-22-2-2-2-1-1-1111-11002222-2-2-2-2−3−33322-2-222-2-2-10000-1-1-11111−3−3−3−33333-1-111-1-1110000002-22-20000−3−333-1-111−3−333-1-111−3−33300000000000000000000
χ34222-22-2-2-2-1-1-1111-11002222-2-2-2-2−3−33322-2-222-2-2-10000-1-1-11111−3−3−3−33333-1-111-1-111000000-22-220000−3−33311-1-133−3−311-1-133−3−300000000000000000000
χ35222-22-2-2-2-1-1-1111-11002222-2-2-2-2−3−333-2-222-2-222-10000-1-1-11111−3−3−3−3333311-1-111-1-10000002i−2i−2i2i000033−3−3−i−iii−i3−i3i3i3ii−i−ii3i3−i3−i300000000000000000000
χ36222-22-2-2-2-1-1-1111-11002222-2-2-2-2−3−333-2-222-2-222-10000-1-1-11111−3−3−3−3333311-1-111-1-1000000−2i2i2i−2i000033−3−3ii−i−ii3i3−i3−i3−i−iii−i3−i3i3i300000000000000000000
χ3722-22-2-22-222-22-22-2-20022-2-2-222-200002i−2i2i−2i2i−2i2i−2i200002-2-22-2-22000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000000000000000002ζ7+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+2ζ10900
χ3822-22-2-22-222-22-22-2-20022-2-2-222-200002i−2i2i−2i2i−2i2i−2i200002-2-22-2-22000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900
χ3922-22-2-22-222-22-22-2-20022-2-2-222-20000−2i2i−2i2i−2i2i−2i2i200002-2-22-2-2200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900
χ4022-22-2-22-222-22-22-2-20022-2-2-222-20000−2i2i−2i2i−2i2i−2i2i200002-2-22-2-2200000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000002ζ13+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+2ζ11900
χ4122-2-2-22-2222-2-22-2-220022-2-22-2-2200002i−2i−2i2i2i−2i−2i2i200002-2-2-222-2000000002i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000002i2i−2i−2i00002-20000000000
χ4222-2-2-22-2222-2-22-2-220022-2-22-2-2200002i−2i−2i2i2i−2i−2i2i200002-2-2-222-2000000002i−2i−2i2i2i−2i−2i2i−2i2i00000000000000000000000000000000−2i−2i2i2i0000-220000000000
χ4322-2-2-22-2222-2-22-2-220022-2-22-2-220000−2i2i2i−2i−2i2i2i−2i200002-2-2-222-200000000−2i2i2i−2i−2i2i2i−2i2i−2i000000000000000000000000000000002i2i−2i−2i0000-220000000000
χ4422-2-2-22-2222-2-22-2-220022-2-22-2-220000−2i2i2i−2i−2i2i2i−2i200002-2-2-222-200000000−2i2i2i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000−2i−2i2i2i00002-20000000000
χ452-222-2-2-222-22-222-2-2002-22-2-22-2200002i−2i2i−2i−2i2i−2i2i20000-22-2-22-22000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119
χ462-222-2-2-222-22-222-2-2002-22-2-22-2200002i−2i2i−2i−2i2i−2i2i20000-22-2-22-22000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000002ζ13+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
χ472-222-2-2-222-22-222-2-2002-22-2-22-220000−2i2i−2i2i2i−2i2i−2i20000-22-2-22-2200000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000002ζ7+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
χ482-222-2-2-222-22-222-2-2002-22-2-22-220000−2i2i−2i2i2i−2i2i−2i20000-22-2-22-2200000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109
χ492-22-2-222-22-222-2-2-22002-22-22-22-200002i−2i−2i2i−2i2i2i−2i20000-22-22-22-2000000002i−2i−2i2i−2i2i2i−2i002i−2i00000000000000000000000000000000002i2i−2i−2i002-200000000
χ502-22-2-222-22-222-2-2-22002-22-22-22-200002i−2i−2i2i−2i2i2i−2i20000-22-22-22-2000000002i−2i−2i2i−2i2i2i−2i00−2i2i0000000000000000000000000000000000−2i−2i2i2i00-2200000000
χ512-22-2-222-22-222-2-2-22002-22-22-22-20000−2i2i2i−2i2i−2i−2i2i20000-22-22-22-200000000−2i2i2i−2i2i−2i−2i2i002i−2i00000000000000000000000000000000002i2i−2i−2i00-2200000000
χ522-22-2-222-22-222-2-2-22002-22-22-22-20000−2i2i2i−2i2i−2i−2i2i20000-22-22-22-200000000−2i2i2i−2i2i−2i−2i2i00−2i2i0000000000000000000000000000000000−2i−2i2i2i002-200000000
χ532-2-2222-2-22-2-2-2-22222-22-2-2222-2-22-22-22222-2-2-2-2222-2-2-2-22-2-22222-2-222-2-22222-2-2-2-200002-2000000002-22-2000000000000000000000000000000000000
χ542-2-2222-2-22-2-2-2-22222-22-2-2222-2-22-22-2-2-2-2-22222222-2-2-2-22-2-22222-2-222-2-2-2-2-2-222220000-2200000000-22-22000000000000000000000000000000000000
χ552-2-2222-2-22-2-2-2-2222-222-2-2222-2-2-22-222222-2-2-2-22-2-222-2-22-2-222-2-222-2-2222222-2-2-2-20000-2200000000-22-22000000000000000000000000000000000000
χ562-2-2222-2-22-2-2-2-2222-222-2-2222-2-2-22-22-2-2-2-222222-2-222-2-22-2-222-2-222-2-222-2-2-2-2222200002-2000000002-22-2000000000000000000000000000000000000
χ572-2-2222-2-2-11111-1-1-12-22-2-2222-2-2-11-112222-2-2-2-2-122-2-211-111-1-1-1-111-1-111-1-1-1-1111100002-200000000-11-113−33−33−33−33−33−33−33−300000000000000000000
χ582-2-2222-2-2-11111-1-1-12-22-2-2222-2-2-11-112222-2-2-2-2-122-2-211-111-1-1-1-111-1-111-1-1-1-1111100002-200000000-11-11−33−33−33−33−33−33−33−3300000000000000000000
χ592-2-2222-2-2-11111-1-1-12-22-2-2222-2-2-11-11-2-2-2-22222-122-2-211-111-1-1-1-111-1-1111111-1-1-1-10000-22000000001-11-1−i3i3−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3i3−i300000000000000000000
χ602-2-2222-2-2-11111-1-1-12-22-2-2222-2-2-11-11-2-2-2-22222-122-2-211-111-1-1-1-111-1-1111111-1-1-1-10000-22000000001-11-1i3−i3i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3−i3i300000000000000000000
χ612-2-2222-2-2-11111-1-1-1-222-2-2222-2-21-11-12222-2-2-2-2-1-2-22211-111-1-111-1-111-1-1-1-1-1-111110000-22000000001-11-13−33−3−33−333−33−3−33−3300000000000000000000
χ622-2-2222-2-2-11111-1-1-1-222-2-2222-2-21-11-12222-2-2-2-2-1-2-22211-111-1-111-1-111-1-1-1-1-1-111110000-22000000001-11-1−33−333−33−3−33−333−33−300000000000000000000
χ632-2-2222-2-2-11111-1-1-1-222-2-2222-2-21-11-1-2-2-2-22222-1-2-22211-111-1-111-1-111-1-11111-1-1-1-100002-200000000-11-11−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3−i3i3−i3i300000000000000000000
χ642-2-2222-2-2-11111-1-1-1-222-2-2222-2-21-11-1-2-2-2-22222-1-2-22211-111-1-111-1-111-1-11111-1-1-1-100002-200000000-11-11i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3i3−i3i3−i300000000000000000000
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χ662-2-2-22-2222-2-222-22-2002-2-22-2-222000022-2-2-2-22220000-2-2222-2-20000000022-2-2-2-2220000000000-22-2200000000-222-20000-222-200000000000000000000
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χ1208-8-8-88-888-444-4-44-4400-222-222-2-2−434343−430000000010000-1-1111-1-133−3−3−3−33300000000000000000000000000000000000000000000000000000000000000

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