Finite Group Databasebeta

← Group #14303296

Character table — Group #14303296

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−i11111111-1-1-1-1ii−i−iii−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−iii−i−iii
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−iii−i−iii
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-1-1-1-1-1-1-1-11111ii−i−iii−i−i
χ91111111111111111-1-111111111-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1
χ101111111111111111-1-111111111-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-11111
χ111111111111111111-1-111111111-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111
χ121111111111111111-1-111111111-1-1-1-1111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1
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
χ25222-22-2-2-2222-2-2-22-2002222-2-2-2-2000022-2-222-2-220000222-2-2-2-2000000002222-2-2-2-200000000000000000000000000000000000000000000002-22-20000
χ26222-22-2-2-2222-2-2-22-2002222-2-2-2-2000022-2-222-2-220000222-2-2-2-2000000002222-2-2-2-20000000000000000000000000000000000000000000000-22-220000
χ27222-22-2-2-2222-2-2-22-2002222-2-2-2-20000-2-222-2-22220000222-2-2-2-200000000-2-2-2-2222200000000000000000000000000000000000000000000002i−2i−2i2i0000
χ28222-22-2-2-2222-2-2-22-2002222-2-2-2-20000-2-222-2-22220000222-2-2-2-200000000-2-2-2-222220000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ2922-22-2-22-222-22-22-2-20022-2-2-222-200002i−2i2i−2i2i−2i2i−2i200002-2-22-2-22000000002i2i−2i−2i2i2i−2i−2i0000002ζ7+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+2ζ109000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109000000000000000000000000
χ3022-22-2-22-222-22-22-2-20022-2-2-222-200002i−2i2i−2i2i−2i2i−2i200002-2-22-2-22000000002i2i−2i−2i2i2i−2i−2i000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ11900002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109000000000000000000000000
χ3122-22-2-22-222-22-22-2-20022-2-2-222-20000−2i2i−2i2i−2i2i−2i2i200002-2-22-2-2200000000−2i−2i2i2i−2i−2i2i2i000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ10900002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119000000000000000000000000
χ3222-22-2-22-222-22-22-2-20022-2-2-222-20000−2i2i−2i2i−2i2i−2i2i200002-2-22-2-2200000000−2i−2i2i2i−2i−2i2i2i0000002ζ13+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+2ζ119000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119000000000000000000000000
χ3322-22-2-22-2-1-11-11-1110022-2-2-222-2−i3−i3i3i32i−2i2i−2i2i−2i2i−2i-10000-111-111-1−i3−i3−i3−i3i3i3i3i3−i−iii−i−iii0000002ζ7+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+2ζ109000033−3−3−ζ7−ζ23−ζ31−ζ47−ζ71−ζ79−ζ103−ζ119−ζ7−ζ23−ζ31−ζ47−ζ71−ζ79−ζ103−ζ119ζ7+ζ23+ζ31+ζ47+ζ71+ζ79+ζ103+ζ119ζ7+ζ23+ζ31+ζ47+ζ71+ζ79+ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109ζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109−ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109−ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ10900000000000000000000
χ3422-22-2-22-2-1-11-11-1110022-2-2-222-2−i3−i3i3i32i−2i2i−2i2i−2i2i−2i-10000-111-111-1−i3−i3−i3−i3i3i3i3i3−i−iii−i−iii000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109000033−3−3ζ7+ζ23+ζ31+ζ47+ζ71+ζ79+ζ103+ζ119ζ7+ζ23+ζ31+ζ47+ζ71+ζ79+ζ103+ζ119−ζ7−ζ23−ζ31−ζ47−ζ71−ζ79−ζ103−ζ119−ζ7−ζ23−ζ31−ζ47−ζ71−ζ79−ζ103−ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119−ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109−ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109ζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109ζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ10900000000000000000000
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Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.