Finite Group Databasebeta

← Group #14284621

Character table — Group #14284621

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222224444444445555888888888888888888888810101010101010101010101020202020202020202020202020202020202020202020202020202020202424484848486060606060606060120120
order1222223446666666451010101212121244441010152020202030303030303030606060606060606044441212121212121212488888888121212122424242424242424242424242424242424101020208888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i111111iiii−i−i−i−i-1-1
χ61111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1−i−i−i−iiiii11
χ71111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii111111−i−i−i−iiiii-1-1
χ81111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1iiii−i−i−i−i11
χ91111-1-11-1-1-1-1-1-11111111111-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1-111-1-1ii−i−iii−i−i-11
χ101111-1-11-1-1-1-1-1-11111111111-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11ii−i−iii−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i-11-1-111−i−iii−i−iii1-1
χ111111-1-11-1-1-1-1-1-11111111111-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii1-111-1-1−i−iii−i−iii-11
χ121111-1-11-1-1-1-1-1-11111111111-1-11111-1-1111-1-111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-11−i−iii−i−iii11-1-1−i−i−i−iiiii−i−i−i−iiiii-11-1-111ii−i−iii−i−i1-1
χ131111-1-11-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-11111-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111-111-1-111-1-1-1-1111-1
χ141111-1-11-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-11111-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-11-1-111-1-11111-1-1-11
χ151111-1-11-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-11-111-1-1-1-11111-1-11-1
χ161111-1-11-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-1-111-11
χ172222222-2-22222222-22222-2-2-2-22222222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-222222222-200000000-2-2-2-200000000000000000000000000000000
χ182222222-2-22222222-22222-2-2-2-2-2-2-2-2222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2200000000222200000000000000000000000000000000
χ19222222-122-1-1-1-1-1-1-122222-1-1-1-1222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222-122-1-1-1-1-1-1-122222-1-1-1-1222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12-2-2-2-2-2-2-2-2-1-1-1-111111111111111110000000000000000
χ21222222-122-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111-22i2i2i2i−2i−2i−2i−2i1111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000
χ22222222-122-1-1-1-1-1-1-122222-1-1-1-1-2-2-2-222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111-2−2i−2i−2i−2i2i2i2i2i1111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000
χ23222222-1-2-2-1-1-1-1-1-1-1-222221111222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-1-1-1-1-1-1-1-1-2000000001111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ24222222-1-2-2-1-1-1-1-1-1-1-222221111222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-2-1-1-1-1-1-1-1-1-2000000001111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ25222222-1-2-2-1-1-1-1-1-1-1-222221111-2-2-2-222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22211111111200000000-1-1-1-133−3−333−3−3−3−333−3−3330000000000000000
χ26222222-1-2-2-1-1-1-1-1-1-1-222221111-2-2-2-222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-22211111111200000000-1-1-1-1−3−333−3−33333−3−333−3−30000000000000000
χ272222-2-2222-2-2-2-2222-22222-2-2222222-2-22-2-22222-2-2-2-22-2-2-2-22222-2-2222222-2-2-2-2-200000000-2-22200000000000000000000000000000000
χ282222-2-2222-2-2-2-2222-22222-2-222-2-2-2-2-2-22-2-22222-2-2-2-22-2-2-2-2222222-2-2-2-2-2-2222220000000022-2-200000000000000000000000000000000
χ292222-2-2-1221111-1-1-1-2222211-1-12222-2-2-1-2-222-1-11111-11111-1-1-1-1-2-222-1-1-1-11111-20000000011-1-133−3−3−3−33333−3−3−3−3330000000000000000
χ302222-2-2-1221111-1-1-1-2222211-1-12222-2-2-1-2-222-1-11111-11111-1-1-1-1-2-222-1-1-1-11111-20000000011-1-1−3−33333−3−3−3−33333−3−30000000000000000
χ312222-2-2-1221111-1-1-1-2222211-1-1-2-2-2-2-2-2-1-2-222-1-11111-11111-1-1-1-122-2-21111-1-1-1-1200000000-1-111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i30000000000000000
χ322222-2-2-1221111-1-1-1-2222211-1-1-2-2-2-2-2-2-1-2-222-1-11111-11111-1-1-1-122-2-21111-1-1-1-1200000000-1-111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i30000000000000000
χ332222-2-2-1-2-21111-1-1-122222-1-1112222-2-2-122-2-2-1-11111-1-1-1-1-11111-2-2-2-2-1-1-1-1111122i2i−2i−2i2i2i−2i−2i-1-111−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ342222-2-2-1-2-21111-1-1-122222-1-1112222-2-2-122-2-2-1-11111-1-1-1-1-11111-2-2-2-2-1-1-1-111112−2i−2i2i2i−2i−2i2i2i-1-111iiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ352222-2-2-1-2-21111-1-1-122222-1-111-2-2-2-2-2-2-122-2-2-1-11111-1-1-1-1-1111122221111-1-1-1-1-222-2-2-2-22211-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ362222-2-2-1-2-21111-1-1-122222-1-111-2-2-2-2-2-2-122-2-2-1-11111-1-1-1-1-1111122221111-1-1-1-1-2-2-22222-2-211-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ372-22-20022i−2i0000-22-2022-2-2002i−2i2i2i−2i−2i002002i−2i2-20000-200002i2i−2i−2i002-22i2i−2i−2i000002−2−i2i2−i2i22−2002-22−22−2−i2i2−i2i2−i2i2−i2i22−22−20000000000000000
χ382-22-20022i−2i0000-22-2022-2-2002i−2i2i2i−2i−2i002002i−2i2-20000-200002i2i−2i−2i002-22i2i−2i−2i00000−22i2−i2i2−i2−22002-2−22−22i2−i2i2−i2i2−i2i2−i2−22−220000000000000000
χ392-22-20022i−2i0000-22-2022-2-2002i−2i−2i−2i2i2i002002i−2i2-20000-200002i2i−2i−2i00-22−2i−2i2i2i00000−i2i2−222−2i2−i200-22−i2i2−i2i2−22−222−22−2i2−i2i2−i20000000000000000
χ402-22-20022i−2i0000-22-2022-2-2002i−2i−2i−2i2i2i002002i−2i2-20000-200002i2i−2i−2i00-22−2i−2i2i2i00000i2−i22−2−22−i2i200-22i2−i2i2−i22−22−2−22−22−i2i2−i2i20000000000000000
χ412-22-2002−2i2i0000-22-2022-2-200−2i2i2i2i−2i−2i00200−2i2i2-20000-20000−2i−2i2i2i00-222i2i−2i−2i00000−i2i22−2−22i2−i200-22−i2i2−i2i22−22−2−22−22i2−i2i2−i20000000000000000
χ422-22-2002−2i2i0000-22-2022-2-200−2i2i2i2i−2i−2i00200−2i2i2-20000-20000−2i−2i2i2i00-222i2i−2i−2i00000i2−i2−222−2−i2i200-22i2−i2i2−i2−22−222−22−2−i2i2−i2i20000000000000000
χ432-22-2002−2i2i0000-22-2022-2-200−2i2i−2i−2i2i2i00200−2i2i2-20000-20000−2i−2i2i2i002-2−2i−2i2i2i000002−2i2−i2i2−i22−2002-22−22−2i2−i2i2−i2i2−i2i2−i22−22−20000000000000000
χ442-22-2002−2i2i0000-22-2022-2-200−2i2i−2i−2i2i2i00200−2i2i2-20000-20000−2i−2i2i2i002-2−2i−2i2i2i00000−22−i2i2−i2i2−22002-2−22−22−i2i2−i2i2−i2i2−i2i2−22−220000000000000000
χ452-22-200-12i−2i−i3−i3i3i31-11022-2-23−3−ii2i2i−2i−2i00-1002i−2i-11−i3−i3i3i3133−3−3−i−iii002-2−i−iii3−33−302−2−i2i2−i2i22−2−i3i3-11−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ1030000000000000000
χ462-22-200-12i−2i−i3−i3i3i31-11022-2-23−3−ii2i2i−2i−2i00-1002i−2i-11−i3−i3i3i3133−3−3−i−iii002-2−i−iii3−33−30−22i2−i2i2−i2−22−i3i3-11ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ1030000000000000000
χ472-22-200-12i−2i−i3−i3i3i31-11022-2-23−3−ii−2i−2i2i2i00-1002i−2i-11−i3−i3i3i3133−3−3−i−iii00-22ii−i−i−33−330−i2i2−222−2i2−i2i3−i31-1ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ1190000000000000000
χ482-22-200-12i−2i−i3−i3i3i31-11022-2-23−3−ii−2i−2i2i2i00-1002i−2i-11−i3−i3i3i3133−3−3−i−iii00-22ii−i−i−33−330i2−i22−2−22−i2i2i3−i31-1−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ119ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103ζ7−ζ29+ζ31−ζ53−ζ77+ζ79−ζ101+ζ103−ζ7+ζ29−ζ31+ζ53+ζ77−ζ79+ζ101−ζ103−ζ13+ζ23−ζ37+ζ47−ζ61+ζ71−ζ109+ζ119ζ13−ζ23+ζ37−ζ47+ζ61−ζ71+ζ109−ζ119ζ7+ζ29+ζ31+ζ53+ζ77+ζ79+ζ101+ζ103−ζ7−ζ29−ζ31−ζ53−ζ77−ζ79−ζ101−ζ103ζ13+ζ23+ζ37+ζ47+ζ61+ζ71+ζ109+ζ119−ζ13−ζ23−ζ37−ζ47−ζ61−ζ71−ζ109−ζ1190000000000000000
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χ978-88-80088i−8i0000-88-80-2-222008i−8i000000-200−2i2i-22000020000−2i−2i2i2i000000000000000000000000000000000000000000000000000000000
χ988-88-8008−8i8i0000-88-80-2-22200−8i8i000000-2002i−2i-220000200002i2i−2i−2i000000000000000000000000000000000000000000000000000000000
χ998-88-800-48i−8i−4i3−4i34i34i34-440-2-22243−43−4i4i000000100−2i2i1-1i3i3−i3−i3-1−3−333ii−i−i000000000000000000000000000000000000000000000000000000000
χ1008-88-800-48i−8i4i34i3−4i3−4i34-440-2-222−4343−4i4i000000100−2i2i1-1−i3−i3i3i3-133−3−3ii−i−i000000000000000000000000000000000000000000000000000000000
χ1018-88-800-4−8i8i−4i3−4i34i34i34-440-2-222−43434i−4i0000001002i−2i1-1i3i3−i3−i3-133−3−3−i−iii000000000000000000000000000000000000000000000000000000000
χ1028-88-800-4−8i8i4i34i3−4i3−4i34-440-2-22243−434i−4i0000001002i−2i1-1−i3−i3i3i3-1−3−333−i−iii000000000000000000000000000000000000000000000000000000000
χ1038-8-888-88008-88-8-8-880-222-200000000-22-200002-2-22-22200000000000000000000000000000000000000000000000000000000000000000
χ1048-8-888-8-400-44-4444-40-222-200000000-2210000-111-11-1-1−151515−1515−15−1515000000000000000000000000000000000000000000000000000000000
χ1058-8-888-8-400-44-4444-40-222-200000000-2210000-111-11-1-115−15−1515−151515−15000000000000000000000000000000000000000000000000000000000
χ1068-8-88-88800-88-88-8-880-222-2000000002-2-200002-22-22-2200000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-88-4004-44-444-40-222-2000000002-210000-11-11-11-1−151515−15−151515−15000000000000000000000000000000000000000000000000000000000
χ1088-8-88-88-4004-44-444-40-222-2000000002-210000-11-11-11-115−15−151515−15−1515000000000000000000000000000000000000000000000000000000000

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