Finite Group Databasebeta

← Group #14286962

Character table — Group #14286962

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size1111222222444444444444555588888888888888888888881010101010101212202020202020202020202020243030303040404040404040404040484848486060606060606060120
order1222344666588101010121224242424444415202030303040404040606060601201201201201201201201204412121212228888881212242424244888888242424242424242410102020448888884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11
χ3111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1
χ51111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-111-1-1ii−i−i-1-1-1-1-1-11ii−i−ii−iiiii−i−i−i−i1111-1-1i−iii−i−i-1
χ61111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-111-1-1−i−iii-1-1-1-1-1-11−i−iii−ii−i−i−i−iiiii1111-1-1−ii−i−iii-1
χ71111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1-1−i−iiii−iiiii−i−i−i−i-1-1-1-111−ii−i−iii1
χ81111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-1-1-1-1ii−i−i−ii−i−i−i−iiiii-1-1-1-111i−iii−i−i1
χ911111111111-1-111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-11111-1-111-1-111-1-111-1-11111-1-1-1-1-1
χ1011111111111-1-111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-11111-1
χ1111111111111-1-111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-111111
χ1211111111111-1-111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-111-1-111-1-111-1-111-1-1-1-11
χ1311111111111-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i-1-11111-1ii−i−i−iiii−i−i−i−iii11-1-1-1-1i−i−i−iii1
χ1411111111111-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii-1-11111-1−i−iiii−i−i−iiiii−i−i11-1-1-1-1−iiii−i−i1
χ1511111111111-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i-1-111111−i−iii−iiii−i−i−i−iii-1-11111−iiii−i−i-1
χ1611111111111-1-111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii-1-111111ii−i−ii−i−i−iiiii−i−i-1-11111i−i−i−iii-1
χ1722222-2-2222200222-2-2000022222-2-22220000-2-2-2-200000000-2-2222200000000-2-20000022220000000000000000-2-200000
χ1822222-2-2222200222-2-2000022222-2-22220000-2-2-2-200000000-2-2222200000000-2-200000-2-2-2-200000000000000002200000
χ1922222-2-2222200222-2-20000-2-2-2-22-2-22220000-2-2-2-20000000022-2-2-2-20000000022000002i2i−2i−2i0000000000000000−2i2i00000
χ2022222-2-2222200222-2-20000-2-2-2-22-2-22220000-2-2-2-20000000022-2-2-2-2000000002200000−2i−2i2i2i00000000000000002i−2i00000
χ212222-122-1-1-1222222-1-1-1-1-1-12222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100222222-1-1-1-1-1-10000022-1-1-1-1-1-1-1-10000000000000
χ222222-122-1-1-1222222-1-1-1-1-1-12222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10022-2-2-2-2-1-1-1-1-1-100000-2-2111111110000000000000
χ232222-122-1-1-1222222-1-1-1-1-1-1-2-2-2-2-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2111100-2-22i2i−2i−2i111111000002i−2i−i−i−i−iiiii0000000000000
χ242222-122-1-1-1222222-1-1-1-1-1-1-2-2-2-2-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2111100-2-2−2i−2i2i2i11111100000−2i2iiiii−i−i−i−i0000000000000
χ252222-122-1-1-12-2-2222-1-111112222-122-1-1-1-2-2-2-2-1-1-1-11111111122-1-1-1-100-2-22222-1-1111100000-2-2-1-111-1-1110000000000000
χ262222-122-1-1-12-2-2222-1-111112222-122-1-1-1-2-2-2-2-1-1-1-11111111122-1-1-1-100-2-2-2-2-2-2-1-11111000002211-1-111-1-10000000000000
χ272222-122-1-1-12-2-2222-1-11111-2-2-2-2-122-1-1-1-2-2-2-2-1-1-1-111111111-2-2111100222i2i−2i−2i11-1-1-1-100000−2i2i−i−iiiii−i−i0000000000000
χ282222-122-1-1-12-2-2222-1-11111-2-2-2-2-122-1-1-1-2-2-2-2-1-1-1-111111111-2-211110022−2i−2i2i2i11-1-1-1-1000002i−2iii−i−i−i−iii0000000000000
χ2922-2-2200-22-222−2-2-220022−2−22i−2i2i−2i2002-2-222−2−200002222−2−2−2−2002i−2i2i−2i00−i2i2000000−i2−i2i2i202ζ7+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+2ζ1090000000000000000001+i−1−i1−i−1+i0
χ3022-2-2200-22-222−2-2-220022−2−22i−2i2i−2i2002-2-222−2−200002222−2−2−2−2002i−2i2i−2i00−i2i2000000−i2−i2i2i20−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109000000000000000000−1−i1+i−1+i1−i0
χ3122-2-2200-22-222−2-2-220022−2−2−2i2i−2i2i2002-2-222−2−200002222−2−2−2−200−2i2i−2i2i00i2−i2000000i2i2−i2−i20−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190000000000000000001−i−1+i1+i−1−i0
χ3222-2-2200-22-222−2-2-220022−2−2−2i2i−2i2i2002-2-222−2−200002222−2−2−2−200−2i2i−2i2i00i2−i2000000i2i2−i2−i202ζ13+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+2ζ119000000000000000000−1+i1−i−1−i1+i0
χ3322-2-2200-22-22−22-2-2200−2−2222i−2i2i−2i2002-2-2−2−2220000−2−2−2−22222002i−2i2i−2i00i2−i2000000i2i2−i2−i202ζ7+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+2ζ109000000000000000000−1−i1+i−1+i1−i0
χ3422-2-2200-22-22−22-2-2200−2−2222i−2i2i−2i2002-2-2−2−2220000−2−2−2−22222002i−2i2i−2i00i2−i2000000i2i2−i2−i20−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090000000000000000001+i−1−i1−i−1+i0
χ3522-2-2200-22-22−22-2-2200−2−222−2i2i−2i2i2002-2-2−2−2220000−2−2−2−2222200−2i2i−2i2i00−i2i2000000−i2−i2i2i20−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119000000000000000000−1+i1−i−1−i1+i0
χ3622-2-2200-22-22−22-2-2200−2−222−2i2i−2i2i2002-2-2−2−2220000−2−2−2−2222200−2i2i−2i2i00−i2i2000000−i2−i2i2i202ζ13+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+2ζ1190000000000000000001−i−1+i1+i−1−i0
χ372-22-222-22-2-2200-22-22-200002i−2i−2i2i2-22-2-220000-2-222000000002i−2i2i−2i−2i2i0000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192i−2i00000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119000000000000000
χ382-22-222-22-2-2200-22-22-200002i−2i−2i2i2-22-2-220000-2-222000000002i−2i2i−2i−2i2i00002ζ13+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+2ζ1192i−2i000000000002ζ13+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+2ζ119000000000000000
χ392-22-222-22-2-2200-22-22-20000−2i2i2i−2i2-22-2-220000-2-22200000000−2i2i−2i2i2i−2i00002ζ7+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+2ζ109−2i2i000000000002ζ7+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+2ζ109000000000000000
χ402-22-222-22-2-2200-22-22-20000−2i2i2i−2i2-22-2-220000-2-22200000000−2i2i−2i2i2i−2i0000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2i2i00000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109000000000000000
χ412-22-22-222-2-2200-22-2-2200002i−2i−2i2i22-2-2-22000022-2-200000000−2i2i2i−2i−2i2i2-2000000−2i2i00000000000000000002-2002i−2i0000000
χ422-22-22-222-2-2200-22-2-2200002i−2i−2i2i22-2-2-22000022-2-200000000−2i2i2i−2i−2i2i-22000000−2i2i0000000000000000000-2200−2i2i0000000
χ432-22-22-222-2-2200-22-2-220000−2i2i2i−2i22-2-2-22000022-2-2000000002i−2i−2i2i2i−2i2-20000002i−2i00000000000000000002-200−2i2i0000000
χ442-22-22-222-2-2200-22-2-220000−2i2i2i−2i22-2-2-22000022-2-2000000002i−2i−2i2i2i−2i-220000002i−2i0000000000000000000-22002i−2i0000000
χ452-22-2-12-2-111200-22-2-11−i3i3−i3i32i−2i−2i2i-1-2211-1000011-1-1−i3−i3i3i3−i3−i3i3i32i−2i−iii−i0000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−ii3−33−30000000ζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109−ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109−ζ7−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+ζ1190000000000000
χ462-22-2-12-2-111200-22-2-11−i3i3−i3i32i−2i−2i2i-1-2211-1000011-1-1−i3−i3i3i3−i3−i3i3i32i−2i−iii−i00002ζ13+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−ii3−33−30000000−ζ13−ζ29−ζ37−ζ53−ζ61−ζ77−ζ101−ζ109ζ13+ζ29+ζ37+ζ53+ζ61+ζ77+ζ101+ζ109−ζ13+ζ29−ζ37+ζ53−ζ61+ζ77+ζ101−ζ109ζ13−ζ29+ζ37−ζ53+ζ61−ζ77−ζ101+ζ109ζ7+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−ζ1190000000000000
χ472-22-2-12-2-111200-22-2-11−i3i3−i3i3−2i2i2i−2i-1-2211-1000011-1-1−i3−i3i3i3−i3−i3i3i3−2i2ii−i−ii00002ζ7+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+2ζ109i−i−33−330000000−ζ7−ζ23−ζ31−ζ47−ζ71−ζ79−ζ103−ζ119ζ7+ζ23+ζ31+ζ47+ζ71+ζ79+ζ103+ζ119−ζ7+ζ23−ζ31+ζ47+ζ71−ζ79−ζ103+ζ119ζ7−ζ23+ζ31−ζ47−ζ71+ζ79+ζ103−ζ119ζ13+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+ζ1090000000000000
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Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.