Finite Group Databasebeta

← Group #14287390

Character table — Group #14287390

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222244444455556666888888888101010101010101010101010101016161616161616162020202020202020202024242424243030303030303030303030304040404040404040404848120120120
order12223446665101010121244448888412121520203030304488888888121212122020606060606060121224242424242424244404040408888888888884881212242424242020288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1111-1-1
χ3111111111111111111111111-1-1-111111111111111111111-1-111-1-1-1-11111111111-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-111
χ511111111111111111111-1-1-1-111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1
χ611111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-1-1-1-1-111
χ711111111111111111111-1-1-1-1-1-1-111111111111111111111-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ811111111111111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-111-1-11111111-1-1
χ91111111111111111-1-1-1-11111111111111-1-1ii−i−iii−i−i-1-1-1-111111111-1-1ii−i−iii−i−i11111-1-1-1-1iiii−i−i−i−i-1i−i-1-1ii−i−i11-1i−i
χ101111111111111111-1-1-1-11111111111111-1-1−i−iii−i−iii-1-1-1-111111111-1-1−i−iii−i−iii11111-1-1-1-1−i−i−i−iiiii-1−ii-1-1−i−iii11-1−ii
χ111111111111111111-1-1-1-11111-1-1-1111111-1-1ii−i−iii−i−i-1-1-1-1-1-111-1-1-1-1-1-1ii−i−iii−i−i-11111-1-1-1-1iiii−i−i−i−i1−ii11−i−iii-1-11−ii
χ121111111111111111-1-1-1-11111-1-1-1111111-1-1−i−iii−i−iii-1-1-1-1-1-111-1-1-1-1-1-1−i−iii−i−iii-11111-1-1-1-1−i−i−i−iiiii1i−i11ii−i−i-1-11i−i
χ131111111111111111-1-1-1-1-1-1-1-1111111111-1-1ii−i−iii−i−i-1-1-1-111111111-1-1ii−i−iii−i−i-1-1-1-1-11111−i−i−i−iiiii-1i−i-1-1ii−i−i-1-11−ii
χ141111111111111111-1-1-1-1-1-1-1-1111111111-1-1−i−iii−i−iii-1-1-1-111111111-1-1−i−iii−i−iii-1-1-1-1-11111iiii−i−i−i−i-1−ii-1-1−i−iii-1-11i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1ii−i−iii−i−i-1-1-1-1-1-111-1-1-1-1-1-1ii−i−iii−i−i1-1-1-1-11111−i−i−i−iiiii1−ii11−i−iii11-1i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−iii−i−iii-1-1-1-1-1-111-1-1-1-1-1-1−i−iii−i−iii1-1-1-1-11111iiii−i−i−i−i1i−i11ii−i−i11-1−ii
χ1722222-2-22222222-2-2222200000002-2-2222-2-22222-2-2-2-2222200-2-20000-2-2-2-2-2-222220000000000000000000000000000000
χ1822222-2-22222222-2-2222200000002-2-2222-2-2-2-2-2-22222222200-2-20000-2-22222-2-2-2-20000000000000000000000000000000
χ1922222-2-22222222-2-2-2-2-2-200000002-2-2222222i2i−2i−2i−2i−2i2i2i-2-2-2-200-2-2000022−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000
χ2022222-2-22222222-2-2-2-2-2-200000002-2-222222−2i−2i2i2i2i2i−2i−2i-2-2-2-200-2-20000222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000
χ212222-122-1-1-12222-1-1222200002-1-1-122-1-1-12222222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000222-1-1-1-1-1-100000
χ222222-122-1-1-12222-1-1222200002-1-1-122-1-1-122-2-2-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-1-1-111111111000000000000000002-2-2-1-1111100000
χ232222-122-1-1-12222-1-122220000-211-122-1-1-12222222222-1-1-1-1-2-2-1-11111-1-1-1-1-1-1-1-1-1-100000000000000000-2-2-211111100000
χ242222-122-1-1-12222-1-122220000-211-122-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-2-2-1-11111-1-11111111100000000000000000-22211-1-1-1-100000
χ252222-122-1-1-12222-1-1-2-2-2-200002-1-1-122-1-1-1-2-22i2i−2i−2i2i2i−2i−2i111122-1-1-1-1-1-111−i−iii−i−iii00000000000000000-22i−2i11−i−iii00000
χ262222-122-1-1-12222-1-1-2-2-2-200002-1-1-122-1-1-1-2-2−2i−2i2i2i−2i−2i2i2i111122-1-1-1-1-1-111ii−i−iii−i−i00000000000000000-2−2i2i11ii−i−i00000
χ272222-122-1-1-12222-1-1-2-2-2-20000-211-122-1-1-1-2-22i2i−2i−2i2i2i−2i−2i1111-2-2-1-1111111−i−iii−i−iii000000000000000002−2i2i-1-1ii−i−i00000
χ282222-122-1-1-12222-1-1-2-2-2-20000-211-122-1-1-1-2-2−2i−2i2i2i−2i−2i2i2i1111-2-2-1-1111111ii−i−iii−i−i0000000000000000022i−2i-1-1−i−iii00000
χ292222-1-2-2-1-1-1222211222200000−i3i3-1-2-2-1-1-1-2-22222-2-2-2-2-1-1-1-10011−i3−i3i3i3111111-1-1-1-100000000000000000000−i3i3−i3i3−i3i300000
χ302222-1-2-2-1-1-1222211222200000−i3i3-1-2-2-1-1-1-2-2-2-2-2-22222-1-1-1-10011−i3−i3i3i311-1-1-1-1111100000000000000000000−i3i3i3−i3i3−i300000
χ312222-1-2-2-1-1-1222211222200000i3−i3-1-2-2-1-1-1-2-22222-2-2-2-2-1-1-1-10011i3i3−i3−i3111111-1-1-1-100000000000000000000i3−i3i3−i3i3−i300000
χ322222-1-2-2-1-1-1222211222200000i3−i3-1-2-2-1-1-1-2-2-2-2-2-22222-1-1-1-10011i3i3−i3−i311-1-1-1-1111100000000000000000000i3−i3−i3i3−i3i300000
χ332222-1-2-2-1-1-1222211-2-2-2-200000−i3i3-1-2-2-1-1-1222i2i−2i−2i−2i−2i2i2i11110011−i3−i3i3i3-1-1ii−i−i−i−iii00000000000000000000i3−i33−3−3300000
χ342222-1-2-2-1-1-1222211-2-2-2-200000−i3i3-1-2-2-1-1-122−2i−2i2i2i2i2i−2i−2i11110011−i3−i3i3i3-1-1−i−iiiii−i−i00000000000000000000i3−i3−333−300000
χ352222-1-2-2-1-1-1222211-2-2-2-200000i3−i3-1-2-2-1-1-1222i2i−2i−2i−2i−2i2i2i11110011i3i3−i3−i3-1-1ii−i−i−i−iii00000000000000000000−i3i3−333−300000
χ362222-1-2-2-1-1-1222211-2-2-2-200000i3−i3-1-2-2-1-1-122−2i−2i2i2i2i2i−2i−2i11110011i3i3−i3−i3-1-1−i−iiiii−i−i00000000000000000000−i3i33−3−3300000
χ3722-2-2200-22-22-22-2002i−2i2i−2i−i2−i2i2i2000200-2-22002ζ7+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+2ζ10900002i−2i2i−2i000000000000002ζ7+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+2ζ1090−i2−i2i2i222−2−21−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000
χ3822-2-2200-22-22-22-2002i−2i2i−2i−i2−i2i2i2000200-2-2200−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900002i−2i2i−2i00000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090−i2−i2i2i222−2−2−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000
χ3922-2-2200-22-22-22-2002i−2i2i−2ii2i2−i2−i2000200-2-22002ζ7+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+2ζ10900002i−2i2i−2i000000000000002ζ7+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+2ζ1090i2i2−i2−i2−2−222−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000
χ4022-2-2200-22-22-22-2002i−2i2i−2ii2i2−i2−i2000200-2-2200−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900002i−2i2i−2i00000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090i2i2−i2−i2−2−2221−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000
χ4122-2-2200-22-22-22-200−2i2i−2i2i−i2−i2i2i2000200-2-2200−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190000−2i2i−2i2i00000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190−i2−i2i2i2−2−222−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000
χ4222-2-2200-22-22-22-200−2i2i−2i2i−i2−i2i2i2000200-2-22002ζ13+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+2ζ1190000−2i2i−2i2i000000000000002ζ13+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+2ζ1190−i2−i2i2i2−2−2221+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000
χ4322-2-2200-22-22-22-200−2i2i−2i2ii2i2−i2−i2000200-2-2200−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190000−2i2i−2i2i00000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1190i2i2−i2−i222−2−21+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000
χ4422-2-2200-22-22-22-200−2i2i−2i2ii2i2−i2−i2000200-2-22002ζ13+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+2ζ1190000−2i2i−2i2i000000000000002ζ13+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+2ζ1190i2i2−i2−i222−2−2−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000
χ452-22-22002-2-22-2-220022-2-2−i2i2−i2i20002002-2-20000002i−2i2i−2i-2-22200000000002i−2i2i−2i00000−i2i2−i2i2−i2i2−i2i22−22−22−22−200000000000000
χ462-22-22002-2-22-2-220022-2-2−i2i2−i2i20002002-2-2000000−2i2i−2i2i-2-2220000000000−2i2i−2i2i00000−i2i2−i2i2−i2i2−i2i2−22−22−22−2200000000000000
χ472-22-22002-2-22-2-220022-2-2i2−i2i2−i20002002-2-20000002i−2i2i−2i-2-22200000000002i−2i2i−2i00000i2−i2i2−i2i2−i2i2−i2−22−22−22−2200000000000000
χ482-22-22002-2-22-2-220022-2-2i2−i2i2−i20002002-2-2000000−2i2i−2i2i-2-2220000000000−2i2i−2i2i00000i2−i2i2−i2i2−i2i2−i22−22−22−22−200000000000000
χ492-22-22002-2-22-2-2200-2-222−i2i2−i2i20002002-2-20000002-2-2222-2-200000000002-2-2200000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i200000000000000
χ502-22-22002-2-22-2-2200-2-222−i2i2−i2i20002002-2-2000000-222-222-2-20000000000-222-200000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i200000000000000
χ512-22-22002-2-22-2-2200-2-222i2−i2i2−i20002002-2-20000002-2-2222-2-200000000002-2-2200000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i200000000000000
χ522-22-22002-2-22-2-2200-2-222i2−i2i2−i20002002-2-2000000-222-222-2-20000000000-222-200000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i200000000000000
χ532-2-2222-2-2-2222-2-22-22i−2i−2i2i2-2-220002-22-22-22i−2i00000000−2i2i2i−2i002-200002i−2i0000000002-2-222i−2i−2i2i0000000000000000000000
χ542-2-2222-2-2-2222-2-22-22i−2i−2i2i-222-20002-22-22-22i−2i00000000−2i2i2i−2i002-200002i−2i000000000-222-2−2i2i2i−2i0000000000000000000000
χ552-2-2222-2-2-2222-2-22-2−2i2i2i−2i2-2-220002-22-22-2−2i2i000000002i−2i−2i2i002-20000−2i2i0000000002-2-22−2i2i2i−2i0000000000000000000000
χ562-2-2222-2-2-2222-2-22-2−2i2i2i−2i-222-20002-22-22-2−2i2i000000002i−2i−2i2i002-20000−2i2i000000000-222-22i−2i−2i2i0000000000000000000000
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Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.