Finite Group Databasebeta

← Group #14287398

Character table — Group #14287398

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222244444455556666888888888101010101010101010101010101016161616161616162020202020202020202024242424243030303030303030303030304040404040404040404848120120120
order122234466651010101212444488884121215202030303044888888881212121220206060606060601212242424242424242444040404088888888888826688242424242020488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1
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
χ4111111111111111111111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111
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
χ611111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-111
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
χ811111111111111111111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1111111111-1-1
χ91111111111111111-1-1-1-11111111111111-1-1iiii−i−i−i−i-1-1-1-111111111-1-1iiii−i−i−i−i11111-1-1-1-1ii−i−iii−i−i-1-1-1i−iii−i−i11-1i−i
χ101111111111111111-1-1-1-11111111111111-1-1−i−i−i−iiiii-1-1-1-111111111-1-1−i−i−i−iiiii11111-1-1-1-1−i−iii−i−iii-1-1-1−ii−i−iii11-1−ii
χ111111111111111111-1-1-1-11111-1-1-1111111-1-1iiii−i−i−i−i-1-1-1-1-1-111-1-1-1-1-1-1iiii−i−i−i−i-11111-1-1-1-1ii−i−iii−i−i111−ii−i−iii-1-11−ii
χ121111111111111111-1-1-1-11111-1-1-1111111-1-1−i−i−i−iiiii-1-1-1-1-1-111-1-1-1-1-1-1−i−i−i−iiiii-11111-1-1-1-1−i−iii−i−iii111i−iii−i−i-1-11i−i
χ131111111111111111-1-1-1-1-1-1-1-1111111111-1-1iiii−i−i−i−i-1-1-1-111111111-1-1iiii−i−i−i−i-1-1-1-1-11111−i−iii−i−iii-1-1-1i−iii−i−i-1-11−ii
χ141111111111111111-1-1-1-1-1-1-1-1111111111-1-1−i−i−i−iiiii-1-1-1-111111111-1-1−i−i−i−iiiii-1-1-1-1-11111ii−i−iii−i−i-1-1-1−ii−i−iii-1-11i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−i-1-1-1-1-1-111-1-1-1-1-1-1iiii−i−i−i−i1-1-1-1-11111−i−iii−i−iii111−ii−i−iii11-1i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii-1-1-1-1-1-111-1-1-1-1-1-1−i−i−i−iiiii1-1-1-1-11111ii−i−iii−i−i111i−iii−i−i11-1−ii
χ1722222-2-22222222-2-2222200000002-2-2222-2-200000000222200-2-20000-2-2000000000000000002222-2-2-2-200000000000000
χ1822222-2-22222222-2-2222200000002-2-2222-2-200000000222200-2-20000-2-200000000000000000-2-2-2-2222200000000000000
χ1922222-2-22222222-2-2-2-2-2-200000002-2-22222200000000-2-2-2-200-2-2000022000000000000000002i2i−2i−2i−2i−2i2i2i00000000000000
χ2022222-2-22222222-2-2-2-2-2-200000002-2-22222200000000-2-2-2-200-2-200002200000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000
χ212222-122-1-1-12222-1-1222200002-1-1-122-1-1-12222222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000002-1-122-1-1-1-100000
χ222222-122-1-1-12222-1-1222200002-1-1-122-1-1-122-2-2-2-2-2-2-2-2-1-1-1-122-1-1-1-1-1-1-1-111111111000000000000000002-1-1-2-2111100000
χ232222-122-1-1-12222-1-122220000-211-122-1-1-12222222222-1-1-1-1-2-2-1-11111-1-1-1-1-1-1-1-1-1-100000000000000000-211-2-2111100000
χ242222-122-1-1-12222-1-122220000-211-122-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-2-2-1-11111-1-11111111100000000000000000-21122-1-1-1-100000
χ252222-122-1-1-12222-1-1-2-2-2-200002-1-1-122-1-1-1-2-22i2i2i2i−2i−2i−2i−2i111122-1-1-1-1-1-111−i−i−i−iiiii00000000000000000-2112i−2i−i−iii00000
χ262222-122-1-1-12222-1-1-2-2-2-200002-1-1-122-1-1-1-2-2−2i−2i−2i−2i2i2i2i2i111122-1-1-1-1-1-111iiii−i−i−i−i00000000000000000-211−2i2iii−i−i00000
χ272222-122-1-1-12222-1-1-2-2-2-20000-211-122-1-1-1-2-22i2i2i2i−2i−2i−2i−2i1111-2-2-1-1111111−i−i−i−iiiii000000000000000002-1-1−2i2iii−i−i00000
χ282222-122-1-1-12222-1-1-2-2-2-20000-211-122-1-1-1-2-2−2i−2i−2i−2i2i2i2i2i1111-2-2-1-1111111iiii−i−i−i−i000000000000000002-1-12i−2i−i−iii00000
χ2922-2-2200-2-222-22-20022-2-2−i2−i2i2i2000200-2-220022−2−222−2−2-2-222000000000022−2−222−2−20−i2−i2i2i2−i2−i2i2i200002i−2i2i−2i00000000000000
χ3022-2-2200-2-222-22-20022-2-2−i2−i2i2i2000200-2-2200−2−222−2−222-2-2220000000000−2−222−2−2220−i2−i2i2i2−i2−i2i2i20000−2i2i−2i2i00000000000000
χ3122-2-2200-2-222-22-20022-2-2i2i2−i2−i2000200-2-220022−2−222−2−2-2-222000000000022−2−222−2−20i2i2−i2−i2i2i2−i2−i20000−2i2i−2i2i00000000000000
χ3222-2-2200-2-222-22-20022-2-2i2i2−i2−i2000200-2-2200−2−222−2−222-2-2220000000000−2−222−2−2220i2i2−i2−i2i2i2−i2−i200002i−2i2i−2i00000000000000
χ3322-2-2200-2-222-22-200-2-222−i2−i2i2i2000200-2-2200−i2−i2i2i2i2i2−i2−i222-2-20000000000−i2−i2i2i2i2i2−i2−i20−i2−i2i2i2i2i2−i2−i200002-2-2200000000000000
χ3422-2-2200-2-222-22-200-2-222−i2−i2i2i2000200-2-2200i2i2−i2−i2−i2−i2i2i222-2-20000000000i2i2−i2−i2−i2−i2i2i20−i2−i2i2i2i2i2−i2−i20000-222-200000000000000
χ3522-2-2200-2-222-22-200-2-222i2i2−i2−i2000200-2-2200−i2−i2i2i2i2i2−i2−i222-2-20000000000−i2−i2i2i2i2i2−i2−i20i2i2−i2−i2−i2−i2i2i20000-222-200000000000000
χ3622-2-2200-2-222-22-200-2-222i2i2−i2−i2000200-2-2200i2i2−i2−i2−i2−i2i2i222-2-20000000000i2i2−i2−i2−i2−i2i2i20i2i2−i2−i2−i2−i2i2i200002-2-2200000000000000
χ372-22-2200-22-22-2-22002i−2i2i−2i−i2i2−i2i20002002-2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i2i−2i2i−2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0−i2i2−i2i22−22−2−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119000000000000000000
χ382-22-2200-22-22-2-22002i−2i2i−2i−i2i2−i2i20002002-2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i2i−2i2i−2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0−i2i2−i2i22−22−22ζ13+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
χ392-22-2200-22-22-2-22002i−2i2i−2ii2−i2i2−i20002002-2-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i2i−2i2i−2i00000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0i2−i2i2−i2−22−222ζ13+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
χ402-22-2200-22-22-2-22002i−2i2i−2ii2−i2i2−i20002002-2-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i2i−2i2i−2i0000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0i2−i2i2−i2−22−22−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119000000000000000000
χ412-22-2200-22-22-2-2200−2i2i−2i2i−i2i2−i2i20002002-2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2i2i−2i2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0−i2i2−i2i2−22−22−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109000000000000000000
χ422-22-2200-22-22-2-2200−2i2i−2i2i−i2i2−i2i20002002-2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2i2i−2i2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0−i2i2−i2i2−22−222ζ7+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
χ432-22-2200-22-22-2-2200−2i2i−2i2ii2−i2i2−i20002002-2-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i−2i2i−2i2i00000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0i2−i2i2−i22−22−22ζ7+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
χ442-22-2200-22-22-2-2200−2i2i−2i2ii2−i2i2−i20002002-2-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2i2i−2i2i0000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0i2−i2i2−i22−22−2−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109000000000000000000
χ452-2-2222-22-2-222-2-22-22i−2i−2i2i2-2-220002-22-22-22i−2i00000000−2i2i2i−2i002-200002i−2i0000000002-2-222i−2i−2i2i0000000000000000000000
χ462-2-2222-22-2-222-2-22-22i−2i−2i2i-222-20002-22-22-22i−2i00000000−2i2i2i−2i002-200002i−2i000000000-222-2−2i2i2i−2i0000000000000000000000
χ472-2-2222-22-2-222-2-22-2−2i2i2i−2i2-2-220002-22-22-2−2i2i000000002i−2i−2i2i002-20000−2i2i0000000002-2-22−2i2i2i−2i0000000000000000000000
χ482-2-2222-22-2-222-2-22-2−2i2i2i−2i-222-20002-22-22-2−2i2i000000002i−2i−2i2i002-20000−2i2i000000000-222-22i−2i−2i2i0000000000000000000000
χ492-2-222-222-2-222-2-2-222i−2i−2i2i000000022-2-22-2−2i2i2ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2i2i2i−2i00-220000−2i2i2ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090000000000000000000000000000000
χ502-2-222-222-2-222-2-2-222i−2i−2i2i000000022-2-22-2−2i2i−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2i2i2i−2i00-220000−2i2i−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1090000000000000000000000000000000
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Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.