Finite Group Databasebeta

← Group #13052122

Character table — Group #13052122

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size11112222444446666666677777777121212121212121212121212141414141414141428282828282828282828282828282828282828282828565656565656
order1222224422224714141414141414336666661414141414141414282828286666121212126666666688881212242424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ4111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-1−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-11+i321−i321+i321−i32
χ5111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ6111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-1−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-11−i321+i321−i321+i32
χ711111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ811111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ911111111-1-1-1-1111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-11111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-11+i321−i321+i321−i32
χ1011111111-1-1-1-1111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-11111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-1−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1+i32−1−i32−1+i32
χ1111111111-1-1-1-1111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-11111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-11−i321+i321−i321+i32
χ1211111111-1-1-1-1111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-11111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-1−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1−i32−1+i32−1−i32
χ131111-1-11111-1-1-1111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111-1-111-1-11-111-1-1
χ141111-1-11111-1-1-1111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-1-111-1-1-1-111-1-111-11-1-111
χ151111-1-11111-1-1-1111-1-1-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111-1-1-1-111-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211-1-11+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1−1−i32−1+i321+i321−i32
χ161111-1-11111-1-1-1111-1-1-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111-1-1-1-111-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-1111+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-111+i321−i32−1−i32−1+i32
χ171111-1-11111-1-1-1111-1-1-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111-1-1-1-111-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211-1-11−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1−1+i32−1−i321−i321+i32
χ181111-1-11111-1-1-1111-1-1-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111-1-1-1-111-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-1111−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-111−i321+i32−1+i32−1−i32
χ191111-1-111-1-111-1111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-111-1-1-11-1-111
χ201111-1-111-1-111-1111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-1-111-1-1111-111-1-1
χ211111-1-111-1-111-1111-1-1-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1111111-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-1-11+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-111+i321−i32−1−i32−1+i32
χ221111-1-111-1-111-1111-1-1-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1111111-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-1111+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-1−1−i32−1+i321+i321−i32
χ231111-1-111-1-111-1111-1-1-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1111111-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-1-11−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-111−i321+i32−1+i32−1−i32
χ241111-1-111-1-111-1111-1-1-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1111111-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-1111−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-1−1+i32−1−i321−i321+i32
χ25222222-2-20000-2222222222222222200000000-2-2-2-22222-2-2-2-2000000000000-2-200000000000000
χ26222222-2-20000-222222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i300000000-2-2-2-2−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i30000000000001+i31−i300000000000000
χ27222222-2-20000-222222222−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i300000000-2-2-2-2−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i30000000000001−i31+i300000000000000
χ282222-2-2-2-200002222-2-2-2-222222222200000000-2-222-2-2-2-2-2-2-2-20000000000002200000000000000
χ292222-2-2-2-200002222-2-2-2-22−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i300000000-2-2221+i31+i31−i31−i31+i31+i31−i31−i3000000000000−1−i3−1+i300000000000000
χ302222-2-2-2-200002222-2-2-2-22−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i300000000-2-2221−i31−i31+i31+i31−i31−i31+i31+i3000000000000−1+i3−1−i300000000000000
χ312-22-2002-2002-202-2-20000222-2-22-22-2000022-2-22-20000002-22-2002-2002-200000000000000000000
χ322-22-2002-2002-202-2-200002−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i3000022-2-22-2000000−1−i31+i3−1+i31−i300−1−i31+i300−1+i31−i300000000000000000000
χ332-22-2002-2002-202-2-200002−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i3000022-2-22-2000000−1+i31−i3−1−i31+i300−1+i31−i300−1−i31+i300000000000000000000
χ342-22-2002-200-2202-2-20000222-2-22-22-20000-2-2222-20000002-22-200-2200-2200000000000000000000
χ352-22-2002-200-2202-2-200002−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i30000-2-2222-2000000−1−i31+i3−1+i31−i3001+i3−1−i3001−i3−1+i300000000000000000000
χ362-22-2002-200-2202-2-200002−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i30000-2-2222-2000000−1+i31−i3−1−i31+i3001−i3−1+i3001+i3−1−i300000000000000000000
χ372-22-200-222-20002-2-20000222-2-22-22-222-2-20000-22000000-22-222-2002-20000000000000000000000
χ382-22-200-222-20002-2-200002−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i322-2-20000-220000001+i3−1−i31−i3−1+i3−1−i31+i300−1+i31−i30000000000000000000000
χ392-22-200-222-20002-2-200002−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i322-2-20000-220000001−i3−1+i31+i3−1−i3−1+i31−i300−1−i31+i30000000000000000000000
χ402-22-200-22-220002-2-20000222-2-22-22-2-2-2220000-22000000-22-22-2200-220000000000000000000000
χ412-22-200-22-220002-2-200002−1−i3−1+i31+i31−i3−1−i31+i3−1+i31−i3-2-2220000-220000001+i3−1−i31−i3−1+i31+i3−1−i3001−i3−1+i30000000000000000000000
χ422-22-200-22-220002-2-200002−1+i3−1−i31−i31+i3−1+i31−i3−1−i31+i3-2-2220000-220000001−i3−1+i31+i3−1−i31−i3−1+i3001+i3−1−i30000000000000000000000
χ432-2-222-2000000022-222-2-2-222-2-2-22-220000000000002-22-20000000000002−22−2002−22−22−22−2000000
χ442-2-222-2000000022-222-2-2-222-2-2-22-220000000000002-22-2000000000000−22−2200−22−22−22−22000000
χ452-2-222-2000000022-222-2-2-2−1−i3−1+i31+i31−i31+i3−1−i31−i3−1+i3000000000000−1−i31+i3−1+i31−i30000000000002−22−200−ζ13+ζ31−ζ37+ζ55−ζ61+ζ79−ζ85+ζ103−ζ109+ζ127+ζ151−ζ157ζ13−ζ31+ζ37−ζ55+ζ61−ζ79+ζ85−ζ103+ζ109−ζ127−ζ151+ζ157−ζ13+ζ31−ζ37+ζ55−ζ61+ζ79−ζ85+ζ103−ζ109+ζ127+ζ151−ζ157ζ13−ζ31+ζ37−ζ55+ζ61−ζ79+ζ85−ζ103+ζ109−ζ127−ζ151+ζ157−ζ5+ζ23−ζ29+ζ47−ζ53+ζ71+ζ95−ζ101−ζ125+ζ143−ζ149+ζ167ζ5−ζ23+ζ29−ζ47+ζ53−ζ71−ζ95+ζ101+ζ125−ζ143+ζ149−ζ167−ζ5+ζ23−ζ29+ζ47−ζ53+ζ71+ζ95−ζ101−ζ125+ζ143−ζ149+ζ167ζ5−ζ23+ζ29−ζ47+ζ53−ζ71−ζ95+ζ101+ζ125−ζ143+ζ149−ζ167000000
χ462-2-222-2000000022-222-2-2-2−1−i3−1+i31+i31−i31+i3−1−i31−i3−1+i3000000000000−1−i31+i3−1+i31−i3000000000000−22−2200ζ13−ζ31+ζ37−ζ55+ζ61−ζ79+ζ85−ζ103+ζ109−ζ127−ζ151+ζ157−ζ13+ζ31−ζ37+ζ55−ζ61+ζ79−ζ85+ζ103−ζ109+ζ127+ζ151−ζ157ζ13−ζ31+ζ37−ζ55+ζ61−ζ79+ζ85−ζ103+ζ109−ζ127−ζ151+ζ157−ζ13+ζ31−ζ37+ζ55−ζ61+ζ79−ζ85+ζ103−ζ109+ζ127+ζ151−ζ157ζ5−ζ23+ζ29−ζ47+ζ53−ζ71−ζ95+ζ101+ζ125−ζ143+ζ149−ζ167−ζ5+ζ23−ζ29+ζ47−ζ53+ζ71+ζ95−ζ101−ζ125+ζ143−ζ149+ζ167ζ5−ζ23+ζ29−ζ47+ζ53−ζ71−ζ95+ζ101+ζ125−ζ143+ζ149−ζ167−ζ5+ζ23−ζ29+ζ47−ζ53+ζ71+ζ95−ζ101−ζ125+ζ143−ζ149+ζ167000000
χ472-2-222-2000000022-222-2-2-2−1+i3−1−i31−i31+i31−i3−1+i31+i3−1−i3000000000000−1+i31−i3−1−i31+i30000000000002−22−200−ζ5+ζ23−ζ29+ζ47−ζ53+ζ71+ζ95−ζ101−ζ125+ζ143−ζ149+ζ167ζ5−ζ23+ζ29−ζ47+ζ53−ζ71−ζ95+ζ101+ζ125−ζ143+ζ149−ζ167−ζ5+ζ23−ζ29+ζ47−ζ53+ζ71+ζ95−ζ101−ζ125+ζ143−ζ149+ζ167ζ5−ζ23+ζ29−ζ47+ζ53−ζ71−ζ95+ζ101+ζ125−ζ143+ζ149−ζ167−ζ13+ζ31−ζ37+ζ55−ζ61+ζ79−ζ85+ζ103−ζ109+ζ127+ζ151−ζ157ζ13−ζ31+ζ37−ζ55+ζ61−ζ79+ζ85−ζ103+ζ109−ζ127−ζ151+ζ157−ζ13+ζ31−ζ37+ζ55−ζ61+ζ79−ζ85+ζ103−ζ109+ζ127+ζ151−ζ157ζ13−ζ31+ζ37−ζ55+ζ61−ζ79+ζ85−ζ103+ζ109−ζ127−ζ151+ζ157000000
χ482-2-222-2000000022-222-2-2-2−1+i3−1−i31−i31+i31−i3−1+i31+i3−1−i3000000000000−1+i31−i3−1−i31+i3000000000000−22−2200ζ5−ζ23+ζ29−ζ47+ζ53−ζ71−ζ95+ζ101+ζ125−ζ143+ζ149−ζ167−ζ5+ζ23−ζ29+ζ47−ζ53+ζ71+ζ95−ζ101−ζ125+ζ143−ζ149+ζ167ζ5−ζ23+ζ29−ζ47+ζ53−ζ71−ζ95+ζ101+ζ125−ζ143+ζ149−ζ167−ζ5+ζ23−ζ29+ζ47−ζ53+ζ71+ζ95−ζ101−ζ125+ζ143−ζ149+ζ167ζ13−ζ31+ζ37−ζ55+ζ61−ζ79+ζ85−ζ103+ζ109−ζ127−ζ151+ζ157−ζ13+ζ31−ζ37+ζ55−ζ61+ζ79−ζ85+ζ103−ζ109+ζ127+ζ151−ζ157ζ13−ζ31+ζ37−ζ55+ζ61−ζ79+ζ85−ζ103+ζ109−ζ127−ζ151+ζ157−ζ13+ζ31−ζ37+ζ55−ζ61+ζ79−ζ85+ζ103−ζ109+ζ127+ζ151−ζ157000000
χ492-2-22-22000000022-2-2-222-222-2-2-22-22000000000000-22-220000000000002−2−22002−2−222−2−22000000
χ502-2-22-22000000022-2-2-222-222-2-2-22-22000000000000-22-22000000000000−222−200−222−2−222−2000000
χ512-2-22-22000000022-2-2-222-2−1−i3−1+i31+i31−i31+i3−1−i31−i3−1+i30000000000001+i3−1−i31−i3−1+i30000000000002−2−2200−ζ13+ζ31−ζ37+ζ55−ζ61+ζ79−ζ85+ζ103−ζ109+ζ127+ζ151−ζ157ζ13−ζ31+ζ37−ζ55+ζ61−ζ79+ζ85−ζ103+ζ109−ζ127−ζ151+ζ157ζ13−ζ31+ζ37−ζ55+ζ61−ζ79+ζ85−ζ103+ζ109−ζ127−ζ151+ζ157−ζ13+ζ31−ζ37+ζ55−ζ61+ζ79−ζ85+ζ103−ζ109+ζ127+ζ151−ζ157−ζ5+ζ23−ζ29+ζ47−ζ53+ζ71+ζ95−ζ101−ζ125+ζ143−ζ149+ζ167ζ5−ζ23+ζ29−ζ47+ζ53−ζ71−ζ95+ζ101+ζ125−ζ143+ζ149−ζ167ζ5−ζ23+ζ29−ζ47+ζ53−ζ71−ζ95+ζ101+ζ125−ζ143+ζ149−ζ167−ζ5+ζ23−ζ29+ζ47−ζ53+ζ71+ζ95−ζ101−ζ125+ζ143−ζ149+ζ167000000
χ522-2-22-22000000022-2-2-222-2−1−i3−1+i31+i31−i31+i3−1−i31−i3−1+i30000000000001+i3−1−i31−i3−1+i3000000000000−222−200ζ13−ζ31+ζ37−ζ55+ζ61−ζ79+ζ85−ζ103+ζ109−ζ127−ζ151+ζ157−ζ13+ζ31−ζ37+ζ55−ζ61+ζ79−ζ85+ζ103−ζ109+ζ127+ζ151−ζ157−ζ13+ζ31−ζ37+ζ55−ζ61+ζ79−ζ85+ζ103−ζ109+ζ127+ζ151−ζ157ζ13−ζ31+ζ37−ζ55+ζ61−ζ79+ζ85−ζ103+ζ109−ζ127−ζ151+ζ157ζ5−ζ23+ζ29−ζ47+ζ53−ζ71−ζ95+ζ101+ζ125−ζ143+ζ149−ζ167−ζ5+ζ23−ζ29+ζ47−ζ53+ζ71+ζ95−ζ101−ζ125+ζ143−ζ149+ζ167−ζ5+ζ23−ζ29+ζ47−ζ53+ζ71+ζ95−ζ101−ζ125+ζ143−ζ149+ζ167ζ5−ζ23+ζ29−ζ47+ζ53−ζ71−ζ95+ζ101+ζ125−ζ143+ζ149−ζ167000000
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Here ζ is a primitive root of unity of order 168 (ζ168 = 1); i = ζ42.