Finite Group Databasebeta

← Group #72245627

Character table — Group #72245627

Order 2016.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1124667777121212141414141414141428282828282248121214141414242424282828282828282856565656563361218182121212136363642424242424242428484848484
order12427143366141428881212242424242666636126214233664242842424121224242424666662242141466661414288812122424242426666
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111-1-111-1-1-1-1-111-1-11111111111111-1-111-1-1-1-1-111-1-11111111111111-1-111-1-1-1-1-111-1-1
χ3111111−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32
χ4111111−1−i32−1+i32−1−i32−1+i32111-1-1−1−i32−1+i321+i321+i321−i321−i32-1−1−i32−1+i321+i321−i32111111−1−i32−1+i32−1−i32−1+i32111-1-1−1−i32−1+i321+i321+i321−i321−i32-1−1−i32−1+i321+i321−i32111111−1−i32−1+i32−1−i32−1+i32111-1-1−1−i32−1+i321+i321+i321−i321−i32-1−1−i32−1+i321+i321−i32
χ5111111−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32
χ6111111−1+i32−1−i32−1+i32−1−i32111-1-1−1+i32−1−i321−i321−i321+i321+i32-1−1+i32−1−i321−i321+i32111111−1+i32−1−i32−1+i32−1−i32111-1-1−1+i32−1−i321−i321−i321+i321+i32-1−1+i32−1−i321−i321+i32111111−1+i32−1−i32−1+i32−1−i32111-1-1−1+i32−1−i321−i321−i321+i321+i32-1−1+i32−1−i321−i321+i32
χ7111-1111111-1-1111111111-1-1-1-1-1111-1111111-1-1111111111-1-1-1-1-1111-1111111-1-1111111111-1-1-1-1-1
χ8111-1111111-1-11-1-111-1-1-1-11-1-111111-1111111-1-11-1-111-1-1-1-11-1-111111-1111111-1-11-1-111-1-1-1-11-1-111
χ9111-111−1−i32−1+i32−1−i32−1+i32-1-1111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11+i321−i321+i321−i32111-111−1−i32−1+i32−1−i32−1+i32-1-1111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11+i321−i321+i321−i32111-111−1−i32−1+i32−1−i32−1+i32-1-1111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11+i321−i321+i321−i32
χ10111-111−1−i32−1+i32−1−i32−1+i32-1-11-1-1−1−i32−1+i321+i321+i321−i321−i3211+i321−i32−1−i32−1+i32111-111−1−i32−1+i32−1−i32−1+i32-1-11-1-1−1−i32−1+i321+i321+i321−i321−i3211+i321−i32−1−i32−1+i32111-111−1−i32−1+i32−1−i32−1+i32-1-11-1-1−1−i32−1+i321+i321+i321−i321−i3211+i321−i32−1−i32−1+i32
χ11111-111−1+i32−1−i32−1+i32−1−i32-1-1111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11−i321+i321−i321+i32111-111−1+i32−1−i32−1+i32−1−i32-1-1111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11−i321+i321−i321+i32111-111−1+i32−1−i32−1+i32−1−i32-1-1111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11−i321+i321−i321+i32
χ12111-111−1+i32−1−i32−1+i32−1−i32-1-11-1-1−1+i32−1−i321−i321−i321+i321+i3211−i321+i32−1+i32−1−i32111-111−1+i32−1−i32−1+i32−1−i32-1-11-1-1−1+i32−1−i321−i321−i321+i321+i3211−i321+i32−1+i32−1−i32111-111−1+i32−1−i32−1+i32−1−i32-1-11-1-1−1+i32−1−i321−i321−i321+i321+i3211−i321+i32−1+i32−1−i32
χ1322-2022222200-200-2-200000000022-2022222200-200-2-200000000022-2022222200-200-2-2000000000
χ1422-2022−1−i3−1+i3−1−i3−1+i300-2001+i31−i300000000022-2022−1−i3−1+i3−1−i3−1+i300-2001+i31−i300000000022-2022−1−i3−1+i3−1−i3−1+i300-2001+i31−i3000000000
χ1522-2022−1+i3−1−i3−1+i3−1−i300-2001−i31+i300000000022-2022−1+i3−1−i3−1+i3−1−i300-2001−i31+i300000000022-2022−1+i3−1−i3−1+i3−1−i300-2001−i31+i3000000000
χ162-2002-222-2-20002−2002−22−2000002-2002-222-2-20002−2002−22−2000002-2002-222-2-20002−2002−22−200000
χ172-2002-222-2-2000−2200−22−22000002-2002-222-2-2000−2200−22−22000002-2002-222-2-2000−2200−22−2200000
χ182-2002-2−1−i3−1+i31+i31−i30002−200−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−ζ167000002-2002-2−1−i3−1+i31+i31−i30002−200−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−ζ167000002-2002-2−1−i3−1+i31+i31−i30002−200−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−ζ16700000
χ192-2002-2−1−i3−1+i31+i31−i3000−2200ζ13−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+ζ167000002-2002-2−1−i3−1+i31+i31−i3000−2200ζ13−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+ζ167000002-2002-2−1−i3−1+i31+i31−i3000−2200ζ13−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+ζ16700000
χ202-2002-2−1+i3−1−i31−i31+i30002−200−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+ζ157000002-2002-2−1+i3−1−i31−i31+i30002−200−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+ζ157000002-2002-2−1+i3−1−i31−i31+i30002−200−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+ζ15700000
χ212-2002-2−1+i3−1−i31−i31+i3000−2200ζ5−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−ζ157000002-2002-2−1+i3−1−i31−i31+i3000−2200ζ5−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−ζ157000002-2002-2−1+i3−1−i31−i31+i3000−2200ζ5−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−ζ15700000
χ226666-1-10000-1-1-100000000000006666-1-10000-1-1-100000000000006666-1-10000-1-1-10000000000000
χ23666-6-1-1000011-10000000000000666-6-1-1000011-10000000000000666-6-1-1000011-10000000000000
χ2466-60-1-10000−i7i71000000000000066-60-1-10000−i7i71000000000000066-60-1-10000−i7i710000000000000
χ2566-60-1-10000i7−i71000000000000066-60-1-10000i7−i71000000000000066-60-1-10000i7−i710000000000000
χ2612-1200-220000000000000000000012-1200-220000000000000000000012-1200-2200000000000000000000
χ271111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ281111111111111-1-111-1-1-1-1-111-1-11111111111111-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-111
χ29111111−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-11+i321−i321+i321−i32-1-1-1-1-11+i321−i321+i321+i321−i321−i32-11+i321−i321+i321−i32
χ30111111−1−i32−1+i32−1−i32−1+i32111-1-1−1−i32−1+i321+i321+i321−i321−i32-1−1−i32−1+i321+i321−i32111111−1−i32−1+i32−1−i32−1+i32111-1-1−1−i32−1+i321+i321+i321−i321−i32-1−1−i32−1+i321+i321−i32-1-1-1-1-1-11+i321−i321+i321−i32-1-1-1111+i321−i32−1−i32−1−i32−1+i32−1+i3211+i321−i32−1−i32−1+i32
χ31111111−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-11−i321+i321−i321+i32-1-1-1-1-11−i321+i321−i321−i321+i321+i32-11−i321+i321−i321+i32
χ32111111−1+i32−1−i32−1+i32−1−i32111-1-1−1+i32−1−i321−i321−i321+i321+i32-1−1+i32−1−i321−i321+i32111111−1+i32−1−i32−1+i32−1−i32111-1-1−1+i32−1−i321−i321−i321+i321+i32-1−1+i32−1−i321−i321+i32-1-1-1-1-1-11−i321+i321−i321+i32-1-1-1111−i321+i32−1+i32−1+i32−1−i32−1−i3211−i321+i32−1+i32−1−i32
χ33111-1111111-1-1111111111-1-1-1-1-1111-1111111-1-1111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111
χ34111-1111111-1-11-1-111-1-1-1-11-1-111111-1111111-1-11-1-111-1-1-1-11-1-111-1-1-11-1-1-1-1-1-111-111-1-11111-111-1-1
χ35111-111−1−i32−1+i32−1−i32−1+i32-1-1111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11+i321−i321+i321−i32111-111−1−i32−1+i32−1−i32−1+i32-1-1111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11+i321−i321+i321−i32-1-1-11-1-11+i321−i321+i321−i3211-1-1-11+i321−i321+i321+i321−i321−i321−1−i32−1+i32−1−i32−1+i32
χ36111-111−1−i32−1+i32−1−i32−1+i32-1-11-1-1−1−i32−1+i321+i321+i321−i321−i3211+i321−i32−1−i32−1+i32111-111−1−i32−1+i32−1−i32−1+i32-1-11-1-1−1−i32−1+i321+i321+i321−i321−i3211+i321−i32−1−i32−1+i32-1-1-11-1-11+i321−i321+i321−i3211-1111+i321−i32−1−i32−1−i32−1+i32−1+i32-1−1−i32−1+i321+i321−i32
χ37111-111−1+i32−1−i32−1+i32−1−i32-1-1111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11−i321+i321−i321+i32111-111−1+i32−1−i32−1+i32−1−i32-1-1111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11−i321+i321−i321+i32-1-1-11-1-11−i321+i321−i321+i3211-1-1-11−i321+i321−i321−i321+i321+i321−1+i32−1−i32−1+i32−1−i32
χ38111-111−1+i32−1−i32−1+i32−1−i32-1-11-1-1−1+i32−1−i321−i321−i321+i321+i3211−i321+i32−1+i32−1−i32111-111−1+i32−1−i32−1+i32−1−i32-1-11-1-1−1+i32−1−i321−i321−i321+i321+i3211−i321+i32−1+i32−1−i32-1-1-11-1-11−i321+i321−i321+i3211-1111−i321+i32−1+i32−1+i32−1−i32−1−i32-1−1+i32−1−i321−i321+i32
χ3922-2022222200-200-2-200000000022-2022222200-200-2-2000000000-2-220-2-2-2-2-2-20020022000000000
χ4022-2022−1−i3−1+i3−1−i3−1+i300-2001+i31−i300000000022-2022−1−i3−1+i3−1−i3−1+i300-2001+i31−i3000000000-2-220-2-21+i31−i31+i31−i300200−1−i3−1+i3000000000
χ4122-2022−1+i3−1−i3−1+i3−1−i300-2001−i31+i300000000022-2022−1+i3−1−i3−1+i3−1−i300-2001−i31+i3000000000-2-220-2-21−i31+i31−i31+i300200−1+i3−1−i3000000000
χ422-2002-222-2-20002−2002−22−2000002-2002-222-2-20002−2002−22−200000-2200-22-2-222000−2200−22−2200000
χ432-2002-222-2-2000−2200−22−22000002-2002-222-2-2000−2200−22−2200000-2200-22-2-2220002−2002−22−200000
χ442-2002-2−1−i3−1+i31+i31−i30002−200−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−ζ167000002-2002-2−1−i3−1+i31+i31−i30002−200−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−ζ16700000-2200-221+i31−i3−1−i3−1+i3000−2200ζ13−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+ζ16700000
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Here ζ is a primitive root of unity of order 168 (ζ168 = 1); i = ζ42.