Finite Group Databasebeta

← Group #13051631

Character table — Group #13051631

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size11112222444446666666677777777121212121212121212121212141414141414141428282828282828282828282828282828282828282828565656565656
order122222444888871414142828282833666666141428285656565656565656666612121212222266666666121224242424242424244412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
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+i321111−1−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+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+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−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
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−i321111−1+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−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−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+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
χ7111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ8111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ9111111111-1-1-1-111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111-1-1-1-1-1-1-1-1−1−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+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-11+i321−i321+i321−i32
χ10111111111-1-1-1-111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111-1-1-1-1-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211−1−i32−1+i32−1−i32−1+i32
χ11111111111-1-1-1-111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111-1-1-1-1-1-1-1-1−1+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−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-11−i321+i321−i321+i32
χ12111111111-1-1-1-111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1−i32−1+i32−1−i32
χ131111-1-111-111-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111-1-111-1-11-111-1-1
χ141111-1-111-111-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-111-1-111-1-1-11-1-111
χ151111-1-111-111-1-111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-11111-1-1-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1−1−i32−1+i321+i321−i32
χ161111-1-111-111-1-111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-11111-1-1-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-111+i321−i32−1−i32−1+i32
χ171111-1-111-111-1-111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-11111-1-1-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1−1+i32−1−i321−i321+i32
χ181111-1-111-111-1-111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-11111-1-1-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-111−i321+i32−1+i32−1−i32
χ191111-1-111-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-111-1-111-11-1-111
χ201111-1-111-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111-1-1-1-111-1-1111-111-1-1
χ211111-1-111-1-1-11111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-111111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i3211-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-111+i321−i32−1−i32−1+i32
χ221111-1-111-1-1-11111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-111111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-1−1−i32−1+i321+i321−i32
χ231111-1-111-1-1-11111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-111111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i3211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-111−i321+i32−1+i32−1−i32
χ241111-1-111-1-1-11111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-111111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-1−1+i32−1−i321−i321+i32
χ25222222-2-2-200002222-2-2-2-22222222222-2-2000000002222-2-2-2-2000000000000-2-200000000000000
χ26222222-2-2-200002222-2-2-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322-2-200000000−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i30000000000001+i31−i300000000000000
χ27222222-2-2-200002222-2-2-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322-2-200000000−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i30000000000001−i31+i300000000000000
χ282222-2-2-2-2200002222-2-2-2-222222222-2-22200000000-2-2-2-2-2-2-2-20000000000002200000000000000
χ292222-2-2-2-2200002222-2-2-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-2-222000000001+i31+i31−i31−i31+i31+i31−i31−i3000000000000−1−i3−1+i300000000000000
χ302222-2-2-2-2200002222-2-2-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-2-222000000001−i31−i31+i31+i31−i31−i31+i31+i3000000000000−1+i3−1−i300000000000000
χ3122-2-22-2000−i2i2−i2i222-2-200002222-2-2-2-22-200−i2−i2i2i2−i2−i2i2i22-22-2000000000000000000−i2i2−i2i2−i2i2−i2i2000000
χ3222-2-22-2000−i2i2−i2i222-2-20000−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i32-200−i2−i2i2i2−i2−i2i2i2−1−i31+i3−1+i31−i3000000000000000000ζ13+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
χ3322-2-22-2000−i2i2−i2i222-2-20000−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i32-200−i2−i2i2i2−i2−i2i2i2−1+i31−i3−1−i31+i3000000000000000000ζ5+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
χ3422-2-22-2000i2−i2i2−i222-2-200002222-2-2-2-22-200i2i2−i2−i2i2i2−i2−i22-22-2000000000000000000i2−i2i2−i2i2−i2i2−i2000000
χ3522-2-22-2000i2−i2i2−i222-2-20000−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i32-200i2i2−i2−i2i2i2−i2−i2−1−i31+i3−1+i31−i3000000000000000000−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
χ3622-2-22-2000i2−i2i2−i222-2-20000−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i32-200i2i2−i2−i2i2i2−i2−i2−1+i31−i3−1−i31+i3000000000000000000−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
χ3722-2-2-22000−i2i2i2−i222-2-200002222-2-2-2-2-2200−i2−i2i2i2i2i2−i2−i2-22-22000000000000000000−i2i2i2−i2−i2i2i2−i2000000
χ3822-2-2-22000−i2i2i2−i222-2-20000−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3-2200−i2−i2i2i2i2i2−i2−i21+i3−1−i31−i3−1+i3000000000000000000ζ13+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
χ3922-2-2-22000−i2i2i2−i222-2-20000−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3-2200−i2−i2i2i2i2i2−i2−i21−i3−1+i31+i3−1−i3000000000000000000ζ5+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+ζ167ζ13+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+ζ157000000
χ4022-2-2-22000i2−i2−i2i222-2-200002222-2-2-2-2-2200i2i2−i2−i2−i2−i2i2i2-22-22000000000000000000i2−i2−i2i2i2−i2−i2i2000000
χ4122-2-2-22000i2−i2−i2i222-2-20000−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3-2200i2i2−i2−i2−i2−i2i2i21+i3−1−i31−i3−1+i3000000000000000000−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
χ4222-2-2-22000i2−i2−i2i222-2-20000−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3-2200i2i2−i2−i2−i2−i2i2i21−i3−1+i31+i3−1−i3000000000000000000−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−ζ167−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−ζ157000000
χ432-2-22002-2000002-2-2222-2-222-2-2-2-22200000000000000002-22-2002-2002-2002-20000000000000000
χ442-2-22002-2000002-2-2222-2-222-2-2-2-22200000000000000002-22-200-2200-2200-220000000000000000
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Here ζ is a primitive root of unity of order 168 (ζ168 = 1); i = ζ42.