Finite Group Databasebeta

← Group #13051748

Character table — Group #13051748

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size11112222444446666666677777777121212121212121212121212141414141414141428282828282828282828282828282828282828282828565656565656
order12224444488887141414282828283366666628282828565656565656565612121212121212122244666612121212121224242424242424244412121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1
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−i32−1−i32−1+i321+i321+i321−i321−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+i32−1+i32−1−i321−i321−i321+i321+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
χ8111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
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−i32−1−i32−1+i321+i321+i321−i321−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+i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i3211−1+i32−1+i32−1−i32−1−i32
χ1311111-1-11-111-1-11111111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-111-1-11-11-11-1
χ1411111-1-11-111-1-11111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-111-1-1-11-11-11
χ1511111-1-11-111-1-111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-11111-1-1-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321-1−1−i321+i32−1+i321−i32
χ1611111-1-11-111-1-111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-11111-1-1-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32-1-1111+i321+i321−i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-111+i32−1−i321−i32−1+i32
χ1711111-1-11-111-1-111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-11111-1-1-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321-1−1+i321−i32−1−i321+i32
χ1811111-1-11-111-1-111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-11111-1-1-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32-1-1111−i321−i321+i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-111−i32−1+i321+i32−1−i32
χ1911111-1-11-1-1-1111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-111-11-11-11
χ2011111-1-11-1-1-1111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-111-1-1111-11-11-1
χ2111111-1-11-1-1-11111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-11111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i32
χ2211111-1-11-1-1-11111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-11111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32-1-1111+i321+i321−i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i32
χ2311111-1-11-1-1-11111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-11111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i32
χ2411111-1-11-1-1-11111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-11111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32-1-1111−i321−i321+i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i32
χ252222-222-2-200002222-2-2-2-22222222222-2-200000000-2-22222-2-200000000-2-2000000000000000000
χ262222-222-2-200002222-2-2-2-2−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i322-2-2000000001+i31−i3−1−i3−1−i3−1+i3−1+i31+i31−i3000000001+i31−i3000000000000000000
χ272222-222-2-200002222-2-2-2-2−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i322-2-2000000001−i31+i3−1+i3−1+i3−1−i3−1−i31−i31+i3000000001−i31+i3000000000000000000
χ282222-2-2-2-2200002222-2-2-2-222222222-2-22200000000-2-2-2-2-2-2-2-20000000022000000000000000000
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−i300000000−1−i3−1+i3000000000000000000
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+i300000000−1+i3−1−i3000000000000000000
χ3122-2-2200-20000022-2-222-2-2222-22-2-2-2000000000000220000-2-22-2002-22-200000000000000000000
χ3222-2-2200-20000022-2-222-2-2222-22-2-2-2000000000000220000-2-2-2200-22-2200000000000000000000
χ3322-2-2200-20000022-2-222-2-2−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i3000000000000−1−i3−1+i300001+i31−i32-200−1−i31+i3−1+i31−i300000000000000000000
χ3422-2-2200-20000022-2-222-2-2−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i3000000000000−1−i3−1+i300001+i31−i3-22001+i3−1−i31−i3−1+i300000000000000000000
χ3522-2-2200-20000022-2-222-2-2−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i3000000000000−1+i3−1−i300001−i31+i32-200−1+i31−i3−1−i31+i300000000000000000000
χ3622-2-2200-20000022-2-222-2-2−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i3000000000000−1+i3−1−i300001−i31+i3-22001−i3−1+i31+i3−1−i300000000000000000000
χ3722-2-2-20020000022-2-2-2-222222-22-2-2-2000000000000-2-2000022002i−2i0000002i−2i2i−2i00000000000000
χ3822-2-2-20020000022-2-2-2-222222-22-2-2-2000000000000-2-200002200−2i2i000000−2i2i−2i2i00000000000000
χ3922-2-2-20020000022-2-2-2-222−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i30000000000001+i31−i30000−1−i3−1+i3002i−2i0000002ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1662ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ15800000000000000
χ4022-2-2-20020000022-2-2-2-222−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i30000000000001+i31−i30000−1−i3−1+i300−2i2i000000−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1662ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1582ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ15800000000000000
χ4122-2-2-20020000022-2-2-2-222−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i30000000000001−i31+i30000−1+i3−1−i3002i−2i0000002ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1582ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ16600000000000000
χ4222-2-2-20020000022-2-2-2-222−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i30000000000001−i31+i30000−1+i3−1−i300−2i2i000000−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1582ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1662ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ16600000000000000
χ432-2-2202-2002−22−22-22-2000022-2-2-2-2222-20022−2−222−2−2002-22-200000000000000002−22−22−22−2000000
χ442-2-2202-2002−22−22-22-20000−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i32-20022−2−222−2−200−1−i31+i3−1+i31−i30000000000000000−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
χ452-2-2202-2002−22−22-22-20000−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i32-20022−2−222−2−200−1+i31−i3−1−i31+i30000000000000000−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
χ462-2-2202-200−22−222-22-2000022-2-2-2-2222-200−2−222−2−222002-22-20000000000000000−22−22−22−22000000
χ472-2-2202-200−22−222-22-20000−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i32-200−2−222−2−22200−1−i31+i3−1+i31−i30000000000000000ζ13−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
χ482-2-2202-200−22−222-22-20000−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i32-200−2−222−2−22200−1+i31−i3−1−i31+i30000000000000000ζ5−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
χ492-2-220-22002−2−222-22-2000022-2-2-2-222-220022−2−2−2−22200-22-2200000000000000002−2−222−2−22000000
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Here ζ is a primitive root of unity of order 168 (ζ168 = 1); i = ζ42.