Finite Group Databasebeta

← Group #13054994

Character table — Group #13054994

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size111122223333333344444444466666666777777778812121212121212121212121212121212121214141414141414142424242428282828282828282828282828282828282856565656
order12224444771414141414142244488882828282828282828336666662414141414282828282828565656565656565612121212121212121414282866661212121212122424242424242424661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111111111111111−1−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+i32−1−i32−1+i32−1−i32−1+i32
χ3111111111111111111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111111111111111−1+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−i32−1+i32−1−i32−1+i32−1−i32
χ4111111111111111111111-1-1-1-11111111111111111-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ5111111111111111111111-1-1-1-111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11111111111-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i32-1-1-1-1−1−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−i321+i321−i321+i321−i32
χ6111111111111111111111-1-1-1-111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11111111111-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i32-1-1-1-1−1+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+i321−i321+i321−i321+i32
χ71111111111111111-1-11-1-111111111111111111111-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ81111111111111111-1-11-1-1111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-111-1-1-1-111111111−1−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+i321+i321−i321+i321−i32
χ91111111111111111-1-11-1-1111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-111-1-1-1-111111111−1+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−i321−i321+i321−i321+i32
χ101111111111111111-1-11-1-1-1-1-1-1111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ111111111111111111-1-11-1-1-1-1-1-111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1+i3211111+i321+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1+i32−1−i32−1+i32
χ121111111111111111-1-11-1-1-1-1-1-111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1−i3211111−i321−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1−i32−1+i32−1−i32
χ1311111-1-111111111111-1-1-111-1-111-1-1-1-111111111111-11111-1-1-1-1-1-11111-1-1-1-11-1-11-1-11111-1-11111-1-1-1-1-1-111-1-111-1-111-1-1
χ1411111-1-111111111111-1-1-111-1-111-1-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-11111-1-1-1-1-1-11111-1-1-1-1−1−i321+i321+i32−1+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−i32−1−i32−1+i321+i321−i32
χ1511111-1-111111111111-1-1-111-1-111-1-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-11111-1-1-1-1-1-11111-1-1-1-1−1+i321−i321−i32−1−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+i32−1+i32−1−i321−i321+i32
χ1611111-1-111111111111-1-1-1-1-11111-1-1-1-11111111111-111111-1-1-1-1-1-1-1-1-1-111111-1-11-1-111-1-1111111-1-1-1-1-1-1-1-111-1-111-1-111
χ1711111-1-111111111111-1-1-1-1-11111-1-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-111111-1-1-1-1-1-1-1-1-1-11111−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i32-1-111−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321−i32−1−i32−1+i32
χ1811111-1-111111111111-1-1-1-1-11111-1-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-111111-1-1-1-1-1-1-1-1-1-11111−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i32-1-111−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321+i32−1+i32−1−i32
χ1911111-1-1111111111-1-1-11111-1-111-1-1-1-11111111111-11-1-1-1-1-1-111111111-1-1-1-11-1-11-1-111-1-111-1-1-1-1-1-1111111-1-111-1-1-1-111
χ2011111-1-1111111111-1-1-11111-1-111-1-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11-1-1-1-1-1-111111111-1-1-1-1−1−i321+i321+i32−1+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−i321+i321−i32−1−i32−1+i32
χ2111111-1-1111111111-1-1-11111-1-111-1-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11-1-1-1-1-1-111111111-1-1-1-1−1+i321−i321−i32−1−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+i321−i321+i32−1+i32−1−i32
χ2211111-1-1111111111-1-1-111-1-11111-1-1-1-111111111111-1-1-1-1-1-1-11111-1-1-1-111111-1-11-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1
χ2311111-1-1111111111-1-1-111-1-11111-1-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-1-1-1-1-1-11111-1-1-1-11111−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i3211-1-11+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+i32−1−i32−1+i321+i321−i32
χ2411111-1-1111111111-1-1-111-1-11111-1-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-1-1-1-1-1-11111-1-1-1-11111−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i3211-1-11−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−i32−1+i32−1−i321−i321+i32
χ252222-222-22222222200-2000000-2-22222-2-222222222000000-2-2000000000000-222-222-2-200000000-2-20000000000000000
χ262222-222-22222222200-2000000-2-22222-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3000000-2-20000000000001+i3−1−i3−1−i31−i3−1+i3−1+i31+i31−i3000000001+i31−i30000000000000000
χ272222-222-22222222200-2000000-2-22222-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3000000-2-20000000000001−i3−1+i3−1+i31+i3−1−i3−1−i31−i31+i3000000001−i31+i30000000000000000
χ282222-2-2-2-222222222002000000-2-2-2-2-2-2-2-22222222200000022000000000000-2-2-2-2-2-2-2-200000000220000000000000000
χ292222-2-2-2-222222222002000000-2-2-2-2-2-2-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3000000220000000000001+i31+i31+i31−i31−i31−i31+i31−i300000000−1−i3−1+i30000000000000000
χ302222-2-2-2-222222222002000000-2-2-2-2-2-2-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3000000220000000000001−i31−i31−i31+i31+i31+i31−i31+i300000000−1+i3−1−i30000000000000000
χ3122-2-202i−2i02222-2-2-2-2000002−2−i2i2002i2i−2i−2i002222-2-2-2-200000000000022−2−2−i2−i2i2i202i−2i02i−2i00000000000000002−2−i2i22−2−i2i20000
χ3222-2-202i−2i02222-2-2-2-2000002−2−i2i2002i2i−2i−2i00−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i300000000000022−2−2−i2−i2i2i202ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ16602ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1580000000000000000−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−ζ1670000
χ3322-2-202i−2i02222-2-2-2-2000002−2−i2i2002i2i−2i−2i00−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i300000000000022−2−2−i2−i2i2i202ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ15802ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1660000000000000000−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−ζ1570000
χ3422-2-202i−2i02222-2-2-2-200000−22i2−i2002i2i−2i−2i002222-2-2-2-2000000000000−2−222i2i2−i2−i202i−2i02i−2i0000000000000000−22i2−i2−22i2−i20000
χ3522-2-202i−2i02222-2-2-2-200000−22i2−i2002i2i−2i−2i00−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i3000000000000−2−222i2i2−i2−i202ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ16602ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1580000000000000000ζ13−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+ζ1670000
χ3622-2-202i−2i02222-2-2-2-200000−22i2−i2002i2i−2i−2i00−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i3000000000000−2−222i2i2−i2−i202ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ15802ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1660000000000000000ζ5−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+ζ1570000
χ3722-2-20−2i2i02222-2-2-2-2000002−2i2−i200−2i−2i2i2i002222-2-2-2-200000000000022−2−2i2i2−i2−i20−2i2i0−2i2i00000000000000002−2i2−i22−2i2−i20000
χ3822-2-20−2i2i02222-2-2-2-2000002−2i2−i200−2i−2i2i2i00−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i300000000000022−2−2i2i2−i2−i20−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1662ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ1660−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1582ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ1580000000000000000−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+ζ1670000
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χ9412-12-12120000−2−2i7−2+2i72+2i72−2i72+2i72−2i7−2−2i7−2+2i70000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-12120000−2+2i7−2−2i72−2i72+2i72−2i72+2i7−2+2i7−2−2i70000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 168 (ζ168 = 1); i = ζ42.