Finite Group Databasebeta

← Group #13054992

Character table — Group #13054992

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size111122223333333344444444466666666777777778812121212121212121212121212121212121214141414141414142424242428282828282828282828282828282828282856565656
order1222444477141414141414224448888282828282828282833666666441414141428282828282856565656565656561212121212121212282828286666121212121212242424242424242412121212
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
χ131111-1-1111111111111-1-1-111-1-1-1-1-1-11111111111111-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-111-1-11-11-1
χ141111-1-1111111111111-1-1-111-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-11111-1-1-1-1-1-11111-1-1-1-11+i321+i321−i321−i32−1−i32−1+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−i321+i32−1+i321−i32
χ151111-1-1111111111111-1-1-111-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-11111-1-1-1-1-1-11111-1-1-1-11−i321−i321+i321+i32−1+i32−1−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+i321−i32−1−i321+i32
χ161111-1-1111111111111-1-1-1-1-111-1-1-1-1111111111111-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-111-11-11
χ171111-1-1111111111111-1-1-1-1-111-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-111111-1-1-1-1-1-1-1-1-1-111111+i321+i321−i321−i32−1−i32−1+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+i32−1−i321−i32−1+i32
χ181111-1-1111111111111-1-1-1-1-111-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-111111-1-1-1-1-1-1-1-1-1-111111−i321−i321+i321+i32−1+i32−1−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−i32−1+i321+i32−1−i32
χ191111-1-11111111111-1-1-11111-1-1-1-1-1-1111111111111-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-111-1-1-11-11
χ201111-1-11111111111-1-1-11111-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11-1-1-1-1-1-111111111-1-1-1-11+i321+i321−i321−i32−1−i32−1+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+i32−1−i321−i32−1+i32
χ211111-1-11111111111-1-1-11111-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11-1-1-1-1-1-111111111-1-1-1-11−i321−i321+i321+i32−1+i32−1−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−i32−1+i321+i32−1−i32
χ221111-1-11111111111-1-1-111-1-111-1-1-1-11111111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1111-11-1
χ231111-1-11111111111-1-1-111-1-111-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-1-1-1-1-11111-1-1-1-111111+i321+i321−i321−i32−1−i32−1+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−i321+i32−1+i321−i32
χ241111-1-11111111111-1-1-111-1-111-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-1-1-1-1-11111-1-1-1-111111−i321−i321+i321+i32−1+i32−1−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+i321−i32−1−i321+i32
χ25222222-2-22222222200-20000002222-2-2-2-222222222000000-2-20000000000002222-2-2-2-200000000-2-20000000000000000
χ26222222-2-22222222200-20000002222-2-2-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3000000-2-2000000000000−1−i3−1−i3−1+i3−1+i31+i31−i31+i31−i3000000001+i31−i30000000000000000
χ27222222-2-22222222200-20000002222-2-2-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3000000-2-2000000000000−1+i3−1+i3−1−i3−1−i31−i31+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
χ312-22-22-20022-2-222-2-200000−i2i2−i2i222-2-2000022-2-222-2-2000000000000−i2−i2i2i2−i2−i2i2i22-22-2000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ322-22-22-20022-2-222-2-200000−i2i2−i2i222-2-20000−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i3000000000000−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−ζ1670000
χ332-22-22-20022-2-222-2-200000−i2i2−i2i222-2-20000−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i3000000000000−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−ζ1570000
χ342-22-22-20022-2-222-2-200000i2−i2i2−i222-2-2000022-2-222-2-2000000000000i2i2−i2−i2i2i2−i2−i22-22-2000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ352-22-22-20022-2-222-2-200000i2−i2i2−i222-2-20000−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i3000000000000i2i2−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+ζ1670000
χ362-22-22-20022-2-222-2-200000i2−i2i2−i222-2-20000−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i3000000000000i2i2−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+ζ1570000
χ372-22-2-220022-2-222-2-200000−i2i2i2−i2-2-222000022-2-222-2-2000000000000−i2−i2i2i2i2i2−i2−i2-22-22000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ382-22-2-220022-2-222-2-200000−i2i2i2−i2-2-2220000−1−i3−1+i31+i31−i3−1−i3−1+i31+i31−i3000000000000−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+ζ1670000
χ392-22-2-220022-2-222-2-200000−i2i2i2−i2-2-2220000−1+i3−1−i31−i31+i3−1+i3−1−i31−i31+i3000000000000−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+ζ1570000
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χ926-6-6600-66−1+i7−1−i71−i71+i71−i71+i7−1+i7−1−i76-6000000000001−i71+i7−1+i7−1−i70000000000−1+i7−1−i71−i71+i7000000000000000000000000000000000000000000000000
χ936-6-6600-66−1+i7−1−i71−i71+i71−i71+i7−1+i7−1−i7-66000000000001−i71+i7−1+i7−1−i700000000001−i71+i7−1+i7−1−i7000000000000000000000000000000000000000000000000
χ941212-12-120000−2−2i7−2+2i7−2−2i7−2+2i72+2i72−2i72+2i72−2i70000000000000000000000000000000000000000000000000000000000000000000000000000000
χ951212-12-120000−2+2i7−2−2i7−2+2i7−2−2i72−2i72+2i72−2i72+2i70000000000000000000000000000000000000000000000000000000000000000000000000000000

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