Finite Group Databasebeta

← Group #11710922

Character table — Group #11710922

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222223333666666666666666666666666666666666666661616161616161616323232323232323232323232
order122244444422222222222222222222222222224444444444444433666666121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111−1+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
χ31111111111111111111111111111111111111111111111111111−1−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
χ4111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ5111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32
χ6111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32
χ71111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-111111111-1-111-1-1-1-111-1-1
χ81111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1−1+i32−1−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−i321+i321+i32
χ91111-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1−1−i32−1+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+i321−i321−i32
χ101111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111111111-1-1-1-111-1-1-1-111
χ111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32
χ121111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32
χ131-1-111-11-11-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-11-111-1-1-1-1111-11-11-11-11-11-1
χ141-1-111-11-11-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-11-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1−i321+i32
χ151-1-111-11-11-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-11-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1+i321−i32
χ161-1-111-1-11-1111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11-1111-1-1-1-1111-1-11-111-1-11-11
χ171-1-111-1-11-1111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11-11−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i321−i321−i32−1+i321−i32−1+i32−1−i321+i321+i32−1−i321+i32−1−i32
χ181-1-111-1-11-1111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11-11−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i321−i321−i32−1+i321−i32−1+i32
χ191-1-11-111-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-1111-1-1-1-111-111-1-11-111-1-11
χ201-1-11-111-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i32−1+i32−1+i321−i321−i32−1+i321+i32−1−i32−1−i321+i321+i32−1−i32
χ211-1-11-111-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1-11−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i32−1−i32−1−i321+i321+i32−1−i321−i32−1+i32−1+i321−i321−i32−1+i32
χ221-1-11-11-111-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-111-111-1-1-1-111-11-111-1-11-111-1
χ231-1-11-11-111-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-111-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i32−1+i321−i32−1+i32−1+i321−i321+i32−1−i321+i32−1−i32−1−i321+i32
χ241-1-11-11-111-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-11-111-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i32−1−i321+i32−1−i32−1−i321+i321−i32−1+i321−i32−1+i32−1+i321−i32
χ2533333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133333300000000000000000000
χ263333333333-1-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-1-1-1-1-1-1-100000000000000000000
χ273333333333-1-1-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-1-1-1-1-1-100000000000000000000
χ283333333333-1-1-1-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-1-1-1-1-100000000000000000000
χ293333333333-1-1-1-1-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-1-1-1-100000000000000000000
χ30333333-3-3-3-33333-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-133-3-3-3-300000000000000000000
χ31333333-3-3-3-3-1-1-1-13-1-1-13-1-1-1-3111-3111-3111-31113-1-1-13-1-1-1-1-1111100000000000000000000
χ32333333-3-3-3-3-1-1-1-1-13-1-1-13-1-11-3111-3111-3111-311-13-1-1-13-1-1-1-1111100000000000000000000
χ33333333-3-3-3-3-1-1-1-1-1-13-1-1-13-111-3111-3111-3111-31-1-13-1-1-13-1-1-1111100000000000000000000
χ34333333-3-3-3-3-1-1-1-1-1-1-13-1-1-13111-3111-3111-3111-3-1-1-13-1-1-13-1-1111100000000000000000000
χ353333-3-333-3-3333311111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-3-333-3-300000000000000000000
χ363333-3-333-3-3-1-1-1-1111-3111-3-1-1-13-1-1-13111-3111-3-1-1-13-1-1-1311-1-11100000000000000000000
χ373333-3-333-3-3-1-1-1-111-3111-31-1-13-1-1-13-111-3111-31-1-13-1-1-13-111-1-11100000000000000000000
χ383333-3-333-3-3-1-1-1-11-3111-311-13-1-1-13-1-11-3111-311-13-1-1-13-1-111-1-11100000000000000000000
χ393333-3-333-3-3-1-1-1-1-3111-31113-1-1-13-1-1-1-3111-31113-1-1-13-1-1-111-1-11100000000000000000000
χ403333-3-3-3-33333331111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-33300000000000000000000
χ413333-3-3-3-333-1-1-1-1111-3111-3111-3111-3-1-1-13-1-1-13-1-1-13-1-1-131111-1-100000000000000000000
χ423333-3-3-3-333-1-1-1-111-3111-3111-3111-31-1-13-1-1-13-1-1-13-1-1-13-11111-1-100000000000000000000
χ433333-3-3-3-333-1-1-1-11-3111-3111-3111-311-13-1-1-13-1-1-13-1-1-13-1-11111-1-100000000000000000000
χ443333-3-3-3-333-1-1-1-1-3111-3111-3111-31113-1-1-13-1-1-13-1-1-13-1-1-11111-1-100000000000000000000
χ453-3-333-33-33-333-3-3-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111113-33-33-300000000000000000000
χ463-3-333-33-33-3-1-1113-1-1-1-31113-1-1-1-31113-1-1-1-31113-1-1-1-3111-11-11-1100000000000000000000
χ473-3-333-33-33-3-1-111-13-1-11-311-13-1-11-311-13-1-11-311-13-1-11-311-11-11-1100000000000000000000
χ483-3-333-33-33-3-1-111-1-13-111-31-1-13-111-31-1-13-111-31-1-13-111-31-11-11-1100000000000000000000
χ493-3-333-33-33-3-1-111-1-1-13111-3-1-1-13111-3-1-1-13111-3-1-1-13111-3-11-11-1100000000000000000000
χ503-3-333-3-33-3333-3-3-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111113-3-33-3300000000000000000000
χ513-3-333-3-33-33-1-1113-1-1-1-3111-31113-1-1-1-31113-1-1-13-1-1-1-3111-111-11-100000000000000000000
χ523-3-333-3-33-33-1-111-13-1-11-3111-311-13-1-11-311-13-1-1-13-1-11-311-111-11-100000000000000000000
χ533-3-333-3-33-33-1-111-1-13-111-3111-31-1-13-111-31-1-13-1-1-13-111-31-111-11-100000000000000000000
χ543-3-333-3-33-33-1-111-1-1-13111-3111-3-1-1-13111-3-1-1-13-1-1-13111-3-111-11-100000000000000000000
χ553-3-33-333-3-3333-3-31111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-333-3-3300000000000000000000
χ563-3-33-333-3-33-1-111111-3-1-1-13-1-1-13111-3111-3-1-1-13-1-1-13111-31-1-111-100000000000000000000
χ573-3-33-333-3-33-1-11111-31-1-13-1-1-13-111-3111-31-1-13-1-1-13-111-311-1-111-100000000000000000000
χ583-3-33-333-3-33-1-1111-311-13-1-1-13-1-11-3111-311-13-1-1-13-1-11-3111-1-111-100000000000000000000
χ593-3-33-333-3-33-1-111-31113-1-1-13-1-1-1-3111-31113-1-1-13-1-1-1-31111-1-111-100000000000000000000
χ603-3-33-33-333-333-3-31111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-33-333-300000000000000000000
χ613-3-33-33-333-3-1-111111-3-1-1-13111-3-1-1-13-1-1-13111-3-1-1-13111-31-11-1-1100000000000000000000
χ623-3-33-33-333-3-1-11111-31-1-13-111-31-1-13-1-1-13-111-31-1-13-111-311-11-1-1100000000000000000000
χ633-3-33-33-333-3-1-1111-311-13-1-11-311-13-1-1-13-1-11-311-13-1-11-3111-11-1-1100000000000000000000
χ643-3-33-33-333-3-1-111-31113-1-1-1-31113-1-1-13-1-1-1-31113-1-1-1-31111-11-1-1100000000000000000000
χ6544-4-40000004-44-400000000000000000000000000000000000000-2-22-22-222000000000000
χ6644-4-40000004-44-4000000000000000000000000000000000000001−i31+i3−1+i31−i3−1−i31+i3−1+i3−1−i3000000000000
χ6744-4-40000004-44-4000000000000000000000000000000000000001+i31−i3−1−i31+i3−1+i31−i3−1−i3−1+i3000000000000
χ684-44-40000004-4-4400000000000000000000000000000000000000-2-2-22-2222000000000000
χ694-44-40000004-4-44000000000000000000000000000000000000001−i31+i31−i3−1+i31+i3−1−i3−1+i3−1−i3000000000000
χ704-44-40000004-4-44000000000000000000000000000000000000001+i31−i31+i3−1−i31−i3−1+i3−1−i3−1+i3000000000000
χ711212-12-12000000-44-440000000000000000000000000000000000000000000000000000000000
χ7212-1212-12000000-444-40000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).