Finite Group Databasebeta

← Group #11722452

Character table — Group #11722452

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size11199999999912121119999999991212222181818181818181818242422218181818181818181824242221818181818181818182424
order133244661212121233266244661212121266412124441212121212121212412124441212121212121212412124441212121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ21111-1-111-1-1-1-1111111-1-111-1-1-1-1111111-1-111-1-1-1-1111111-1-111-1-1-1-1111111-1-111-1-1-1-111
χ3111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11
χ4111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11
χ53−3−3i32−3+3i321i−i−1−i32−1+i32ζ7ζ11−ζ7−ζ11003−3−3i32−3+3i321i−i−1−i32−1+i32ζ7ζ11−ζ7−ζ11003−3−3i32−3+3i321i−i−1−i32−1+i32ζ7ζ11−ζ7−ζ11003−3−3i32−3+3i321i−i−1−i32−1+i32ζ7ζ11−ζ7−ζ11003−3−3i32−3+3i321i−i−1−i32−1+i32ζ7ζ11−ζ7−ζ1100
χ63−3−3i32−3+3i321−ii−1−i32−1+i32−ζ7−ζ11ζ7ζ11003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ7−ζ11ζ7ζ11003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ7−ζ11ζ7ζ11003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ7−ζ11ζ7ζ11003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ7−ζ11ζ7ζ1100
χ73−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i3200
χ83−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i3200
χ93−3+3i32−3−3i321i−i−1+i32−1−i32ζ11ζ7−ζ11−ζ7003−3+3i32−3−3i321i−i−1+i32−1−i32ζ11ζ7−ζ11−ζ7003−3+3i32−3−3i321i−i−1+i32−1−i32ζ11ζ7−ζ11−ζ7003−3+3i32−3−3i321i−i−1+i32−1−i32ζ11ζ7−ζ11−ζ7003−3+3i32−3−3i321i−i−1+i32−1−i32ζ11ζ7−ζ11−ζ700
χ103−3+3i32−3−3i321−ii−1+i32−1−i32−ζ11−ζ7ζ11ζ7003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ11−ζ7ζ11ζ7003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ11−ζ7ζ11ζ7003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ11−ζ7ζ11ζ7003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ11−ζ7ζ11ζ700
χ113−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i3200
χ123−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i3200
χ134440000000001-24440000000001-24440000000001-24440000000001-24440000000001-2
χ14444000000000-21444000000000-21444000000000-21444000000000-21444000000000-21
χ15111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ161111-1-111-1-1-1-1111111-1-111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-1
χ17111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11-1-1-11−ii11−i−iii-1-1-1-1-11−ii11−i−iii-1-1
χ18111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11-1-1-11i−i11ii−i−i-1-1-1-1-11i−i11ii−i−i-1-1
χ193−3−3i32−3+3i321i−i−1−i32−1+i32ζ7ζ11−ζ7−ζ11003−3−3i32−3+3i321i−i−1−i32−1+i32ζ7ζ11−ζ7−ζ11003−3−3i32−3+3i321i−i−1−i32−1+i32ζ7ζ11−ζ7−ζ1100-33+3i323−3i32-1−ii1+i321−i32−ζ7−ζ11ζ7ζ1100-33+3i323−3i32-1−ii1+i321−i32−ζ7−ζ11ζ7ζ1100
χ203−3−3i32−3+3i321−ii−1−i32−1+i32−ζ7−ζ11ζ7ζ11003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ7−ζ11ζ7ζ11003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ7−ζ11ζ7ζ1100-33+3i323−3i32-1i−i1+i321−i32ζ7ζ11−ζ7−ζ1100-33+3i323−3i32-1i−i1+i321−i32ζ7ζ11−ζ7−ζ1100
χ213−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i3200-33+3i323−3i321-1-1−1−i32−1+i321−i321+i321−i321+i3200-33+3i323−3i321-1-1−1−i32−1+i321−i321+i321−i321+i3200
χ223−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i3200-33+3i323−3i32111−1−i32−1+i32−1+i32−1−i32−1+i32−1−i3200-33+3i323−3i32111−1−i32−1+i32−1+i32−1−i32−1+i32−1−i3200
χ233−3+3i32−3−3i321i−i−1+i32−1−i32ζ11ζ7−ζ11−ζ7003−3+3i32−3−3i321i−i−1+i32−1−i32ζ11ζ7−ζ11−ζ7003−3+3i32−3−3i321i−i−1+i32−1−i32ζ11ζ7−ζ11−ζ700-33−3i323+3i32-1−ii1−i321+i32−ζ11−ζ7ζ11ζ700-33−3i323+3i32-1−ii1−i321+i32−ζ11−ζ7ζ11ζ700
χ243−3+3i32−3−3i321−ii−1+i32−1−i32−ζ11−ζ7ζ11ζ7003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ11−ζ7ζ11ζ7003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ11−ζ7ζ11ζ700-33−3i323+3i32-1i−i1−i321+i32ζ11ζ7−ζ11−ζ700-33−3i323+3i32-1i−i1−i321+i32ζ11ζ7−ζ11−ζ700
χ253−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i3200-33−3i323+3i321-1-1−1+i32−1−i321+i321−i321+i321−i3200-33−3i323+3i321-1-1−1+i32−1−i321+i321−i321+i321−i3200
χ263−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i3200-33−3i323+3i32111−1+i32−1−i32−1−i32−1+i32−1−i32−1+i3200-33−3i323+3i32111−1+i32−1−i32−1−i32−1+i32−1−i32−1+i3200
χ274440000000001-24440000000001-24440000000001-2-4-4-4000000000-12-4-4-4000000000-12
χ28444000000000-21444000000000-21444000000000-21-4-4-40000000002-1-4-4-40000000002-1
χ291111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ301111-1-111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-111-1-11111-1-11111-1-111-1-1-1-111-1-1-1-111-1-11111-1-1
χ31111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11-1-1-11−ii11−i−iii-1-1111-1i−i-1-1ii−i−i11-1-1-11−ii11−i−iii-1-1
χ32111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11-1-1-11i−i11ii−i−i-1-1111-1−ii-1-1−i−iii11-1-1-11i−i11ii−i−i-1-1
χ333−3−3i32−3+3i321i−i−1−i32−1+i32ζ7ζ11−ζ7−ζ11003−3−3i32−3+3i321i−i−1−i32−1+i32ζ7ζ11−ζ7−ζ1100-33+3i323−3i32-1−ii1+i321−i32−ζ7−ζ11ζ7ζ11003−3−3i32−3+3i321i−i−1−i32−1+i32ζ7ζ11−ζ7−ζ1100-33+3i323−3i32-1−ii1+i321−i32−ζ7−ζ11ζ7ζ1100
χ343−3−3i32−3+3i321−ii−1−i32−1+i32−ζ7−ζ11ζ7ζ11003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ7−ζ11ζ7ζ1100-33+3i323−3i32-1i−i1+i321−i32ζ7ζ11−ζ7−ζ11003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ7−ζ11ζ7ζ1100-33+3i323−3i32-1i−i1+i321−i32ζ7ζ11−ζ7−ζ1100
χ353−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i3200-33+3i323−3i321-1-1−1−i32−1+i321−i321+i321−i321+i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i3200-33+3i323−3i321-1-1−1−i32−1+i321−i321+i321−i321+i3200
χ363−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i3200-33+3i323−3i32111−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i3200-33+3i323−3i32111−1−i32−1+i32−1+i32−1−i32−1+i32−1−i3200
χ373−3+3i32−3−3i321i−i−1+i32−1−i32ζ11ζ7−ζ11−ζ7003−3+3i32−3−3i321i−i−1+i32−1−i32ζ11ζ7−ζ11−ζ700-33−3i323+3i32-1−ii1−i321+i32−ζ11−ζ7ζ11ζ7003−3+3i32−3−3i321i−i−1+i32−1−i32ζ11ζ7−ζ11−ζ700-33−3i323+3i32-1−ii1−i321+i32−ζ11−ζ7ζ11ζ700
χ383−3+3i32−3−3i321−ii−1+i32−1−i32−ζ11−ζ7ζ11ζ7003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ11−ζ7ζ11ζ700-33−3i323+3i32-1i−i1−i321+i32ζ11ζ7−ζ11−ζ7003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ11−ζ7ζ11ζ700-33−3i323+3i32-1i−i1−i321+i32ζ11ζ7−ζ11−ζ700
χ393−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i3200-33−3i323+3i321-1-1−1+i32−1−i321+i321−i321+i321−i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i3200-33−3i323+3i321-1-1−1+i32−1−i321+i321−i321+i321−i3200
χ403−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i3200-33−3i323+3i32111−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i3200-33−3i323+3i32111−1+i32−1−i32−1−i32−1+i32−1−i32−1+i3200
χ414440000000001-24440000000001-2-4-4-4000000000-124440000000001-2-4-4-4000000000-12
χ42444000000000-21444000000000-21-4-4-40000000002-1444000000000-21-4-4-40000000002-1
χ431111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111
χ441111-1-111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-111-1-11111-1-11111-1-111-1-1-1-111
χ45111-1i−i-1-1ii−i−i11111-1i−i-1-1ii−i−i11-1-1-11−ii11−i−iii-1-1-1-1-11−ii11−i−iii-1-1111-1i−i-1-1ii−i−i11
χ46111-1−ii-1-1−i−iii11111-1−ii-1-1−i−iii11-1-1-11i−i11ii−i−i-1-1-1-1-11i−i11ii−i−i-1-1111-1−ii-1-1−i−iii11
χ473−3−3i32−3+3i321i−i−1−i32−1+i32ζ7ζ11−ζ7−ζ11003−3−3i32−3+3i321i−i−1−i32−1+i32ζ7ζ11−ζ7−ζ1100-33+3i323−3i32-1−ii1+i321−i32−ζ7−ζ11ζ7ζ1100-33+3i323−3i32-1−ii1+i321−i32−ζ7−ζ11ζ7ζ11003−3−3i32−3+3i321i−i−1−i32−1+i32ζ7ζ11−ζ7−ζ1100
χ483−3−3i32−3+3i321−ii−1−i32−1+i32−ζ7−ζ11ζ7ζ11003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ7−ζ11ζ7ζ1100-33+3i323−3i32-1i−i1+i321−i32ζ7ζ11−ζ7−ζ1100-33+3i323−3i32-1i−i1+i321−i32ζ7ζ11−ζ7−ζ11003−3−3i32−3+3i321−ii−1−i32−1+i32−ζ7−ζ11ζ7ζ1100
χ493−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i3200-33+3i323−3i321-1-1−1−i32−1+i321−i321+i321−i321+i3200-33+3i323−3i321-1-1−1−i32−1+i321−i321+i321−i321+i32003−3−3i32−3+3i32-1111+i321−i32−1+i32−1−i32−1+i32−1−i3200
χ503−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i3200-33+3i323−3i32111−1−i32−1+i32−1+i32−1−i32−1+i32−1−i3200-33+3i323−3i32111−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32003−3−3i32−3+3i32-1-1-11+i321−i321−i321+i321−i321+i3200
χ513−3+3i32−3−3i321i−i−1+i32−1−i32ζ11ζ7−ζ11−ζ7003−3+3i32−3−3i321i−i−1+i32−1−i32ζ11ζ7−ζ11−ζ700-33−3i323+3i32-1−ii1−i321+i32−ζ11−ζ7ζ11ζ700-33−3i323+3i32-1−ii1−i321+i32−ζ11−ζ7ζ11ζ7003−3+3i32−3−3i321i−i−1+i32−1−i32ζ11ζ7−ζ11−ζ700
χ523−3+3i32−3−3i321−ii−1+i32−1−i32−ζ11−ζ7ζ11ζ7003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ11−ζ7ζ11ζ700-33−3i323+3i32-1i−i1−i321+i32ζ11ζ7−ζ11−ζ700-33−3i323+3i32-1i−i1−i321+i32ζ11ζ7−ζ11−ζ7003−3+3i32−3−3i321−ii−1+i32−1−i32−ζ11−ζ7ζ11ζ700
χ533−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i3200-33−3i323+3i321-1-1−1+i32−1−i321+i321−i321+i321−i3200-33−3i323+3i321-1-1−1+i32−1−i321+i321−i321+i321−i32003−3+3i32−3−3i32-1111−i321+i32−1−i32−1+i32−1−i32−1+i3200
χ543−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i3200-33−3i323+3i32111−1+i32−1−i32−1−i32−1+i32−1−i32−1+i3200-33−3i323+3i32111−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32003−3+3i32−3−3i32-1-1-11−i321+i321+i321−i321+i321−i3200
χ554440000000001-24440000000001-2-4-4-4000000000-12-4-4-4000000000-124440000000001-2
χ56444000000000-21444000000000-21-4-4-40000000002-1-4-4-40000000002-1444000000000-21
χ5722222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000
χ582222-2-222-2-2-2-222-2-2-2-222-2-22222-2-2000000000000000000000000000000000000000000
χ59222-22i−2i-2-22i2i−2i−2i22-2-2-22−2i2i22−2i−2i2i2i-2-2000000000000000000000000000000000000000000
χ60222-2−2i2i-2-2−2i−2i2i2i22-2-2-222i−2i222i2i−2i−2i-2-2000000000000000000000000000000000000000000
χ616−3−3i3−3+3i322i−2i−1−i3−1+i32ζ72ζ11−2ζ7−2ζ1100-63+3i33−3i3-2−2i2i1+i31−i3−2ζ7−2ζ112ζ72ζ1100000000000000000000000000000000000000000000
χ626−3−3i3−3+3i32−2i2i−1−i3−1+i3−2ζ7−2ζ112ζ72ζ1100-63+3i33−3i3-22i−2i1+i31−i32ζ72ζ11−2ζ7−2ζ1100000000000000000000000000000000000000000000
χ636−3−3i3−3+3i3-2221+i31−i3−1+i3−1−i3−1+i3−1−i300-63+3i33−3i32-2-2−1−i3−1+i31−i31+i31−i31+i300000000000000000000000000000000000000000000
χ646−3−3i3−3+3i3-2-2-21+i31−i31−i31+i31−i31+i300-63+3i33−3i3222−1−i3−1+i3−1+i3−1−i3−1+i3−1−i300000000000000000000000000000000000000000000
χ656−3+3i3−3−3i322i−2i−1+i3−1−i32ζ112ζ7−2ζ11−2ζ700-63−3i33+3i3-2−2i2i1−i31+i3−2ζ11−2ζ72ζ112ζ700000000000000000000000000000000000000000000
χ666−3+3i3−3−3i32−2i2i−1+i3−1−i3−2ζ11−2ζ72ζ112ζ700-63−3i33+3i3-22i−2i1−i31+i32ζ112ζ7−2ζ11−2ζ700000000000000000000000000000000000000000000
χ676−3+3i3−3−3i3-2221−i31+i3−1−i3−1+i3−1−i3−1+i300-63−3i33+3i32-2-2−1+i3−1−i31+i31−i31+i31−i300000000000000000000000000000000000000000000
χ686−3+3i3−3−3i3-2-2-21−i31+i31+i31−i31+i31−i300-63−3i33+3i3222−1+i3−1−i3−1−i3−1+i3−1−i3−1+i300000000000000000000000000000000000000000000
χ698880000000002-4-8-8-8000000000-24000000000000000000000000000000000000000000
χ70888000000000-42-8-8-80000000004-2000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.