Finite Group Databasebeta

← Group #13181122

Character table — Group #13181122

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1122444444448812121212121212121218363636365454112244444444881212121212121212121836363636545411224444444488121212121212121212183636363654541122444444448812121212121212121218363636365454
order12363333666636412121212121212124412121288226666666666664121212121212121244121212882266666666666641212121212121212441212128822666666666666412121212121212124412121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111-11-1-1-1-1111111111111111111111111-11-1-1-1-1111111111111111111111111-11-1-1-1-1111111111111111111111111-11-1-1-1-1
χ311111111111111-1-1-1-1-1-1-1-1-111111-1-111111111111111-1-1-1-1-1-1-1-1-111111-1-111111111111111-1-1-1-1-1-1-1-1-111111-1-111111111111111-1-1-1-1-1-1-1-1-111111-1-1
χ411111111111111-1-1-1-1-1-1-1-1-11-11-1-11111111111111111-1-1-1-1-1-1-1-1-11-11-1-11111111111111111-1-1-1-1-1-1-1-1-11-11-1-11111111111111111-1-1-1-1-1-1-1-1-11-11-1-111
χ522222222222222000000000-20-2000022222222222222000000000-20-2000022222222222222000000000-20-2000022222222222222000000000-20-20000
χ622-1-122-1-12-1-12-1-10−i3i300−i3−i3i3i3-201000022-1-122-1-12-1-12-1-10−i3i300−i3−i3i3i3-201000022-1-122-1-12-1-12-1-10−i3i300−i3−i3i3i3-201000022-1-122-1-12-1-12-1-10−i3i300−i3−i3i3i3-2010000
χ722-1-122-1-12-1-12-1-10i3−i300i3i3−i3−i3-201000022-1-122-1-12-1-12-1-10i3−i300i3i3−i3−i3-201000022-1-122-1-12-1-12-1-10i3−i300i3i3−i3−i3-201000022-1-122-1-12-1-12-1-10i3−i300i3i3−i3−i3-2010000
χ822-1-122-1-12-1-12-1-12-1-122-1-1-1-120-1000022-1-122-1-12-1-12-1-12-1-122-1-1-1-120-1000022-1-122-1-12-1-12-1-12-1-122-1-1-1-120-1000022-1-122-1-12-1-12-1-12-1-122-1-1-1-120-10000
χ922-1-122-1-12-1-12-1-1-211-2-2111120-1000022-1-122-1-12-1-12-1-1-211-2-2111120-1000022-1-122-1-12-1-12-1-1-211-2-2111120-1000022-1-122-1-12-1-12-1-1-211-2-2111120-10000
χ102-22-22222-2-2-2-22-2000000000000002−22-22-22222-2-2-2-22-2000000000000002−22-22-22222-2-2-2-22-2000000000000002−22-22-22222-2-2-2-22-2000000000000002−2
χ112-22-22222-2-2-2-22-200000000000000−222-22-22222-2-2-2-22-200000000000000−222-22-22222-2-2-2-22-200000000000000−222-22-22222-2-2-2-22-200000000000000−22
χ1244441-211111-2-2-2222-1-1-1-1-1-1000000044441-211111-2-2-2222-1-1-1-1-1-1000000044441-211111-2-2-2222-1-1-1-1-1-1000000044441-211111-2-2-2222-1-1-1-1-1-10000000
χ1344441-211111-2-2-2-2-2-2111111000000044441-211111-2-2-2-2-2-2111111000000044441-211111-2-2-2-2-2-2111111000000044441-211111-2-2-2-2-2-21111110000000
χ144444-21-2-2-2-2-2111000000000020-1-1004444-21-2-2-2-2-2111000000000020-1-1004444-21-2-2-2-2-2111000000000020-1-1004444-21-2-2-2-2-2111000000000020-1-100
χ154444-21-2-2-2-2-21110000000000-2011004444-21-2-2-2-2-21110000000000-2011004444-21-2-2-2-2-21110000000000-2011004444-21-2-2-2-2-21110000000000-201100
χ1644-2-21-2−1−3i32−1+3i321−1−3i32−1+3i32-2112−1−i3−1+i3-1-11+i321+i321−i321−i32000000044-2-21-2−1−3i32−1+3i321−1−3i32−1+3i32-2112−1−i3−1+i3-1-11+i321+i321−i321−i32000000044-2-21-2−1−3i32−1+3i321−1−3i32−1+3i32-2112−1−i3−1+i3-1-11+i321+i321−i321−i32000000044-2-21-2−1−3i32−1+3i321−1−3i32−1+3i32-2112−1−i3−1+i3-1-11+i321+i321−i321−i320000000
χ1744-2-21-2−1−3i32−1+3i321−1−3i32−1+3i32-211-21+i31−i311−1−i32−1−i32−1+i32−1+i32000000044-2-21-2−1−3i32−1+3i321−1−3i32−1+3i32-211-21+i31−i311−1−i32−1−i32−1+i32−1+i32000000044-2-21-2−1−3i32−1+3i321−1−3i32−1+3i32-211-21+i31−i311−1−i32−1−i32−1+i32−1+i32000000044-2-21-2−1−3i32−1+3i321−1−3i32−1+3i32-211-21+i31−i311−1−i32−1−i32−1+i32−1+i320000000
χ1844-2-21-2−1+3i32−1−3i321−1+3i32−1−3i32-2112−1+i3−1−i3-1-11−i321−i321+i321+i32000000044-2-21-2−1+3i32−1−3i321−1+3i32−1−3i32-2112−1+i3−1−i3-1-11−i321−i321+i321+i32000000044-2-21-2−1+3i32−1−3i321−1+3i32−1−3i32-2112−1+i3−1−i3-1-11−i321−i321+i321+i32000000044-2-21-2−1+3i32−1−3i321−1+3i32−1−3i32-2112−1+i3−1−i3-1-11−i321−i321+i321+i320000000
χ1944-2-21-2−1+3i32−1−3i321−1+3i32−1−3i32-211-21−i31+i311−1+i32−1+i32−1−i32−1−i32000000044-2-21-2−1+3i32−1−3i321−1+3i32−1−3i32-211-21−i31+i311−1+i32−1+i32−1−i32−1−i32000000044-2-21-2−1+3i32−1−3i321−1+3i32−1−3i32-211-21−i31+i311−1+i32−1+i32−1−i32−1−i32000000044-2-21-2−1+3i32−1−3i321−1+3i32−1−3i32-211-21−i31+i311−1+i32−1+i32−1−i32−1−i320000000
χ204-44-41-211-1-1-12-220003−33−33−300000004-44-41-211-1-1-12-220003−33−33−300000004-44-41-211-1-1-12-220003−33−33−300000004-44-41-211-1-1-12-220003−33−33−30000000
χ214-44-41-211-1-1-12-22000−33−33−3300000004-44-41-211-1-1-12-22000−33−33−3300000004-44-41-211-1-1-12-22000−33−33−3300000004-44-41-211-1-1-12-22000−33−33−330000000
χ224-44-4-21-2-2222-11-10000000000003−3004-44-4-21-2-2222-11-10000000000003−3004-44-4-21-2-2222-11-10000000000003−3004-44-4-21-2-2222-11-10000000000003−300
χ234-44-4-21-2-2222-11-1000000000000−33004-44-4-21-2-2222-11-1000000000000−33004-44-4-21-2-2222-11-1000000000000−33004-44-4-21-2-2222-11-1000000000000−3300
χ244-4-221-2−1−3i32−1+3i32-11+3i321−3i3221-10003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ2200000004-4-221-2−1−3i32−1+3i32-11+3i321−3i3221-10003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ2200000004-4-221-2−1−3i32−1+3i32-11+3i321−3i3221-10003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ2200000004-4-221-2−1−3i32−1+3i32-11+3i321−3i3221-10003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ220000000
χ254-4-221-2−1−3i32−1+3i32-11+3i321−3i3221-1000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ2200000004-4-221-2−1−3i32−1+3i32-11+3i321−3i3221-1000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ2200000004-4-221-2−1−3i32−1+3i32-11+3i321−3i3221-1000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ2200000004-4-221-2−1−3i32−1+3i32-11+3i321−3i3221-1000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ220000000
χ264-4-221-2−1+3i32−1−3i32-11−3i321+3i3221-10003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ2200000004-4-221-2−1+3i32−1−3i32-11−3i321+3i3221-10003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ2200000004-4-221-2−1+3i32−1−3i32-11−3i321+3i3221-10003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ2200000004-4-221-2−1+3i32−1−3i32-11−3i321+3i3221-10003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ220000000
χ274-4-221-2−1+3i32−1−3i32-11−3i321+3i3221-1000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ2200000004-4-221-2−1+3i32−1−3i32-11−3i321+3i3221-1000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ2200000004-4-221-2−1+3i32−1−3i32-11−3i321+3i3221-1000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ2200000004-4-221-2−1+3i32−1−3i32-11−3i321+3i3221-1000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ220000000
χ284-4-2244-2-2-422-4-2200000000000000004-4-2244-2-2-422-4-2200000000000000004-4-2244-2-2-422-4-2200000000000000004-4-2244-2-2-422-4-220000000000000000
χ2988-4-4-4222-4222-1-1000000000000000088-4-4-4222-4222-1-1000000000000000088-4-4-4222-4222-1-1000000000000000088-4-4-4222-4222-1-10000000000000000
χ308-8-44-42224-2-2-2-1100000000000000008-8-44-42224-2-2-2-1100000000000000008-8-44-42224-2-2-2-1100000000000000008-8-44-42224-2-2-2-110000000000000000
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ32111111111111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111111111111111111111111111-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111
χ3311111111111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-111
χ3411111111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-111111111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-111-1-1
χ3522222222222222000000000-20-20000-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000202000022222222222222000000000-20-20000-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000002020000
χ3622-1-122-1-12-1-12-1-10−i3i300−i3−i3i3i3-2010000-2-211-2-211-211-2110i3−i300i3i3−i3−i320-1000022-1-122-1-12-1-12-1-10−i3i300−i3−i3i3i3-2010000-2-211-2-211-211-2110i3−i300i3i3−i3−i320-10000
χ3722-1-122-1-12-1-12-1-10i3−i300i3i3−i3−i3-2010000-2-211-2-211-211-2110−i3i300−i3−i3i3i320-1000022-1-122-1-12-1-12-1-10i3−i300i3i3−i3−i3-2010000-2-211-2-211-211-2110−i3i300−i3−i3i3i320-10000
χ3822-1-122-1-12-1-12-1-12-1-122-1-1-1-120-10000-2-211-2-211-211-211-211-2-21111-201000022-1-122-1-12-1-12-1-12-1-122-1-1-1-120-10000-2-211-2-211-211-211-211-2-21111-2010000
χ3922-1-122-1-12-1-12-1-1-211-2-2111120-10000-2-211-2-211-211-2112-1-122-1-1-1-1-201000022-1-122-1-12-1-12-1-1-211-2-2111120-10000-2-211-2-211-211-2112-1-122-1-1-1-1-2010000
χ402-22-22222-2-2-2-22-2000000000000002−2-22-22-2-2-2-22222-2200000000000000−222-22-22222-2-2-2-22-2000000000000002−2-22-22-2-2-2-22222-2200000000000000−22
χ412-22-22222-2-2-2-22-200000000000000−22-22-22-2-2-2-22222-22000000000000002−22-22-22222-2-2-2-22-200000000000000−22-22-22-2-2-2-22222-22000000000000002−2
χ4244441-211111-2-2-2222-1-1-1-1-1-10000000-4-4-4-4-12-1-1-1-1-1222-2-2-2111111000000044441-211111-2-2-2222-1-1-1-1-1-10000000-4-4-4-4-12-1-1-1-1-1222-2-2-21111110000000
χ4344441-211111-2-2-2-2-2-21111110000000-4-4-4-4-12-1-1-1-1-1222222-1-1-1-1-1-1000000044441-211111-2-2-2-2-2-21111110000000-4-4-4-4-12-1-1-1-1-1222222-1-1-1-1-1-10000000
χ444444-21-2-2-2-2-2111000000000020-1-100-4-4-4-42-122222-1-1-10000000000-2011004444-21-2-2-2-2-2111000000000020-1-100-4-4-4-42-122222-1-1-10000000000-201100
χ454444-21-2-2-2-2-21110000000000-201100-4-4-4-42-122222-1-1-1000000000020-1-1004444-21-2-2-2-2-21110000000000-201100-4-4-4-42-122222-1-1-1000000000020-1-100
χ4644-2-21-2−1−3i32−1+3i321−1−3i32−1+3i32-2112−1−i3−1+i3-1-11+i321+i321−i321−i320000000-4-422-121+3i321−3i32-11+3i321−3i322-1-1-21+i31−i311−1−i32−1−i32−1+i32−1+i32000000044-2-21-2−1−3i32−1+3i321−1−3i32−1+3i32-2112−1−i3−1+i3-1-11+i321+i321−i321−i320000000-4-422-121+3i321−3i32-11+3i321−3i322-1-1-21+i31−i311−1−i32−1−i32−1+i32−1+i320000000
χ4744-2-21-2−1−3i32−1+3i321−1−3i32−1+3i32-211-21+i31−i311−1−i32−1−i32−1+i32−1+i320000000-4-422-121+3i321−3i32-11+3i321−3i322-1-12−1−i3−1+i3-1-11+i321+i321−i321−i32000000044-2-21-2−1−3i32−1+3i321−1−3i32−1+3i32-211-21+i31−i311−1−i32−1−i32−1+i32−1+i320000000-4-422-121+3i321−3i32-11+3i321−3i322-1-12−1−i3−1+i3-1-11+i321+i321−i321−i320000000
χ4844-2-21-2−1+3i32−1−3i321−1+3i32−1−3i32-2112−1+i3−1−i3-1-11−i321−i321+i321+i320000000-4-422-121−3i321+3i32-11−3i321+3i322-1-1-21−i31+i311−1+i32−1+i32−1−i32−1−i32000000044-2-21-2−1+3i32−1−3i321−1+3i32−1−3i32-2112−1+i3−1−i3-1-11−i321−i321+i321+i320000000-4-422-121−3i321+3i32-11−3i321+3i322-1-1-21−i31+i311−1+i32−1+i32−1−i32−1−i320000000
χ4944-2-21-2−1+3i32−1−3i321−1+3i32−1−3i32-211-21−i31+i311−1+i32−1+i32−1−i32−1−i320000000-4-422-121−3i321+3i32-11−3i321+3i322-1-12−1+i3−1−i3-1-11−i321−i321+i321+i32000000044-2-21-2−1+3i32−1−3i321−1+3i32−1−3i32-211-21−i31+i311−1+i32−1+i32−1−i32−1−i320000000-4-422-121−3i321+3i32-11−3i321+3i322-1-12−1+i3−1−i3-1-11−i321−i321+i321+i320000000
χ504-44-41-211-1-1-12-220003−33−33−30000000-44-44-12-1-1111-22-2000−33−33−3300000004-44-41-211-1-1-12-220003−33−33−30000000-44-44-12-1-1111-22-2000−33−33−330000000
χ514-44-41-211-1-1-12-22000−33−33−330000000-44-44-12-1-1111-22-20003−33−33−300000004-44-41-211-1-1-12-22000−33−33−330000000-44-44-12-1-1111-22-20003−33−33−30000000
χ524-44-4-21-2-2222-11-10000000000003−300-44-442-122-2-2-21-11000000000000−33004-44-4-21-2-2222-11-10000000000003−300-44-442-122-2-2-21-11000000000000−3300
χ534-44-4-21-2-2222-11-1000000000000−3300-44-442-122-2-2-21-110000000000003−3004-44-4-21-2-2222-11-1000000000000−3300-44-442-122-2-2-21-110000000000003−300
χ544-4-221-2−1−3i32−1+3i32-11+3i321−3i3221-10003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ220000000-442-2-121+3i321−3i321−1−3i32−1+3i32-2-11000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ2200000004-4-221-2−1−3i32−1+3i32-11+3i321−3i3221-10003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ220000000-442-2-121+3i321−3i321−1−3i32−1+3i32-2-11000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ220000000
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χ1144-4-221-2−1−3i32−1+3i32-11+3i321−3i3221-10003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ220000000-442-2-121+3i321−3i321−1−3i32−1+3i32-2-11000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ220000000-442-2-121+3i321−3i321−1−3i32−1+3i32-2-11000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ2200000004-4-221-2−1−3i32−1+3i32-11+3i321−3i3221-10003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ220000000
χ1154-4-221-2−1−3i32−1+3i32-11+3i321−3i3221-1000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ220000000-442-2-121+3i321−3i321−1−3i32−1+3i32-2-110003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ220000000-442-2-121+3i321−3i321−1−3i32−1+3i32-2-110003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ2200000004-4-221-2−1−3i32−1+3i32-11+3i321−3i3221-1000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ220000000
χ1164-4-221-2−1+3i32−1−3i32-11−3i321+3i3221-10003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ220000000-442-2-121−3i321+3i321−1+3i32−1−3i32-2-11000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ220000000-442-2-121−3i321+3i321−1+3i32−1−3i32-2-11000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ2200000004-4-221-2−1+3i32−1−3i32-11−3i321+3i3221-10003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ220000000
χ1174-4-221-2−1+3i32−1−3i32-11−3i321+3i3221-1000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ220000000-442-2-121−3i321+3i321−1+3i32−1−3i32-2-110003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ220000000-442-2-121−3i321+3i321−1+3i32−1−3i32-2-110003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ2200000004-4-221-2−1+3i32−1−3i32-11−3i321+3i3221-1000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ220000000
χ1184-4-2244-2-2-422-4-220000000000000000-442-2-4-4224-2-242-20000000000000000-442-2-4-4224-2-242-200000000000000004-4-2244-2-2-422-4-220000000000000000
χ11988-4-4-4222-4222-1-10000000000000000-8-8444-2-2-24-2-2-2110000000000000000-8-8444-2-2-24-2-2-211000000000000000088-4-4-4222-4222-1-10000000000000000
χ1208-8-44-42224-2-2-2-110000000000000000-884-44-2-2-2-42221-10000000000000000-884-44-2-2-2-42221-100000000000000008-8-44-42224-2-2-2-110000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.