Finite Group Databasebeta

← Group #13166737

Character table — Group #13166737

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135
size111122444444444444881212121212121212121212121818242424242424363636363611112244444444444488121212121212121212121212181824242424242436363636361111224444444444448812121212121212121212121218182424242424243636363636
order1222443366666612121212121244441212121212121212444412121212288883666121233666666121212121212121212121212121212121212121212121212121262424242436661212336666661212121212121212121212121212121212121212121212121212624242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111
χ51111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1111-111-1-1-111-1-11111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1111-111-1-1-111-1-11111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1111-111-1-1-111-1-1
χ61111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111-11-1-111-1-1-1111111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111-11-1-111-1-1-1111111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111-11-1-111-1-1-111
χ71111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-111-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-111-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-111-1-1-1-1-111
χ81111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-11-1-111-111-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-11-1-111-111-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-11-1-111-111-1-1
χ922222222222222222222000000000000-2-2000000-2000022222222222222222222000000000000-2-2000000-2000022222222222222222222000000000000-2-2000000-20000
χ102222-2-222222222-2-2-2-2-2-2000000000000-2-2000000200002222-2-222222222-2-2-2-2-2-2000000000000-2-2000000200002222-2-222222222-2-2-2-2-2-2000000000000-2-200000020000
χ112-22-22i−2i22-2-222-2-22i2i−2i−2i2i−2i000000000000000000000−i2i22−22-22-22i−2i22-2-222-2-22i2i−2i−2i2i−2i000000000000000000000−i2i22−22-22-22i−2i22-2-222-2-22i2i−2i−2i2i−2i000000000000000000000−i2i22−2
χ122-22-22i−2i22-2-222-2-22i2i−2i−2i2i−2i000000000000000000000i2−i2−222-22-22i−2i22-2-222-2-22i2i−2i−2i2i−2i000000000000000000000i2−i2−222-22-22i−2i22-2-222-2-22i2i−2i−2i2i−2i000000000000000000000i2−i2−22
χ132-22-2−2i2i22-2-222-2-2−2i−2i2i2i−2i2i000000000000000000000−i2i2−222-22-2−2i2i22-2-222-2-2−2i−2i2i2i−2i2i000000000000000000000−i2i2−222-22-2−2i2i22-2-222-2-2−2i−2i2i2i−2i2i000000000000000000000−i2i2−22
χ142-22-2−2i2i22-2-222-2-2−2i−2i2i2i−2i2i000000000000000000000i2−i22−22-22-2−2i2i22-2-222-2-2−2i−2i2i2i−2i2i000000000000000000000i2−i22−22-22-2−2i2i22-2-222-2-2−2i−2i2i2i−2i2i000000000000000000000i2−i22−2
χ152-2-220022-22-2-2-22000000002i−2i00002i2i−2i−2i2-2000000000002-2-220022-22-2-2-22000000002i−2i00002i2i−2i−2i2-2000000000002-2-220022-22-2-2-22000000002i−2i00002i2i−2i−2i2-200000000000
χ162-2-220022-22-2-2-2200000000−2i2i0000−2i−2i2i2i2-2000000000002-2-220022-22-2-2-2200000000−2i2i0000−2i−2i2i2i2-2000000000002-2-220022-22-2-2-2200000000−2i2i0000−2i−2i2i2i2-200000000000
χ172-2-220022-22-2-2-220000002i−2i002i2i−2i−2i0000-22000000000002-2-220022-22-2-2-220000002i−2i002i2i−2i−2i0000-22000000000002-2-220022-22-2-2-220000002i−2i002i2i−2i−2i0000-2200000000000
χ182-2-220022-22-2-2-22000000−2i2i00−2i−2i2i2i0000-22000000000002-2-220022-22-2-2-22000000−2i2i00−2i−2i2i2i0000-22000000000002-2-220022-22-2-2-22000000−2i2i00−2i−2i2i2i0000-2200000000000
χ194444441-21-21-2-21-2-2-2-2110000000000000022-1-1-1-1000004444441-21-21-2-21-2-2-2-2110000000000000022-1-1-1-1000004444441-21-21-2-21-2-2-2-2110000000000000022-1-1-1-100000
χ204444441-21-21-2-21-2-2-2-21100000000000000-2-21111000004444441-21-21-2-21-2-2-2-21100000000000000-2-21111000004444441-21-21-2-21-2-2-2-21100000000000000-2-2111100000
χ21444444-21-21-211-21111-2-22222-1-1-1-1-1-1-1-10000000000000444444-21-21-211-21111-2-22222-1-1-1-1-1-1-1-10000000000000444444-21-21-211-21111-2-22222-1-1-1-1-1-1-1-10000000000000
χ22444444-21-21-211-21111-2-2-2-2-2-2111111110000000000000444444-21-21-211-21111-2-2-2-2-2-2111111110000000000000444444-21-21-211-21111-2-2-2-2-2-2111111110000000000000
χ234444-4-41-21-21-2-212222-1-1000000000000002-2-1-111000004444-4-41-21-21-2-212222-1-1000000000000002-2-1-111000004444-4-41-21-21-2-212222-1-1000000000000002-2-1-11100000
χ244444-4-41-21-21-2-212222-1-100000000000000-2211-1-1000004444-4-41-21-21-2-212222-1-100000000000000-2211-1-1000004444-4-41-21-21-2-212222-1-100000000000000-2211-1-100000
χ254444-4-4-21-21-211-2-1-1-1-12222-2-2-1-1-1-1111100000000000004444-4-4-21-21-211-2-1-1-1-12222-2-2-1-1-1-1111100000000000004444-4-4-21-21-211-2-1-1-1-12222-2-2-1-1-1-111110000000000000
χ264444-4-4-21-21-211-2-1-1-1-122-2-2221111-1-1-1-100000000000004444-4-4-21-21-211-2-1-1-1-122-2-2221111-1-1-1-100000000000004444-4-4-21-21-211-2-1-1-1-122-2-2221111-1-1-1-10000000000000
χ2744-4-400444-4-4-44-4000000000000000000000000000000044-4-400444-4-4-44-4000000000000000000000000000000044-4-400444-4-4-44-40000000000000000000000000000000
χ2844-4-400-21-2-12-1123i−3i3i−3i000000−i3i3−i3i33−33−3000000000000044-4-400-21-2-12-1123i−3i3i−3i000000−i3i3−i3i33−33−3000000000000044-4-400-21-2-12-1123i−3i3i−3i000000−i3i3−i3i33−33−30000000000000
χ2944-4-400-21-2-12-1123i−3i3i−3i000000i3−i3i3−i3−33−33000000000000044-4-400-21-2-12-1123i−3i3i−3i000000i3−i3i3−i3−33−33000000000000044-4-400-21-2-12-1123i−3i3i−3i000000i3−i3i3−i3−33−330000000000000
χ3044-4-400-21-2-12-112−3i3i−3i3i000000−i3i3−i3i3−33−33000000000000044-4-400-21-2-12-112−3i3i−3i3i000000−i3i3−i3i3−33−33000000000000044-4-400-21-2-12-112−3i3i−3i3i000000−i3i3−i3i3−33−330000000000000
χ3144-4-400-21-2-12-112−3i3i−3i3i000000i3−i3i3−i33−33−3000000000000044-4-400-21-2-12-112−3i3i−3i3i000000i3−i3i3−i33−33−3000000000000044-4-400-21-2-12-112−3i3i−3i3i000000i3−i3i3−i33−33−30000000000000
χ324-44-44i−4i1-2-121-22-1−2i−2i2i2ii−i0000000000000000−i3i33−3000004-44-44i−4i1-2-121-22-1−2i−2i2i2ii−i0000000000000000−i3i33−3000004-44-44i−4i1-2-121-22-1−2i−2i2i2ii−i0000000000000000−i3i33−300000
χ334-44-44i−4i1-2-121-22-1−2i−2i2i2ii−i0000000000000000i3−i3−33000004-44-44i−4i1-2-121-22-1−2i−2i2i2ii−i0000000000000000i3−i3−33000004-44-44i−4i1-2-121-22-1−2i−2i2i2ii−i0000000000000000i3−i3−3300000
χ344-44-44i−4i-212-1-21-12ii−i−i−2i2i00003−3−33−i3i3i3−i300000000000004-44-44i−4i-212-1-21-12ii−i−i−2i2i00003−3−33−i3i3i3−i300000000000004-44-44i−4i-212-1-21-12ii−i−i−2i2i00003−3−33−i3i3i3−i30000000000000
χ354-44-44i−4i-212-1-21-12ii−i−i−2i2i0000−333−3i3−i3−i3i300000000000004-44-44i−4i-212-1-21-12ii−i−i−2i2i0000−333−3i3−i3−i3i300000000000004-44-44i−4i-212-1-21-12ii−i−i−2i2i0000−333−3i3−i3−i3i30000000000000
χ364-44-4−4i4i1-2-121-22-12i2i−2i−2i−ii0000000000000000−i3i3−33000004-44-4−4i4i1-2-121-22-12i2i−2i−2i−ii0000000000000000−i3i3−33000004-44-4−4i4i1-2-121-22-12i2i−2i−2i−ii0000000000000000−i3i3−3300000
χ374-44-4−4i4i1-2-121-22-12i2i−2i−2i−ii0000000000000000i3−i33−3000004-44-4−4i4i1-2-121-22-12i2i−2i−2i−ii0000000000000000i3−i33−3000004-44-4−4i4i1-2-121-22-12i2i−2i−2i−ii0000000000000000i3−i33−300000
χ384-44-4−4i4i-212-1-21-12−i−iii2i−2i00003−3−33i3−i3−i3i300000000000004-44-4−4i4i-212-1-21-12−i−iii2i−2i00003−3−33i3−i3−i3i300000000000004-44-4−4i4i-212-1-21-12−i−iii2i−2i00003−3−33i3−i3−i3i30000000000000
χ394-44-4−4i4i-212-1-21-12−i−iii2i−2i0000−333−3−i3i3i3−i300000000000004-44-4−4i4i-212-1-21-12−i−iii2i−2i0000−333−3−i3i3i3−i300000000000004-44-4−4i4i-212-1-21-12−i−iii2i−2i0000−333−3−i3i3i3−i30000000000000
χ404-4-4400-21212-1-1-23-3-33002i−2i−2i2i−i−iiiii−i−i00000000000004-4-4400-21212-1-1-23-3-33002i−2i−2i2i−i−iiiii−i−i00000000000004-4-4400-21212-1-1-23-3-33002i−2i−2i2i−i−iiiii−i−i0000000000000
χ414-4-4400-21212-1-1-23-3-3300−2i2i2i−2iii−i−i−i−iii00000000000004-4-4400-21212-1-1-23-3-3300−2i2i2i−2iii−i−i−i−iii00000000000004-4-4400-21212-1-1-23-3-3300−2i2i2i−2iii−i−i−i−iii0000000000000
χ424-4-4400-21212-1-1-2-333-3002i−2i2i−2i−i−iii−i−iii00000000000004-4-4400-21212-1-1-2-333-3002i−2i2i−2i−i−iii−i−iii00000000000004-4-4400-21212-1-1-2-333-3002i−2i2i−2i−i−iii−i−iii0000000000000
χ434-4-4400-21212-1-1-2-333-300−2i2i−2i2iii−i−iii−i−i00000000000004-4-4400-21212-1-1-2-333-300−2i2i−2i2iii−i−iii−i−i00000000000004-4-4400-21212-1-1-2-333-300−2i2i−2i2iii−i−iii−i−i0000000000000
χ4488-8-8002-424-24-4-2000000000000000000000000000000088-8-8002-424-24-4-2000000000000000000000000000000088-8-8002-424-24-4-20000000000000000000000000000000
χ458-8-88002-4-2-4-244200000000000000000000000000000008-8-88002-4-2-4-244200000000000000000000000000000008-8-88002-4-2-4-24420000000000000000000000000000000
χ46111111111111111111111111111111111111111111111−1+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+i32−1+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+i32−1+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−i32−1−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−i32−1−i32−1−i32
χ471111111111111111111111111111111111-1-1-1-1-1-11-1-1-1-1−1+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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i321−i321−i321−i321−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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i321+i321+i321+i321+i32
χ4811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−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−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−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ4911111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i321−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−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ501111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1111-111-1-1-111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32
χ511111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111-11-1-111-1-1-111−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32
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χ1334-4-4400-21212-1-1-2-333-300−2i2i−2i2iii−i−iii−i−i0000000000000−2−2i32+2i32+2i3−2−2i3001+i3−1−i32−1−i3−1−i32−1−i31+i321+i321+i33+3i32−3−3i32−3−3i323+3i3200−2ζ222ζ22−2ζ222ζ22ζ22ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ220000000000000−2+2i32−2i32−2i3−2+2i3001−i3−1+i32−1+i3−1+i32−1+i31−i321−i321−i33−3i32−3+3i32−3+3i323−3i3200−2ζ142ζ14−2ζ142ζ14ζ14ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ140000000000000
χ13488-8-8002-424-24-4-20000000000000000000000000000000−4−4i3−4−4i34+4i34+4i300−1−i32+2i3−1−i3−2−2i31+i3−2−2i32+2i31+i30000000000000000000000000000000−4+4i3−4+4i34−4i34−4i300−1+i32−2i3−1+i3−2+2i31−i3−2+2i32−2i31−i30000000000000000000000000000000
χ1358-8-88002-4-2-4-24420000000000000000000000000000000−4−4i34+4i34+4i3−4−4i300−1−i32+2i31+i32+2i31+i3−2−2i3−2−2i3−1−i30000000000000000000000000000000−4+4i34−4i34−4i3−4+4i300−1+i32−2i31−i32−2i31−i3−2+2i3−2+2i3−1+i30000000000000000000000000000000

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