Finite Group Databasebeta

← Group #13166804

Character table — Group #13166804

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135
size111122444444444444881212121212121212121212121818242424242424363636363611112244444444444488121212121212121212121212181824242424242436363636361111224444444444448812121212121212121212121218182424242424243636363636
order1222443366666612121212121244441212121212121212442466121248888366612123366666612121212121212121212121212121212121212126126612121224242424366612123366666612121212121212121212121212121212121212126126612121224242424
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−2i222-2-22-2-22i2i−2i−2i2i−2i0000000000000000000002−2−i2i22-22-22i−2i222-2-22-2-22i2i−2i−2i2i−2i0000000000000000000002−2−i2i22-22-22i−2i222-2-22-2-22i2i−2i−2i2i−2i0000000000000000000002−2−i2i2
χ122-22-22i−2i222-2-22-2-22i2i−2i−2i2i−2i000000000000000000000−22i2−i22-22-22i−2i222-2-22-2-22i2i−2i−2i2i−2i000000000000000000000−22i2−i22-22-22i−2i222-2-22-2-22i2i−2i−2i2i−2i000000000000000000000−22i2−i2
χ132-22-2−2i2i222-2-22-2-2−2i−2i2i2i−2i2i0000000000000000000002−2i2−i22-22-2−2i2i222-2-22-2-2−2i−2i2i2i−2i2i0000000000000000000002−2i2−i22-22-2−2i2i222-2-22-2-2−2i−2i2i2i−2i2i0000000000000000000002−2i2−i2
χ142-22-2−2i2i222-2-22-2-2−2i−2i2i2i−2i2i000000000000000000000−22−i2i22-22-2−2i2i222-2-22-2-2−2i−2i2i2i−2i2i000000000000000000000−22−i2i22-22-2−2i2i222-2-22-2-2−2i−2i2i2i−2i2i000000000000000000000−22−i2i2
χ152-2-220022-2-2-2-222000000002-2000022-2-2-22000000000002-2-220022-2-2-2-222000000002-2000022-2-2-22000000000002-2-220022-2-2-2-222000000002-2000022-2-2-2200000000000
χ162-2-220022-2-2-2-22200000000-220000-2-222-22000000000002-2-220022-2-2-2-22200000000-220000-2-222-22000000000002-2-220022-2-2-2-22200000000-220000-2-222-2200000000000
χ172-2-220022-2-2-2-2220000002i−2i002i2i−2i−2i00002-2000000000002-2-220022-2-2-2-2220000002i−2i002i2i−2i−2i00002-2000000000002-2-220022-2-2-2-2220000002i−2i002i2i−2i−2i00002-200000000000
χ182-2-220022-2-2-2-222000000−2i2i00−2i−2i2i2i00002-2000000000002-2-220022-2-2-2-222000000−2i2i00−2i−2i2i2i00002-2000000000002-2-220022-2-2-2-222000000−2i2i00−2i−2i2i2i00002-200000000000
χ194444441-2-21-211-21111-2-22222-1-1-1-1-1-1-1-100000000000004444441-2-21-211-21111-2-22222-1-1-1-1-1-1-1-100000000000004444441-2-21-211-21111-2-22222-1-1-1-1-1-1-1-10000000000000
χ204444441-2-21-211-21111-2-2-2-2-2-21111111100000000000004444441-2-21-211-21111-2-2-2-2-2-21111111100000000000004444441-2-21-211-21111-2-2-2-2-2-2111111110000000000000
χ21444444-211-21-2-21-2-2-2-2110000000000000022-1-1-1-100000444444-211-21-2-21-2-2-2-2110000000000000022-1-1-1-100000444444-211-21-2-21-2-2-2-2110000000000000022-1-1-1-100000
χ22444444-211-21-2-21-2-2-2-21100000000000000-2-2111100000444444-211-21-2-21-2-2-2-21100000000000000-2-2111100000444444-211-21-2-21-2-2-2-21100000000000000-2-2111100000
χ234444-4-41-2-21-211-2-1-1-1-12222-2-2-1-1-1-1111100000000000004444-4-41-2-21-211-2-1-1-1-12222-2-2-1-1-1-1111100000000000004444-4-41-2-21-211-2-1-1-1-12222-2-2-1-1-1-111110000000000000
χ244444-4-41-2-21-211-2-1-1-1-122-2-2221111-1-1-1-100000000000004444-4-41-2-21-211-2-1-1-1-122-2-2221111-1-1-1-100000000000004444-4-41-2-21-211-2-1-1-1-122-2-2221111-1-1-1-10000000000000
χ254444-4-4-211-21-2-212222-1-1000000000000002-2-1-111000004444-4-4-211-21-2-212222-1-1000000000000002-2-1-111000004444-4-4-211-21-2-212222-1-1000000000000002-2-1-11100000
χ264444-4-4-211-21-2-212222-1-100000000000000-2211-1-1000004444-4-4-211-21-2-212222-1-100000000000000-2211-1-1000004444-4-4-211-21-2-212222-1-100000000000000-2211-1-100000
χ2744-4-4001-221-2-1-123-33-30000003−33−33−33−3000000000000044-4-4001-221-2-1-123-33-30000003−33−33−33−3000000000000044-4-4001-221-2-1-123-33-30000003−33−33−33−30000000000000
χ2844-4-4001-221-2-1-123-33-3000000−33−33−33−33000000000000044-4-4001-221-2-1-123-33-3000000−33−33−33−33000000000000044-4-4001-221-2-1-123-33-3000000−33−33−33−330000000000000
χ2944-4-4001-221-2-1-12-33-330000003−33−3−33−33000000000000044-4-4001-221-2-1-12-33-330000003−33−3−33−33000000000000044-4-4001-221-2-1-12-33-330000003−33−3−33−330000000000000
χ3044-4-4001-221-2-1-12-33-33000000−33−333−33−3000000000000044-4-4001-221-2-1-12-33-33000000−33−333−33−3000000000000044-4-4001-221-2-1-12-33-33000000−33−333−33−30000000000000
χ3144-4-40044-444-4-4-4000000000000000000000000000000044-4-40044-444-4-4-4000000000000000000000000000000044-4-40044-444-4-4-40000000000000000000000000000000
χ324-44-44i−4i1-2-2-121-12ii−i−i−2i2i0000−i3i3i3−i33−3−3300000000000004-44-44i−4i1-2-2-121-12ii−i−i−2i2i0000−i3i3i3−i33−3−3300000000000004-44-44i−4i1-2-2-121-12ii−i−i−2i2i0000−i3i3i3−i33−3−330000000000000
χ334-44-44i−4i1-2-2-121-12ii−i−i−2i2i0000i3−i3−i3i3−333−300000000000004-44-44i−4i1-2-2-121-12ii−i−i−2i2i0000i3−i3−i3i3−333−300000000000004-44-44i−4i1-2-2-121-12ii−i−i−2i2i0000i3−i3−i3i3−333−30000000000000
χ344-44-44i−4i-2112-1-22-1−2i−2i2i2ii−i0000000000000000−i3i33−3000004-44-44i−4i-2112-1-22-1−2i−2i2i2ii−i0000000000000000−i3i33−3000004-44-44i−4i-2112-1-22-1−2i−2i2i2ii−i0000000000000000−i3i33−300000
χ354-44-44i−4i-2112-1-22-1−2i−2i2i2ii−i0000000000000000i3−i3−33000004-44-44i−4i-2112-1-22-1−2i−2i2i2ii−i0000000000000000i3−i3−33000004-44-44i−4i-2112-1-22-1−2i−2i2i2ii−i0000000000000000i3−i3−3300000
χ364-44-4−4i4i1-2-2-121-12−i−iii2i−2i0000−i3i3i3−i3−333−300000000000004-44-4−4i4i1-2-2-121-12−i−iii2i−2i0000−i3i3i3−i3−333−300000000000004-44-4−4i4i1-2-2-121-12−i−iii2i−2i0000−i3i3i3−i3−333−30000000000000
χ374-44-4−4i4i1-2-2-121-12−i−iii2i−2i0000i3−i3−i3i33−3−3300000000000004-44-4−4i4i1-2-2-121-12−i−iii2i−2i0000i3−i3−i3i33−3−3300000000000004-44-4−4i4i1-2-2-121-12−i−iii2i−2i0000i3−i3−i3i33−3−330000000000000
χ384-44-4−4i4i-2112-1-22-12i2i−2i−2i−ii0000000000000000−i3i3−33000004-44-4−4i4i-2112-1-22-12i2i−2i−2i−ii0000000000000000−i3i3−33000004-44-4−4i4i-2112-1-22-12i2i−2i−2i−ii0000000000000000−i3i3−3300000
χ394-44-4−4i4i-2112-1-22-12i2i−2i−2i−ii0000000000000000i3−i33−3000004-44-4−4i4i-2112-1-22-12i2i−2i−2i−ii0000000000000000i3−i33−3000004-44-4−4i4i-2112-1-22-12i2i−2i−2i−ii0000000000000000i3−i33−300000
χ404-4-44001-22-12-11-23i−3i−3i3i002i−2i-22−i−iii11-1-100000000000004-4-44001-22-12-11-23i−3i−3i3i002i−2i-22−i−iii11-1-100000000000004-4-44001-22-12-11-23i−3i−3i3i002i−2i-22−i−iii11-1-10000000000000
χ414-4-44001-22-12-11-23i−3i−3i3i00−2i2i2-2ii−i−i-1-11100000000000004-4-44001-22-12-11-23i−3i−3i3i00−2i2i2-2ii−i−i-1-11100000000000004-4-44001-22-12-11-23i−3i−3i3i00−2i2i2-2ii−i−i-1-1110000000000000
χ424-4-44001-22-12-11-2−3i3i3i−3i002i−2i2-2−i−iii-1-11100000000000004-4-44001-22-12-11-2−3i3i3i−3i002i−2i2-2−i−iii-1-11100000000000004-4-44001-22-12-11-2−3i3i3i−3i002i−2i2-2−i−iii-1-1110000000000000
χ434-4-44001-22-12-11-2−3i3i3i−3i00−2i2i-22ii−i−i11-1-100000000000004-4-44001-22-12-11-2−3i3i3i−3i00−2i2i-22ii−i−i11-1-100000000000004-4-44001-22-12-11-2−3i3i3i−3i00−2i2i-22ii−i−i11-1-10000000000000
χ4488-8-800-42-2-4244-2000000000000000000000000000000088-8-800-42-2-4244-2000000000000000000000000000000088-8-800-42-2-4244-20000000000000000000000000000000
χ458-8-8800-42-24-24-4200000000000000000000000000000008-8-8800-42-24-24-4200000000000000000000000000000008-8-8800-42-24-24-420000000000000000000000000000000
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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χ1314-4-44001-22-12-11-23i−3i−3i3i00−2i2i2-2ii−i−i-1-1110000000000000−2−2i32+2i32+2i3−2−2i300−1−i321+i3−1−i31+i32−1−i31+i32−1−i321+i33ζ22−3ζ22−3ζ223ζ2200−2ζ222ζ22−1−i31+i3ζ22ζ22−ζ22−ζ221+i321+i32−1−i32−1−i320000000000000−2+2i32−2i32−2i3−2+2i300−1+i321−i3−1+i31−i32−1+i31−i32−1+i321−i33ζ14−3ζ14−3ζ143ζ1400−2ζ142ζ14−1+i31−i3ζ14ζ14−ζ14−ζ141−i321−i32−1+i32−1+i320000000000000
χ1324-4-44001-22-12-11-2−3i3i3i−3i002i−2i2-2−i−iii-1-1110000000000000−2−2i32+2i32+2i3−2−2i300−1−i321+i3−1−i31+i32−1−i31+i32−1−i321+i3−3ζ223ζ223ζ22−3ζ22002ζ22−2ζ22−1−i31+i3−ζ22−ζ22ζ22ζ221+i321+i32−1−i32−1−i320000000000000−2+2i32−2i32−2i3−2+2i300−1+i321−i3−1+i31−i32−1+i31−i32−1+i321−i3−3ζ143ζ143ζ14−3ζ14002ζ14−2ζ14−1+i31−i3−ζ14−ζ14ζ14ζ141−i321−i32−1+i32−1+i320000000000000
χ1334-4-44001-22-12-11-2−3i3i3i−3i00−2i2i-22ii−i−i11-1-10000000000000−2−2i32+2i32+2i3−2−2i300−1−i321+i3−1−i31+i32−1−i31+i32−1−i321+i3−3ζ223ζ223ζ22−3ζ2200−2ζ222ζ221+i3−1−i3ζ22ζ22−ζ22−ζ22−1−i32−1−i321+i321+i320000000000000−2+2i32−2i32−2i3−2+2i300−1+i321−i3−1+i31−i32−1+i31−i32−1+i321−i3−3ζ143ζ143ζ14−3ζ1400−2ζ142ζ141−i3−1+i3ζ14ζ14−ζ14−ζ14−1+i32−1+i321−i321−i320000000000000
χ13488-8-800-42-2-4244-20000000000000000000000000000000−4−4i3−4−4i34+4i34+4i3002+2i3−1−i31+i32+2i3−1−i3−2−2i3−2−2i31+i30000000000000000000000000000000−4+4i3−4+4i34−4i34−4i3002−2i3−1+i31−i32−2i3−1+i3−2+2i3−2+2i31−i30000000000000000000000000000000
χ1358-8-8800-42-24-24-420000000000000000000000000000000−4−4i34+4i34+4i3−4−4i3002+2i3−1−i31+i3−2−2i31+i3−2−2i32+2i3−1−i30000000000000000000000000000000−4+4i34−4i34−4i3−4+4i3002−2i3−1+i31−i3−2+2i31−i3−2+2i32−2i3−1+i30000000000000000000000000000000

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