Finite Group Databasebeta

← Group #13166738

Character table — Group #13166738

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135
size111122444444444444881212121212121212121212121818242424242424363636363611112244444444444488121212121212121212121212181824242424242436363636361111224444444444448812121212121212121212121218182424242424243636363636
order122244336666661212121212124444121212121212121244441212121248888366612123366666612121212121212121212121212121212121212121212121212121224242424366612123366666612121212121212121212121212121212121212121212121212121224242424
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
χ51111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-1-111-111-1-11111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-1-111-111-1-11111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-1-111-111-1-1
χ61111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111-1111-1-1-1-1-1111111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111-1111-1-1-1-1-1111111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111-1111-1-1-1-1-111
χ71111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-111-1-1-1111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-111-1-1-1111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-111-1-1-111
χ81111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1111-1-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1111-1-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1111-1-1-111-1-1
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
χ112-22-200222-22-2-2-2000000002i−2i00002i2i−2i−2i-22000000000002-22-200222-22-2-2-2000000002i−2i00002i2i−2i−2i-22000000000002-22-200222-22-2-2-2000000002i−2i00002i2i−2i−2i-2200000000000
χ122-22-200222-22-2-2-200000000−2i2i0000−2i−2i2i2i-22000000000002-22-200222-22-2-2-200000000−2i2i0000−2i−2i2i2i-22000000000002-22-200222-22-2-2-200000000−2i2i0000−2i−2i2i2i-2200000000000
χ132-22-200222-22-2-2-20000002-20022-2-200002-2000000000002-22-200222-22-2-2-20000002-20022-2-200002-2000000000002-22-200222-22-2-2-20000002-20022-2-200002-200000000000
χ142-22-200222-22-2-2-2000000-2200-2-22200002-2000000000002-22-200222-22-2-2-2000000-2200-2-22200002-2000000000002-22-200222-22-2-2-2000000-2200-2-22200002-200000000000
χ152-2-222i−2i22-2-2-222-22i2i−2i−2i2i−2i0000000000000000000002−2−i2i22-2-222i−2i22-2-2-222-22i2i−2i−2i2i−2i0000000000000000000002−2−i2i22-2-222i−2i22-2-2-222-22i2i−2i−2i2i−2i0000000000000000000002−2−i2i2
χ162-2-222i−2i22-2-2-222-22i2i−2i−2i2i−2i000000000000000000000−22i2−i22-2-222i−2i22-2-2-222-22i2i−2i−2i2i−2i000000000000000000000−22i2−i22-2-222i−2i22-2-2-222-22i2i−2i−2i2i−2i000000000000000000000−22i2−i2
χ172-2-22−2i2i22-2-2-222-2−2i−2i2i2i−2i2i0000000000000000000002−2i2−i22-2-22−2i2i22-2-2-222-2−2i−2i2i2i−2i2i0000000000000000000002−2i2−i22-2-22−2i2i22-2-2-222-2−2i−2i2i2i−2i2i0000000000000000000002−2i2−i2
χ182-2-22−2i2i22-2-2-222-2−2i−2i2i2i−2i2i000000000000000000000−22−i2i22-2-22−2i2i22-2-2-222-2−2i−2i2i2i−2i2i000000000000000000000−22−i2i22-2-22−2i2i22-2-2-222-2−2i−2i2i2i−2i2i000000000000000000000−22−i2i2
χ194444441-21-2-21-21-2-2-2-2110000000000000022-1-1-1-1000004444441-21-2-21-21-2-2-2-2110000000000000022-1-1-1-1000004444441-21-2-21-21-2-2-2-2110000000000000022-1-1-1-100000
χ204444441-21-2-21-21-2-2-2-21100000000000000-2-21111000004444441-21-2-21-21-2-2-2-21100000000000000-2-21111000004444441-21-2-21-21-2-2-2-21100000000000000-2-2111100000
χ21444444-21-211-21-21111-2-22222-1-1-1-1-1-1-1-10000000000000444444-21-211-21-21111-2-22222-1-1-1-1-1-1-1-10000000000000444444-21-211-21-21111-2-22222-1-1-1-1-1-1-1-10000000000000
χ22444444-21-211-21-21111-2-2-2-2-2-2111111110000000000000444444-21-211-21-21111-2-2-2-2-2-2111111110000000000000444444-21-211-21-21111-2-2-2-2-2-2111111110000000000000
χ234444-4-41-21-2-21-212222-1-1000000000000002-211-1-1000004444-4-41-21-2-21-212222-1-1000000000000002-211-1-1000004444-4-41-21-2-21-212222-1-1000000000000002-211-1-100000
χ244444-4-41-21-2-21-212222-1-100000000000000-22-1-111000004444-4-41-21-2-21-212222-1-100000000000000-22-1-111000004444-4-41-21-2-21-212222-1-100000000000000-22-1-11100000
χ254444-4-4-21-211-21-2-1-1-1-12222-2-2-1-1-1-1111100000000000004444-4-4-21-211-21-2-1-1-1-12222-2-2-1-1-1-1111100000000000004444-4-4-21-211-21-2-1-1-1-12222-2-2-1-1-1-111110000000000000
χ264444-4-4-21-211-21-2-1-1-1-122-2-2221111-1-1-1-100000000000004444-4-4-21-211-21-2-1-1-1-122-2-2221111-1-1-1-100000000000004444-4-4-21-211-21-2-1-1-1-122-2-2221111-1-1-1-10000000000000
χ2744-4-40044-44-4-4-44000000000000000000000000000000044-4-40044-44-4-4-44000000000000000000000000000000044-4-40044-44-4-4-440000000000000000000000000000000
χ2844-4-400-2121-12-1-23-33-30000003−33−33−33−3000000000000044-4-400-2121-12-1-23-33-30000003−33−33−33−3000000000000044-4-400-2121-12-1-23-33-30000003−33−33−33−30000000000000
χ2944-4-400-2121-12-1-23-33-3000000−33−33−33−33000000000000044-4-400-2121-12-1-23-33-3000000−33−33−33−33000000000000044-4-400-2121-12-1-23-33-3000000−33−33−33−330000000000000
χ3044-4-400-2121-12-1-2-33-330000003−33−3−33−33000000000000044-4-400-2121-12-1-2-33-330000003−33−3−33−33000000000000044-4-400-2121-12-1-2-33-330000003−33−3−33−330000000000000
χ3144-4-400-2121-12-1-2-33-33000000−33−333−33−3000000000000044-4-400-2121-12-1-2-33-33000000−33−333−33−3000000000000044-4-400-2121-12-1-2-33-33000000−33−333−33−30000000000000
χ324-44-400-21-2-112-123i−3i−3i3i002-22i−2i-1-111−i−iii00000000000004-44-400-21-2-112-123i−3i−3i3i002-22i−2i-1-111−i−iii00000000000004-44-400-21-2-112-123i−3i−3i3i002-22i−2i-1-111−i−iii0000000000000
χ334-44-400-21-2-112-123i−3i−3i3i00-22−2i2i11-1-1ii−i−i00000000000004-44-400-21-2-112-123i−3i−3i3i00-22−2i2i11-1-1ii−i−i00000000000004-44-400-21-2-112-123i−3i−3i3i00-22−2i2i11-1-1ii−i−i0000000000000
χ344-44-400-21-2-112-12−3i3i3i−3i002-2−2i2i-1-111ii−i−i00000000000004-44-400-21-2-112-12−3i3i3i−3i002-2−2i2i-1-111ii−i−i00000000000004-44-400-21-2-112-12−3i3i3i−3i002-2−2i2i-1-111ii−i−i0000000000000
χ354-44-400-21-2-112-12−3i3i3i−3i00-222i−2i11-1-1−i−iii00000000000004-44-400-21-2-112-12−3i3i3i−3i00-222i−2i11-1-1−i−iii00000000000004-44-400-21-2-112-12−3i3i3i−3i00-222i−2i11-1-1−i−iii0000000000000
χ364-4-444i−4i1-2-1221-2-1−2i−2i2i2ii−i0000000000000000−i3i33−3000004-4-444i−4i1-2-1221-2-1−2i−2i2i2ii−i0000000000000000−i3i33−3000004-4-444i−4i1-2-1221-2-1−2i−2i2i2ii−i0000000000000000−i3i33−300000
χ374-4-444i−4i1-2-1221-2-1−2i−2i2i2ii−i0000000000000000i3−i3−33000004-4-444i−4i1-2-1221-2-1−2i−2i2i2ii−i0000000000000000i3−i3−33000004-4-444i−4i1-2-1221-2-1−2i−2i2i2ii−i0000000000000000i3−i3−3300000
χ384-4-444i−4i-212-1-1-212ii−i−i−2i2i00003−3−33i3−i3−i3i300000000000004-4-444i−4i-212-1-1-212ii−i−i−2i2i00003−3−33i3−i3−i3i300000000000004-4-444i−4i-212-1-1-212ii−i−i−2i2i00003−3−33i3−i3−i3i30000000000000
χ394-4-444i−4i-212-1-1-212ii−i−i−2i2i0000−333−3−i3i3i3−i300000000000004-4-444i−4i-212-1-1-212ii−i−i−2i2i0000−333−3−i3i3i3−i300000000000004-4-444i−4i-212-1-1-212ii−i−i−2i2i0000−333−3−i3i3i3−i30000000000000
χ404-4-44−4i4i1-2-1221-2-12i2i−2i−2i−ii0000000000000000−i3i3−33000004-4-44−4i4i1-2-1221-2-12i2i−2i−2i−ii0000000000000000−i3i3−33000004-4-44−4i4i1-2-1221-2-12i2i−2i−2i−ii0000000000000000−i3i3−3300000
χ414-4-44−4i4i1-2-1221-2-12i2i−2i−2i−ii0000000000000000i3−i33−3000004-4-44−4i4i1-2-1221-2-12i2i−2i−2i−ii0000000000000000i3−i33−3000004-4-44−4i4i1-2-1221-2-12i2i−2i−2i−ii0000000000000000i3−i33−300000
χ424-4-44−4i4i-212-1-1-212−i−iii2i−2i00003−3−33−i3i3i3−i300000000000004-4-44−4i4i-212-1-1-212−i−iii2i−2i00003−3−33−i3i3i3−i300000000000004-4-44−4i4i-212-1-1-212−i−iii2i−2i00003−3−33−i3i3i3−i30000000000000
χ434-4-44−4i4i-212-1-1-212−i−iii2i−2i0000−333−3i3−i3−i3i300000000000004-4-44−4i4i-212-1-1-212−i−iii2i−2i0000−333−3i3−i3−i3i300000000000004-4-44−4i4i-212-1-1-212−i−iii2i−2i0000−333−3i3−i3−i3i30000000000000
χ4488-8-8002-4-2-44-242000000000000000000000000000000088-8-8002-4-2-44-242000000000000000000000000000000088-8-8002-4-2-44-2420000000000000000000000000000000
χ458-88-8002-424-4-24-200000000000000000000000000000008-88-8002-424-4-24-200000000000000000000000000000008-88-8002-424-4-24-20000000000000000000000000000000
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
χ501111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-1-111-111-1-1−1+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−i321−i321−i32−1+i32−1+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+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32
χ511111-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111-1111-1-1-1-1-111−1+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+i32−1+i32−1+i321−i321−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−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32
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χ1324-4-44−4i4i-212-1-1-212−i−iii2i−2i00003−3−33−i3i3i3−i30000000000000−2−2i32+2i32+2i3−2−2i3−4ζ224ζ221+i3−1−i32−1−i31+i321+i321+i3−1−i32−1−i3−ζ22−ζ22ζ22ζ222ζ22−2ζ2200002ζ14+ζ22−2ζ14−ζ22−2ζ14−ζ222ζ14+ζ22−3+i323−i323−i32−3+i320000000000000−2+2i32−2i32−2i3−2+2i3−4ζ144ζ141−i3−1+i32−1+i31−i321−i321−i3−1+i32−1+i3−ζ14−ζ14ζ14ζ142ζ14−2ζ140000−ζ14−2ζ22ζ14+2ζ22ζ14+2ζ22−ζ14−2ζ223+i32−3−i32−3−i323+i320000000000000
χ1334-4-44−4i4i-212-1-1-212−i−iii2i−2i0000−333−3i3−i3−i3i30000000000000−2−2i32+2i32+2i3−2−2i3−4ζ224ζ221+i3−1−i32−1−i31+i321+i321+i3−1−i32−1−i3−ζ22−ζ22ζ22ζ222ζ22−2ζ220000−2ζ14−ζ222ζ14+ζ222ζ14+ζ22−2ζ14−ζ223−i32−3+i32−3+i323−i320000000000000−2+2i32−2i32−2i3−2+2i3−4ζ144ζ141−i3−1+i32−1+i31−i321−i321−i3−1+i32−1+i3−ζ14−ζ14ζ14ζ142ζ14−2ζ140000ζ14+2ζ22−ζ14−2ζ22−ζ14−2ζ22ζ14+2ζ22−3−i323+i323+i32−3−i320000000000000
χ13488-8-8002-4-2-44-2420000000000000000000000000000000−4−4i3−4−4i34+4i34+4i300−1−i32+2i31+i32+2i3−2−2i31+i3−2−2i3−1−i30000000000000000000000000000000−4+4i3−4+4i34−4i34−4i300−1+i32−2i31−i32−2i3−2+2i31−i3−2+2i3−1+i30000000000000000000000000000000
χ1358-88-8002-424-4-24-20000000000000000000000000000000−4−4i34+4i3−4−4i34+4i300−1−i32+2i3−1−i3−2−2i32+2i31+i3−2−2i31+i30000000000000000000000000000000−4+4i34−4i3−4+4i34−4i300−1+i32−2i3−1+i3−2+2i32−2i31−i3−2+2i31−i30000000000000000000000000000000

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