Finite Group Databasebeta

← Group #13167082

Character table — Group #13167082

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222224444444444444444444444444444888888888812121212121212121212121212121212121212121212121212121212121212121212121218181818363636363636363672727272108108108108
order122234466612121212333366666666666612121212121212121212121236661212121212124444121212121212121212121212121212121212121212121212121212121212121222444444661212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ511111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1
χ611111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111
χ711111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-111
χ811111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-111-1-11111-1-1
χ91-11-111-1-1-1111-1-11111-11111-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-111-1-1i−ii−iii−i−iii−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i1-1-11i−ii−i1-11-1i−ii−i1-11-1
χ101-11-111-1-1-1111-1-11111-11111-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-111-1-1i−ii−iii−i−iii−i−iiiiiii−i−i−i−i−i−iiiiiii−i−i−i−i−i−i1-1-11−ii−ii1-11-1−ii−ii-11-11
χ111-11-111-1-1-1111-1-11111-11111-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-111-1-1−ii−ii−i−iii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii1-1-11i−ii−i1-11-1i−ii−i-11-11
χ121-11-111-1-1-1111-1-11111-11111-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-111-1-1−ii−ii−i−iii−i−iii−i−i−i−i−i−iiiiiii−i−i−i−i−i−iiiiiii1-1-11−ii−ii1-11-1−ii−ii1-11-1
χ131-11-11-11-1-11-1-1111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-11-1-111i−i−iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-11-11i−i−ii-111-1i−i−ii1-1-11
χ141-11-11-11-1-11-1-1111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-11-1-111i−i−iiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiii-11-11−iii−i-111-1−iii−i-111-1
χ151-11-11-11-1-11-1-1111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-11-1-111−iii−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-11-11i−i−ii-111-1i−i−ii-111-1
χ161-11-11-11-1-11-1-1111111-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11-11-1-111−iii−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i-11-11−iii−i-111-1−iii−i1-1-11
χ172222222222222222222222222222222222222222222222222222000000000000000000000000000000000000-2-2-2-20000-2-2-2-200000000
χ1822222-2-2222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-200000000000000000000000000000000000022-2-2000022-2-200000000
χ192222-122-1-1-1-1-1-1-122-1-1222-1-122-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10000−i3i3−i3i3−i3i3−i3i300−i3−i3i3i300−i3−i3i3i300−i3−i3i3i300−i3−i3i3i3-2-2-2-20000111100000000
χ202222-122-1-1-1-1-1-1-122-1-1222-1-122-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10000i3−i3i3−i3i3−i3i3−i300i3i3−i3−i300i3i3−i3−i300i3i3−i3−i300i3i3−i3−i3-2-2-2-20000111100000000
χ212222-122-1-1-1-1-1-1-122-1-1222-1-122-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122220000-1-1-1-100000000
χ222222-122-1-1-1-1-1-1-122-1-1222-1-122-1-1-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-21111-2-21111-2-21111-2-2111122220000-1-1-1-100000000
χ232222-1-2-2-1-1-1111122-1-1222-1-122-1-1-1-12-2-21111-2-21111-1-1-1-1-2-211110000−i3i3−i3i3i3−i3i3−i300−i3−i3i3i300−i3−i3i3i300i3i3−i3−i300i3i3−i3−i322-2-20000-1-11100000000
χ242222-1-2-2-1-1-1111122-1-1222-1-122-1-1-1-12-2-21111-2-21111-1-1-1-1-2-211110000i3−i3i3−i3−i3i3−i3i300i3i3−i3−i300i3i3−i3−i300−i3−i3i3i300−i3−i3i3i322-2-20000-1-11100000000
χ252222-1-2-2-1-1-1111122-1-1222-1-122-1-1-1-12-2-21111-2-21111-1-1-1-1-2-2111122-2-2-1-1-1-1111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-222000011-1-100000000
χ262222-1-2-2-1-1-1111122-1-1222-1-122-1-1-1-12-2-21111-2-21111-1-1-1-1-2-21111-2-2221111-1-1-1-1-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-222000011-1-100000000
χ272-22-222-2-2-2222-2-22222-22222-2-2-2-2-2-2-2222222-2-2-2-2-2-22-2-222-222-2-2000000000000000000000000000000000000-222-20000-22-2200000000
χ282-22-22-22-2-22-2-2222222-22222-2-2-2-2-2-2-2-2-2-2-2-2-22222222-2-22-22-2-2220000000000000000000000000000000000002-22-200002-2-2200000000
χ292-22-2-12-211-1-1-11122-1-1-222-1-1-2-21111-222-1-1-1-1-2-21111-111-12-2-1-11100003−3−333−3−330033−3−300−3−3330033−3−300−3−333-222-200001-11-100000000
χ302-22-2-12-211-1-1-11122-1-1-222-1-1-2-21111-222-1-1-1-1-2-21111-111-12-2-1-1110000−333−3−333−300−3−3330033−3−300−3−3330033−3−3-222-200001-11-100000000
χ312-22-2-12-211-1-1-11122-1-1-222-1-1-2-21111-222-1-1-1-1-2-21111-111-12-2-1-1112i−2i2i−2i−i−iii−i−iii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2-2-220000-11-1100000000
χ322-22-2-12-211-1-1-11122-1-1-222-1-1-2-21111-222-1-1-1-1-2-21111-111-12-2-1-111−2i2i−2i2iii−i−iii−i−i−2i−2iiiii2i2i−i−i−i−i−2i−2iiiii2i2i−i−i−i−i2-2-220000-11-1100000000
χ332-22-2-1-2211-111-1-122-1-1-222-1-1-2-21111-2-2-2111122-1-1-1-1-111-1-2211-1-100003−3−33−333−30033−3−300−3−33300−3−3330033−3−32-22-20000-111-100000000
χ342-22-2-1-2211-111-1-122-1-1-222-1-1-2-21111-2-2-2111122-1-1-1-1-111-1-2211-1-10000−333−33−3−3300−3−3330033−3−30033−3−300−3−3332-22-20000-111-100000000
χ352-22-2-1-2211-111-1-122-1-1-222-1-1-2-21111-2-2-2111122-1-1-1-1-111-1-2211-1-12i−2i−2i2i−i−iiiii−i−i2i2i−i−i−i−i−2i−2iiiii−2i−2iiiii2i2i−i−i−i−i-22-2200001-1-1100000000
χ362-22-2-1-2211-111-1-122-1-1-222-1-1-2-21111-2-2-2111122-1-1-1-1-111-1-2211-1-1−2i2i2i−2iii−i−i−i−iii−2i−2iiiii2i2i−i−i−i−i2i2i−i−i−i−i−2i−2iiiii-22-2200001-1-1100000000
χ37444444444444441-211-21-211111111-2111111111111-2-2-2-2-2-2-2-2-2-2222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ38444444444444441-211-21-211111111-2111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111111111111111111100000000000000000000
χ3944444444444444-21-2-21-21-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111000000000000000000000000000000000000000022220000-1-1-1-10000
χ4044444444444444-21-2-21-21-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-211111111110000000000000000000000000000000000000000-2-2-2-2000011110000
χ4144444-4-4444-4-4-4-41-211-21-211111111-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222222222-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000000000000000
χ4244444-4-4444-4-4-4-41-211-21-211111111-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222222-2-222-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ4344444-4-4444-4-4-4-4-21-2-21-21-2-2-2-2-2-2-2-212222222222221111-1-1-1-1-1-1000000000000000000000000000000000000000022-2-20000-1-1110000
χ4444444-4-4444-4-4-4-4-21-2-21-21-2-2-2-2-2-2-2-212222222222221111-1-1-1-1-1-10000000000000000000000000000000000000000-2-222000011-1-10000
χ454444-244-2-2-2-2-2-2-21-2−1−3i32−1+3i32-21-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i321111-2-211112222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3200000000000000000000
χ464444-244-2-2-2-2-2-2-21-2−1−3i32−1+3i32-21-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-211−1−3i32−1−3i32−1+3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i321111-2-21111-2-2-2-21+i31−i31+i31−i31+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3200000000000000000000
χ474444-244-2-2-2-2-2-2-21-2−1+3i32−1−3i32-21-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i321111-2-211112222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3200000000000000000000
χ484444-244-2-2-2-2-2-2-21-2−1+3i32−1−3i32-21-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-211−1+3i32−1+3i32−1−3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i321111-2-21111-2-2-2-21−i31+i31−i31+i31−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3200000000000000000000
χ494444-2-4-4-2-2-222221-2−1−3i32−1+3i32-21-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i32-1-11+3i321+3i321−3i321−3i32111122-1-1-1-122-2-2−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3200000000000000000000
χ504444-2-4-4-2-2-222221-2−1−3i32−1+3i32-21-2−1−3i32−1+3i3211−1−3i32−1−3i32−1+3i32−1+3i32-2-1-11+3i321+3i321−3i321−3i32-1-11+3i321+3i321−3i321−3i32111122-1-1-1-1-2-2221+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3200000000000000000000
χ514444-2-4-4-2-2-222221-2−1+3i32−1−3i32-21-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i32-1-11−3i321−3i321+3i321+3i32111122-1-1-1-122-2-2−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3200000000000000000000
χ524444-2-4-4-2-2-222221-2−1+3i32−1−3i32-21-2−1+3i32−1−3i3211−1+3i32−1+3i32−1−3i32−1−3i32-2-1-11−3i321−3i321+3i321+3i32-1-11−3i321−3i321+3i321+3i32111122-1-1-1-1-2-2221−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3200000000000000000000
χ5344-4-44004-4-400001-211-2-12-1-11-11-11-123i−3i3i−3i3i−3i3i−3i3i−3i3i−3i-22-22000000000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i33−33−33−33−33−33−300000000000000000000
χ5444-4-44004-4-400001-211-2-12-1-11-11-11-123i−3i3i−3i3i−3i3i−3i3i−3i3i−3i-22-22000000000000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3−33−33−33−33−33−3300000000000000000000
χ5544-4-44004-4-400001-211-2-12-1-11-11-11-12−3i3i−3i3i−3i3i−3i3i−3i3i−3i3i-22-22000000000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−33−33−33−33−33−3300000000000000000000
χ5644-4-44004-4-400001-211-2-12-1-11-11-11-12−3i3i−3i3i−3i3i−3i3i−3i3i−3i3i-22-22000000000000000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i33−33−33−33−33−33−300000000000000000000
χ5744-4-44004-4-4000044444-4-4-4-44-44-44-4-40000000000004-44-400000000000000000000000000000000000000000000000000000000000000
χ5844-4-4-200-22223−2323−231-2−1−3i32−1+3i32-2-121+3i321−3i321-1−1−3i321+3i32−1+3i321−3i3223i−3iζ7+2ζ11−ζ7−2ζ112ζ7+ζ11−2ζ7−ζ113i−3iζ7+2ζ11−ζ7−2ζ112ζ7+ζ11−2ζ7−ζ111-11-1003−33−3000000000000−i3i3−3+i323−i323+i32−3−i32−i3i3−3+i323−i323+i32−3−i323−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ113−32ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ1100000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.