Finite Group Databasebeta

← Group #13167055

Character table — Group #13167055

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111222244444444444444448888121212121212121212121212121212121212181836363636363636365454545411112222444444444444444488881212121212121212121212121212121212121818363636363636363654545454
order12443612123333666612121212121212123612122466666666121212121212121224688122424242444442244661212666666661212121212121212661212246666666612121212121212122468812242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111
χ511-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11-111111111-1-1-1-1-1-1-1-1-11-1i−i1ii−i−iii−i−i11-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11-111111111-1-1-1-1-1-1-1-1-11-1i−i1ii−i−iii−i−i
χ611-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11-111111111-1-1-1-1-1-1-1-1-11-1−ii1−i−iii−i−iii11-1-111-1-111111111-1-1-1-1-1-1-1-111-1-11-111111111-1-1-1-1-1-1-1-1-11-1−ii1−i−iii−i−iii
χ711-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-11-1-1-1-1-1-1-1-111111111-11-1i−i1ii−i−i−i−iii11-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-11-1-1-1-1-1-1-1-111111111-11-1i−i1ii−i−i−i−iii
χ811-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-11-1-1-1-1-1-1-1-111111111-11-1−ii1−i−iiiii−i−i11-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-11-1-1-1-1-1-1-1-111111111-11-1−ii1−i−iiiii−i−i
χ92222222222222222222222222222000000000000000000-2-2-200-2000000002222222222222222222222222222000000000000000000-2-2-200-200000000
χ102222-1-1-1-122-1-122-1-122-1-1-1-122-1-1-1-100−i3i300−i3−i3i3i3−i3i300−i3−i3i3i3-2-21001000000002222-1-1-1-122-1-122-1-122-1-1-1-122-1-1-1-100−i3i300−i3−i3i3i3−i3i300−i3−i3i3i3-2-2100100000000
χ112222-1-1-1-122-1-122-1-122-1-1-1-122-1-1-1-100i3−i300i3i3−i3−i3i3−i300i3i3−i3−i3-2-21001000000002222-1-1-1-122-1-122-1-122-1-1-1-122-1-1-1-100i3−i300i3i3−i3−i3i3−i300i3i3−i3−i3-2-2100100000000
χ122222-1-1-1-122-1-122-1-122-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-122-100-1000000002222-1-1-1-122-1-122-1-122-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-122-100-100000000
χ132222-1-1-1-122-1-122-1-122-1-1-1-122-1-1-1-1-2-211-2-2111111-2-2111122-100-1000000002222-1-1-1-122-1-122-1-122-1-1-1-122-1-1-1-1-2-211-2-2111111-2-2111122-100-100000000
χ1422-2-222-2-222222222-2-2-2-2-2-2-2-222-2-20000000000000000002-2200-20000000022-2-222-2-222222222-2-2-2-2-2-2-2-222-2-20000000000000000002-2200-200000000
χ1522-2-2-1-11122-1-122-1-1-2-21111-2-2-1-11100−i3i300−i3−i3i3i3i3−i300i3i3−i3−i32-2-10010000000022-2-2-1-11122-1-122-1-1-2-21111-2-2-1-11100−i3i300−i3−i3i3i3i3−i300i3i3−i3−i32-2-100100000000
χ1622-2-2-1-11122-1-122-1-1-2-21111-2-2-1-11100i3−i300i3i3−i3−i3−i3i300−i3−i3i3i32-2-10010000000022-2-2-1-11122-1-122-1-1-2-21111-2-2-1-11100i3−i300i3i3−i3−i3−i3i300−i3−i3i3i32-2-100100000000
χ1722-2-2-1-11122-1-122-1-1-2-21111-2-2-1-1112-2-1-122-1-1-1-111-2-21111-22100-10000000022-2-2-1-11122-1-122-1-1-2-21111-2-2-1-1112-2-1-122-1-1-1-111-2-21111-22100-100000000
χ1822-2-2-1-11122-1-122-1-1-2-21111-2-2-1-111-2211-2-21111-1-122-1-1-1-1-22100-10000000022-2-2-1-11122-1-122-1-1-2-21111-2-2-1-111-2211-2-21111-1-122-1-1-1-1-22100-100000000
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χ222-2−2i2i2-2−2i2i2222-2-2-2-2−2i2i−2i−2i2i2i−2i2i2-2−2i2i0000000000000000000000000000−1+i1−i−1−i1+i2-2−2i2i2-2−2i2i2222-2-2-2-2−2i2i−2i−2i2i2i−2i2i2-2−2i2i0000000000000000000000000000−1+i1−i−1−i1+i
χ23444444441-2-2-21-2-2-2-2-2-2-2-2-2111111000000000000000000000220-1-1-1-10000444444441-2-2-21-2-2-2-2-2-2-2-2-2111111000000000000000000000220-1-1-1-10000
χ24444444441-2-2-21-2-2-2-2-2-2-2-2-2111111000000000000000000000-2-2011110000444444441-2-2-21-2-2-2-2-2-2-2-2-2111111000000000000000000000-2-2011110000
χ2544444444-2111-2111111111-2-2-2-2-2-22222-1-1-1-1-1-122-1-1-1-1-1-10000000000000044444444-2111-2111111111-2-2-2-2-2-22222-1-1-1-1-1-122-1-1-1-1-1-100000000000000
χ2644444444-2111-2111111111-2-2-2-2-2-2-2-2-2-2111111-2-21111110000000000000044444444-2111-2111111111-2-2-2-2-2-2-2-2-2-2111111-2-211111100000000000000
χ274444-2-2-2-2-21−1−3i32−1+3i32-21−1−3i32−1+3i3211−1−3i32−1+3i32−1−3i32−1+3i32-2-2111122−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i32000000000000004444-2-2-2-2-21−1−3i32−1+3i32-21−1−3i32−1+3i3211−1−3i32−1+3i32−1−3i32−1+3i32-2-2111122−1−i3−1+i3-1-11+i321+i321−i321−i32−1−i3−1+i3-1-11+i321+i321−i321−i3200000000000000
χ284444-2-2-2-2-21−1−3i32−1+3i32-21−1−3i32−1+3i3211−1−3i32−1+3i32−1−3i32−1+3i32-2-21111-2-21+i31−i311−1−i32−1−i32−1+i32−1+i321+i31−i311−1−i32−1−i32−1+i32−1+i32000000000000004444-2-2-2-2-21−1−3i32−1+3i32-21−1−3i32−1+3i3211−1−3i32−1+3i32−1−3i32−1+3i32-2-21111-2-21+i31−i311−1−i32−1−i32−1+i32−1+i321+i31−i311−1−i32−1−i32−1+i32−1+i3200000000000000
χ294444-2-2-2-2-21−1+3i32−1−3i32-21−1+3i32−1−3i3211−1+3i32−1−3i32−1+3i32−1−3i32-2-2111122−1+i3−1−i3-1-11−i321−i321+i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i32000000000000004444-2-2-2-2-21−1+3i32−1−3i32-21−1+3i32−1−3i3211−1+3i32−1−3i32−1+3i32−1−3i32-2-2111122−1+i3−1−i3-1-11−i321−i321+i321+i32−1+i3−1−i3-1-11−i321−i321+i321+i3200000000000000
χ304444-2-2-2-2-21−1+3i32−1−3i32-21−1+3i32−1−3i3211−1+3i32−1−3i32−1+3i32−1−3i32-2-21111-2-21−i31+i311−1+i32−1+i32−1−i32−1−i321−i31+i311−1+i32−1+i32−1−i32−1−i32000000000000004444-2-2-2-2-21−1+3i32−1−3i32-21−1+3i32−1−3i3211−1+3i32−1−3i32−1+3i32−1−3i32-2-21111-2-21−i31+i311−1+i32−1+i32−1−i32−1−i321−i31+i311−1+i32−1+i32−1−i32−1−i3200000000000000
χ3144-4-444-4-41-2-2-21-2-2-2222222-1-111-1-10000000000000000000002i−2i0−i−iii000044-4-444-4-41-2-2-21-2-2-2222222-1-111-1-10000000000000000000002i−2i0−i−iii0000
χ3244-4-444-4-41-2-2-21-2-2-2222222-1-111-1-1000000000000000000000−2i2i0ii−i−i000044-4-444-4-41-2-2-21-2-2-2222222-1-111-1-1000000000000000000000−2i2i0ii−i−i0000
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χ3444-4-444-4-4-2111-2111-1-1-1-1-1-122-2-222-22-2-211111122-1-1-1-1-1-10000000000000044-4-444-4-4-2111-2111-1-1-1-1-1-122-2-222-22-2-211111122-1-1-1-1-1-100000000000000
χ3544-4-4-2-222-21−1−3i32−1+3i32-21−1−3i32−1+3i32-1-11+3i321−3i321+3i321−3i322211-1-12-2−1−i3−1+i3-1-11+i321+i321−i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i320000000000000044-4-4-2-222-21−1−3i32−1+3i32-21−1−3i32−1+3i32-1-11+3i321−3i321+3i321−3i322211-1-12-2−1−i3−1+i3-1-11+i321+i321−i321−i321+i31−i311−1−i32−1−i32−1+i32−1+i3200000000000000
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χ3744-4-4-2-222-21−1+3i32−1−3i32-21−1+3i32−1−3i32-1-11−3i321+3i321−3i321+3i322211-1-12-2−1+i3−1−i3-1-11−i321−i321+i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i320000000000000044-4-4-2-222-21−1+3i32−1−3i32-21−1+3i32−1−3i32-1-11−3i321+3i321−3i321+3i322211-1-12-2−1+i3−1−i3-1-11−i321−i321+i321+i321−i31+i311−1+i32−1+i32−1−i32−1−i3200000000000000
χ3844-4-4-2-222-21−1+3i32−1−3i32-21−1+3i32−1−3i32-1-11−3i321+3i321−3i321+3i322211-1-1-221−i31+i311−1+i32−1+i32−1−i32−1−i32−1+i3−1−i3-1-11−i321−i321+i321+i320000000000000044-4-4-2-222-21−1+3i32−1−3i32-21−1+3i32−1−3i32-1-11−3i321+3i321−3i321+3i322211-1-1-221−i31+i311−1+i32−1+i32−1−i32−1−i32−1+i3−1−i3-1-11−i321−i321+i321+i3200000000000000
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χ454-44i−4i-22−2i2i-21−1−3i32−1+3i322-11+3i321−3i32i−i−ζ14+2ζ222ζ14−ζ22ζ14−2ζ22−2ζ14+ζ22−2i2i1-1i−i0000i3−i33−i32−3+i32−3−i323+i3200−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22000000000000004-44i−4i-22−2i2i-21−1−3i32−1+3i322-11+3i321−3i32i−i−ζ14+2ζ222ζ14−ζ22ζ14−2ζ22−2ζ14+ζ22−2i2i1-1i−i0000i3−i33−i32−3+i32−3−i323+i3200−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ2200000000000000
χ464-44i−4i-22−2i2i-21−1+3i32−1−3i322-11−3i321+3i32i−i2ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ22−2i2i1-1i−i0000−i3i33+i32−3−i32−3+i323−i32003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ22000000000000004-44i−4i-22−2i2i-21−1+3i32−1−3i322-11−3i321+3i32i−i2ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ22−2i2i1-1i−i0000−i3i33+i32−3−i32−3+i323−i32003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ2200000000000000
χ474-44i−4i-22−2i2i-21−1+3i32−1−3i322-11−3i321+3i32i−i2ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ22−2i2i1-1i−i0000i3−i3−3−i323+i323−i32−3+i3200−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22000000000000004-44i−4i-22−2i2i-21−1+3i32−1−3i322-11−3i321+3i32i−i2ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ22−2i2i1-1i−i0000i3−i3−3−i323+i323−i32−3+i3200−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ2200000000000000
χ484-4−4i4i4-4−4i4i1-2-2-2-12222i−2i2i2i−2i−2i−ii1-1−ii000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300004-4−4i4i4-4−4i4i1-2-2-2-12222i−2i2i2i−2i−2i−ii1-1−ii000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ494-4−4i4i4-4−4i4i1-2-2-2-12222i−2i2i2i−2i−2i−ii1-1−ii000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300004-4−4i4i4-4−4i4i1-2-2-2-12222i−2i2i2i−2i−2i−ii1-1−ii000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ504-4−4i4i4-4−4i4i-21112-1-1-1−ii−i−iii2i−2i-222i−2i0000−i3i3−i3i3−i3i300−33−33−33000000000000004-4−4i4i4-4−4i4i-21112-1-1-1−ii−i−iii2i−2i-222i−2i0000−i3i3−i3i3−i3i300−33−33−3300000000000000
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χ1054-44i−4i-22−2i2i-21−1−3i32−1+3i322-11+3i321−3i32i−i−ζ14+2ζ222ζ14−ζ22ζ14−2ζ22−2ζ14+ζ22−2i2i1-1i−i0000i3−i33−i32−3+i32−3−i323+i3200−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ2200000000000000-44−4i4i2-22i−2i2-11+3i321−3i32-21−1−3i32−1+3i32−iiζ14−2ζ22−2ζ14+ζ22−ζ14+2ζ222ζ14−ζ222i−2i-11−ii0000−i3i3−3+i323−i323+i32−3−i32003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ2200000000000000
χ1064-44i−4i-22−2i2i-21−1+3i32−1−3i322-11−3i321+3i32i−i2ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ22−2i2i1-1i−i0000−i3i33+i32−3−i32−3+i323−i32003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ2200000000000000-44−4i4i2-22i−2i2-11−3i321+3i32-21−1+3i32−1−3i32−ii−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ222i−2i-11−ii0000i3−i3−3−i323+i323−i32−3+i3200−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ2200000000000000
χ1074-44i−4i-22−2i2i-21−1+3i32−1−3i322-11−3i321+3i32i−i2ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ22−2i2i1-1i−i0000i3−i3−3−i323+i323−i32−3+i3200−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ2200000000000000-44−4i4i2-22i−2i2-11−3i321+3i32-21−1+3i32−1−3i32−ii−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ222i−2i-11−ii0000−i3i33+i32−3−i32−3+i323−i32003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ2200000000000000
χ1084-4−4i4i4-4−4i4i1-2-2-2-12222i−2i2i2i−2i−2i−ii1-1−ii000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000-444i−4i-444i−4i-12221-2-2-2−2i2i−2i−2i2i2ii−i-11i−i000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000
χ1094-4−4i4i4-4−4i4i1-2-2-2-12222i−2i2i2i−2i−2i−ii1-1−ii000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000-444i−4i-444i−4i-12221-2-2-2−2i2i−2i−2i2i2ii−i-11i−i000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000
χ1104-4−4i4i4-4−4i4i-21112-1-1-1−ii−i−iii2i−2i-222i−2i0000−i3i3−i3i3−i3i300−33−33−3300000000000000-444i−4i-444i−4i2-1-1-1-2111i−iii−i−i−2i2i2-2−2i2i0000i3−i3i3−i3i3−i3003−33−33−300000000000000
χ1114-4−4i4i4-4−4i4i-21112-1-1-1−ii−i−iii2i−2i-222i−2i0000i3−i3i3−i3i3−i3003−33−33−300000000000000-444i−4i-444i−4i2-1-1-1-2111i−iii−i−i−2i2i2-2−2i2i0000−i3i3−i3i3−i3i300−33−33−3300000000000000
χ1124-4−4i4i-222i−2i44-2-2-4-422−4i4i2i2i−2i−2i−4i4i-222i−2i00000000000000000000000000000000-444i−4i2-2−2i2i-4-42244-2-24i−4i−2i−2i2i2i4i−4i2-2−2i2i00000000000000000000000000000000
χ1134-4−4i4i-222i−2i-21−1−3i32−1+3i322-11+3i321−3i32−iiζ14−2ζ22−2ζ14+ζ22−ζ14+2ζ222ζ14−ζ222i−2i1-1−ii0000−i3i3−3+i323−i323+i32−3−i3200−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ2200000000000000-444i−4i2-2−2i2i2-11+3i321−3i32-21−1−3i32−1+3i32i−i−ζ14+2ζ222ζ14−ζ22ζ14−2ζ22−2ζ14+ζ22−2i2i-11i−i0000i3−i33−i32−3+i32−3−i323+i32003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ2200000000000000
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χ1154-4−4i4i-222i−2i-21−1+3i32−1−3i322-11−3i321+3i32−ii−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ222i−2i1-1−ii0000−i3i33+i32−3−i32−3+i323−i3200−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ2200000000000000-444i−4i2-2−2i2i2-11−3i321+3i32-21−1+3i32−1−3i32i−i2ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ22−2i2i-11i−i0000i3−i3−3−i323+i323−i32−3+i32003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ2200000000000000
χ1164-4−4i4i-222i−2i-21−1+3i32−1−3i322-11−3i321+3i32−ii−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ222i−2i1-1−ii0000i3−i3−3−i323+i323−i32−3+i32003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ2200000000000000-444i−4i2-2−2i2i2-11−3i321+3i32-21−1+3i32−1−3i32i−i2ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ22−2i2i-11i−i0000−i3i33+i32−3−i32−3+i323−i3200−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ2200000000000000
χ1178888-4-4-4-42-4222-422-4-4222222-1-1-1-100000000000000000000000000000000-8-8-8-84444-24-2-2-24-2-244-2-2-2-2-2-2111100000000000000000000000000000000
χ11888-8-8-4-4442-4222-42244-2-2-2-2-2-2-1-11100000000000000000000000000000000-8-88844-4-4-24-2-2-24-2-2-4-422222211-1-100000000000000000000000000000000
χ1198-88i−8i-44−4i4i2-422-24-2-2−4i4i2i2i−2i−2i2i−2i-11−ii00000000000000000000000000000000-88−8i8i4-44i−4i-24-2-22-4224i−4i−2i−2i2i2i−2i2i1-1i−i00000000000000000000000000000000
χ1208-8−8i8i-444i−4i2-422-24-2-24i−4i−2i−2i2i2i−2i2i-11i−i00000000000000000000000000000000-888i−8i4-4−4i4i-24-2-22-422−4i4i2i2i−2i−2i2i−2i1-1−ii00000000000000000000000000000000

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