Finite Group Databasebeta

← Group #13167302

Character table — Group #13167302

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111222244444444444444448888121212121212121212121212121212121212181836363636363636365454545411112222444444444444444488881212121212121212121212121212121212121818363636363636363654545454
order12223666333366666666666636664412121212121212121212121212121212444412121212121288882222666666666666666666666666441212121212121212121212121212121244441212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1
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
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ51-11-11-1-1111111111-1-1-1-1-1-1-1-111-1-1i−iii−i−iiiiiii−i−i−i−i−i−i-11i−i1-1ii−i−i11-1-11-11-11-1-1111111111-1-1-1-1-1-1-1-111-1-1i−iii−i−iiiiiii−i−i−i−i−i−i-11i−i1-1ii−i−i11-1-1
χ61-11-11-1-1111111111-1-1-1-1-1-1-1-111-1-1i−iii−i−iiiiiii−i−i−i−i−i−i-11−ii1-1−i−iii-1-1111-11-11-1-1111111111-1-1-1-1-1-1-1-111-1-1i−iii−i−iiiiiii−i−i−i−i−i−i-11−ii1-1−i−iii-1-111
χ71-11-11-1-1111111111-1-1-1-1-1-1-1-111-1-1−ii−i−iii−i−i−i−i−i−iiiiiii-11i−i1-1ii−i−i-1-1111-11-11-1-1111111111-1-1-1-1-1-1-1-111-1-1−ii−i−iii−i−i−i−i−i−iiiiiii-11i−i1-1ii−i−i-1-111
χ81-11-11-1-1111111111-1-1-1-1-1-1-1-111-1-1−ii−i−iii−i−i−i−i−i−iiiiiii-11−ii1-1−i−iii11-1-11-11-11-1-1111111111-1-1-1-1-1-1-1-111-1-1−ii−i−iii−i−i−i−i−i−iiiiiii-11−ii1-1−i−iii11-1-1
χ92222222222222222222222222222000000000000000000-2-200-2-2000000002222222222222222222222222222000000000000000000-2-200-2-200000000
χ102222-1-1-1-122-1-122-1-122-1-12-1-12-1-1-1-100−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3-2-20011000000002222-1-1-1-122-1-122-1-122-1-12-1-12-1-1-1-100−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3-2-2001100000000
χ112222-1-1-1-122-1-122-1-122-1-12-1-12-1-1-1-100i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3-2-20011000000002222-1-1-1-122-1-122-1-122-1-12-1-12-1-1-1-100i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3-2-2001100000000
χ122222-1-1-1-122-1-122-1-122-1-12-1-12-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12200-1-1000000002222-1-1-1-122-1-122-1-122-1-12-1-12-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12200-1-100000000
χ132222-1-1-1-122-1-122-1-122-1-12-1-12-1-1-1-1-2-21111-2-21111-2-211112200-1-1000000002222-1-1-1-122-1-122-1-122-1-12-1-12-1-1-1-1-2-21111-2-21111-2-211112200-1-100000000
χ1422-2-222-2-22222-2-2-2-22222-2-2-2-22-22-200000000000000000000000000002−22−222-2-222-2-22222-2-2-2-22222-2-2-2-22-22-200000000000000000000000000002−22−2
χ1522-2-222-2-22222-2-2-2-22222-2-2-2-22-22-20000000000000000000000000000−22−2222-2-222-2-22222-2-2-2-22222-2-2-2-22-22-20000000000000000000000000000−22−22
χ162-22-22-2-2222222222-2-2-2-2-2-2-2-222-2-20000000000000000002-200-22000000002-22-22-2-2222222222-2-2-2-2-2-2-2-222-2-20000000000000000002-200-2200000000
χ172-22-2-111-122-1-122-1-1-2-211-211-2-1-111003−3−330033−3−300−3−3332-2001-1000000002-22-2-111-122-1-122-1-1-2-211-211-2-1-111003−3−330033−3−300−3−3332-2001-100000000
χ182-22-2-111-122-1-122-1-1-2-211-211-2-1-11100−333−300−3−3330033−3−32-2001-1000000002-22-2-111-122-1-122-1-1-2-211-211-2-1-11100−333−300−3−3330033−3−32-2001-100000000
χ192-22-2-111-122-1-122-1-1-2-211-211-2-1-1112i−2i−i−iii2i2i−i−i−i−i−2i−2iiiii-2200-11000000002-22-2-111-122-1-122-1-1-2-211-211-2-1-1112i−2i−i−iii2i2i−i−i−i−i−2i−2iiiii-2200-1100000000
χ202-22-2-111-122-1-122-1-1-2-211-211-2-1-111−2i2iii−i−i−2i−2iiiii2i2i−i−i−i−i-2200-11000000002-22-2-111-122-1-122-1-1-2-211-211-2-1-111−2i2iii−i−i−2i−2iiiii2i2i−i−i−i−i-2200-1100000000
χ212-2-222-22-22222-2-2-2-2-2-2-2-222222-2-2200000000000000000000000000002−2−222-2-222-22-22222-2-2-2-2-2-2-2-222222-2-2200000000000000000000000000002−2−22
χ222-2-222-22-22222-2-2-2-2-2-2-2-222222-2-220000000000000000000000000000−222−22-2-222-22-22222-2-2-2-2-2-2-2-222222-2-220000000000000000000000000000−222−2
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χ24444444441-2111-2111-211111-2-2-2-2-2-2-2-2-2-2-211111111111100000000000000444444441-2111-2111-211111-2-2-2-2-2-2-2-2-2-2-211111111111100000000000000
χ2544444444-21-2-2-21-2-2-21-2-2-2-2-211111000000000000000000002200-1-1-1-1000044444444-21-2-2-21-2-2-21-2-2-2-2-211111000000000000000000002200-1-1-1-10000
χ2644444444-21-2-2-21-2-2-21-2-2-2-2-21111100000000000000000000-2-2001111000044444444-21-2-2-21-2-2-21-2-2-2-2-21111100000000000000000000-2-20011110000
χ274444-2-2-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-2111122−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000004444-2-2-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-2111122−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3200000000000000
χ284444-2-2-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-21111-2-21+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000004444-2-2-2-21-2−1−3i32−1+3i321-2−1−3i32−1+3i321-2−1−3i32−1+3i321−1−3i32−1+3i32-21111-2-21+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3200000000000000
χ294444-2-2-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-2111122−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000000004444-2-2-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-2111122−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3200000000000000
χ304444-2-2-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-21111-2-21−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000004444-2-2-2-21-2−1+3i32−1−3i321-2−1+3i32−1−3i321-2−1+3i32−1−3i321−1+3i32−1−3i32-21111-2-21−i31+i31−i31+i311−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i3200000000000000
χ3144-4-444-4-41-211-12-1-11-211-1-1-12-22-220000003−33−33−33−33−33−30000000000000044-4-444-4-41-211-12-1-11-211-1-1-12-22-220000003−33−33−33−33−33−300000000000000
χ3244-4-444-4-41-211-12-1-11-211-1-1-12-22-22000000−33−33−33−33−33−330000000000000044-4-444-4-41-211-12-1-11-211-1-1-12-22-22000000−33−33−33−33−33−3300000000000000
χ3344-4-444-4-4-21-2-22-122-21-2-2222-11-11-10000000000000000000000003−33−3000044-4-444-4-4-21-2-22-122-21-2-2222-11-11-10000000000000000000000003−33−30000
χ3444-4-444-4-4-21-2-22-122-21-2-2222-11-11-1000000000000000000000000−33−33000044-4-444-4-4-21-2-22-122-21-2-2222-11-11-1000000000000000000000000−33−330000
χ3544-4-4-2-2221-2−1−3i32−1+3i32-121+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i3221-11-10000003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ223−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ220000000000000044-4-4-2-2221-2−1−3i32−1+3i32-121+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i3221-11-10000003−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ223−32ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ2200000000000000
χ3644-4-4-2-2221-2−1−3i32−1+3i32-121+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i3221-11-1000000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ220000000000000044-4-4-2-2221-2−1−3i32−1+3i32-121+3i321−3i321-2−1−3i32−1+3i32-11+3i321−3i3221-11-1000000−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22−33−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ2200000000000000
χ3744-4-4-2-2221-2−1+3i32−1−3i32-121−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i3221-11-10000003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ223−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ220000000000000044-4-4-2-2221-2−1+3i32−1−3i32-121−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i3221-11-10000003−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ223−3−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ2200000000000000
χ3844-4-4-2-2221-2−1+3i32−1−3i32-121−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i3221-11-1000000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ220000000000000044-4-4-2-2221-2−1+3i32−1−3i32-121−3i321+3i321-2−1+3i32−1−3i32-11−3i321+3i3221-11-1000000−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22−33ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ2200000000000000
χ3944-4-4-2-22244-2-2-4-42244-2-2-422-4-22-220000000000000000000000000000000044-4-4-2-22244-2-2-4-42244-2-2-422-4-22-2200000000000000000000000000000000
χ404-44-44-4-441-2111-211-12-1-1-1-1-12-2-2222i−2i2i2i−2i−2i−i−i−i−i−i−iiiiiii000000000000004-44-44-4-441-2111-211-12-1-1-1-1-12-2-2222i−2i2i2i−2i−2i−i−i−i−i−i−iiiiiii00000000000000
χ414-44-44-4-441-2111-211-12-1-1-1-1-12-2-222−2i2i−2i−2i2i2iiiiiii−i−i−i−i−i−i000000000000004-44-44-4-441-2111-211-12-1-1-1-1-12-2-222−2i2i−2i−2i2i2iiiiiii−i−i−i−i−i−i00000000000000
χ424-44-44-4-44-21-2-2-21-2-22-122222-111-1-1000000000000000000002i−2i00−i−iii00004-44-44-4-44-21-2-2-21-2-22-122222-111-1-1000000000000000000002i−2i00−i−iii0000
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χ444-44-4-222-21-2−1−3i32−1+3i321-2−1−3i32−1+3i32-121+3i321−3i32-11+3i321−3i32211-1-12i−2i2ζ222ζ14−2ζ22−2ζ14−i−i−ζ22−ζ22−ζ14−ζ14iiζ22ζ22ζ14ζ14000000000000004-44-4-222-21-2−1−3i32−1+3i321-2−1−3i32−1+3i32-121+3i321−3i32-11+3i321−3i32211-1-12i−2i2ζ222ζ14−2ζ22−2ζ14−i−i−ζ22−ζ22−ζ14−ζ14iiζ22ζ22ζ14ζ1400000000000000
χ454-44-4-222-21-2−1−3i32−1+3i321-2−1−3i32−1+3i32-121+3i321−3i32-11+3i321−3i32211-1-1−2i2i−2ζ22−2ζ142ζ222ζ14iiζ22ζ22ζ14ζ14−i−i−ζ22−ζ22−ζ14−ζ14000000000000004-44-4-222-21-2−1−3i32−1+3i321-2−1−3i32−1+3i32-121+3i321−3i32-11+3i321−3i32211-1-1−2i2i−2ζ22−2ζ142ζ222ζ14iiζ22ζ22ζ14ζ14−i−i−ζ22−ζ22−ζ14−ζ1400000000000000
χ464-44-4-222-21-2−1+3i32−1−3i321-2−1+3i32−1−3i32-121−3i321+3i32-11−3i321+3i32211-1-12i−2i2ζ142ζ22−2ζ14−2ζ22−i−i−ζ14−ζ14−ζ22−ζ22iiζ14ζ14ζ22ζ22000000000000004-44-4-222-21-2−1+3i32−1−3i321-2−1+3i32−1−3i32-121−3i321+3i32-11−3i321+3i32211-1-12i−2i2ζ142ζ22−2ζ14−2ζ22−i−i−ζ14−ζ14−ζ22−ζ22iiζ14ζ14ζ22ζ2200000000000000
χ474-44-4-222-21-2−1+3i32−1−3i321-2−1+3i32−1−3i32-121−3i321+3i32-11−3i321+3i32211-1-1−2i2i−2ζ14−2ζ222ζ142ζ22iiζ14ζ14ζ22ζ22−i−i−ζ14−ζ14−ζ22−ζ22000000000000004-44-4-222-21-2−1+3i32−1−3i321-2−1+3i32−1−3i32-121−3i321+3i32-11−3i321+3i32211-1-1−2i2i−2ζ14−2ζ222ζ142ζ22iiζ14ζ14ζ22ζ22−i−i−ζ14−ζ14−ζ22−ζ2200000000000000
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χ534-4-44-22-221-2−1−3i32−1+3i32-121+3i321−3i32-121+3i321−3i321−1−3i32−1+3i32-21-1-11000000i3−i33−i32−3+i32−3−i323+i32−i3i3−3+i323−i323+i32−3−i32000000000000004-4-44-22-221-2−1−3i32−1+3i32-121+3i321−3i32-121+3i321−3i321−1−3i32−1+3i32-21-1-11000000i3−i33−i32−3+i32−3−i323+i32−i3i3−3+i323−i323+i32−3−i3200000000000000
χ544-4-44-22-221-2−1+3i32−1−3i32-121−3i321+3i32-121−3i321+3i321−1+3i32−1−3i32-21-1-11000000−i3i33+i32−3−i32−3+i323−i32i3−i3−3−i323+i323−i32−3+i32000000000000004-4-44-22-221-2−1+3i32−1−3i32-121−3i321+3i32-121−3i321+3i321−1+3i32−1−3i32-21-1-11000000−i3i33+i32−3−i32−3+i323−i32i3−i3−3−i323+i323−i32−3+i3200000000000000
χ554-4-44-22-221-2−1+3i32−1−3i32-121−3i321+3i32-121−3i321+3i321−1+3i32−1−3i32-21-1-11000000i3−i3−3−i323+i323−i32−3+i32−i3i33+i32−3−i32−3+i323−i32000000000000004-4-44-22-221-2−1+3i32−1−3i32-121−3i321+3i32-121−3i321+3i321−1+3i32−1−3i32-21-1-11000000i3−i3−3−i323+i323−i32−3+i32−i3i33+i32−3−i32−3+i323−i3200000000000000
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χ1164-4-44-22-2244-2-2-4-422-4-4224-2-24-222-200000000000000000000000000000000-444-42-22-2-4-42244-2-244-2-2-422-42-2-2200000000000000000000000000000000
χ1178888-4-4-4-4-4222-4222-4222-4222-1-1-1-100000000000000000000000000000000-8-8-8-844444-2-2-24-2-2-24-2-2-24-2-2-2111100000000000000000000000000000000
χ11888-8-8-4-444-42224-2-2-2-42224-2-2-2-11-1100000000000000000000000000000000-8-88844-4-44-2-2-2-42224-2-2-2-42221-11-100000000000000000000000000000000
χ1198-88-8-444-4-4222-42224-2-2-24-2-2-2-1-11100000000000000000000000000000000-88-884-4-444-2-2-24-2-2-2-4222-422211-1-100000000000000000000000000000000
χ1208-8-88-44-44-42224-2-2-24-2-2-2-4222-111-100000000000000000000000000000000-888-84-44-44-2-2-2-4222-42224-2-2-21-1-1100000000000000000000000000000000

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