Finite Group Databasebeta

← Group #13167279

Character table — Group #13167279

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111222244444444444444448888121212121212121212121212121212121212181836363636363636365454545411112222444444444444444488881212121212121212121212121212121212121818363636363636363654545454
order122236663333666666666666366622666666666666666644441212121212128888222266666666666666666666666622666666666666666644441212121212128888
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
χ51-11-11-1-1111111-1111-1-1-1-1-1-1-111-1-11-111-1-1111111-1-1-1-1-1-11-1i−i1-1ii−i−iii−i−i1-11-11-1-1111111-1111-1-1-1-1-1-1-111-1-11-111-1-1111111-1-1-1-1-1-11-1i−i1-1ii−i−iii−i−i
χ61-11-11-1-1111111-1111-1-1-1-1-1-1-111-1-11-111-1-1111111-1-1-1-1-1-11-1−ii1-1−i−iii−i−iii1-11-11-1-1111111-1111-1-1-1-1-1-1-111-1-11-111-1-1111111-1-1-1-1-1-11-1−ii1-1−i−iii−i−iii
χ71-11-11-1-1111111-1111-1-1-1-1-1-1-111-1-1-11-1-111-1-1-1-1-1-11111111-1i−i1-1ii−i−i−i−iii1-11-11-1-1111111-1111-1-1-1-1-1-1-111-1-1-11-1-111-1-1-1-1-1-11111111-1i−i1-1ii−i−i−i−iii
χ81-11-11-1-1111111-1111-1-1-1-1-1-1-111-1-1-11-1-111-1-1-1-1-1-11111111-1−ii1-1−i−iiiii−i−i1-11-11-1-1111111-1111-1-1-1-1-1-1-111-1-1-11-1-111-1-1-1-1-1-11111111-1−ii1-1−i−iiiii−i−i
χ92222222222222222222222222222000000000000000000-2-200-2-2000000002222222222222222222222222222000000000000000000-2-200-2-200000000
χ102222-1-1-1-122-1-1222-1-122-1-1-1-12-1-1-1-100−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3-2-20011000000002222-1-1-1-122-1-1222-1-122-1-1-1-12-1-1-1-100−i3i3−i3i300−i3−i3i3i300−i3−i3i3i3-2-2001100000000
χ112222-1-1-1-122-1-1222-1-122-1-1-1-12-1-1-1-100i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3-2-20011000000002222-1-1-1-122-1-1222-1-122-1-1-1-12-1-1-1-100i3−i3i3−i300i3i3−i3−i300i3i3−i3−i3-2-2001100000000
χ122222-1-1-1-122-1-1222-1-122-1-1-1-12-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12200-1-1000000002222-1-1-1-122-1-1222-1-122-1-1-1-12-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12200-1-100000000
χ132222-1-1-1-122-1-1222-1-122-1-1-1-12-1-1-1-1-2-21111-2-21111-2-211112200-1-1000000002222-1-1-1-122-1-1222-1-122-1-1-1-12-1-1-1-1-2-21111-2-21111-2-211112200-1-100000000
χ1422-2-222-2-22222-22-2-2-22-222-2-2-22-22-20000000000000000000000000000−i2i2−i2i222-2-222-2-22222-22-2-2-22-222-2-2-22-22-20000000000000000000000000000−i2i2−i2i2
χ1522-2-222-2-22222-22-2-2-22-222-2-2-22-22-20000000000000000000000000000i2−i2i2−i222-2-222-2-22222-22-2-2-22-222-2-2-22-22-20000000000000000000000000000i2−i2i2−i2
χ162-22-22-2-2222222-2222-2-2-2-2-2-2-222-2-2000000000000000000-2200-22000000002-22-22-2-2222222-2222-2-2-2-2-2-2-222-2-2000000000000000000-2200-2200000000
χ172-22-2-111-122-1-12-22-1-1-2-21111-2-1-11100−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3-22001-1000000002-22-2-111-122-1-12-22-1-1-2-21111-2-1-11100−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3-22001-100000000
χ182-22-2-111-122-1-12-22-1-1-2-21111-2-1-11100i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3-22001-1000000002-22-2-111-122-1-12-22-1-1-2-21111-2-1-11100i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3-22001-100000000
χ192-22-2-111-122-1-12-22-1-1-2-21111-2-1-1112-2-1-11122-1-1-1-1-2-211112-200-11000000002-22-2-111-122-1-12-22-1-1-2-21111-2-1-1112-2-1-11122-1-1-1-1-2-211112-200-1100000000
χ202-22-2-111-122-1-12-22-1-1-2-21111-2-1-111-2211-1-1-2-2111122-1-1-1-12-200-11000000002-22-2-111-122-1-12-22-1-1-2-21111-2-1-111-2211-1-1-2-2111122-1-1-1-12-200-1100000000
χ212-2-222-22-22222-2-2-2-2-2-22-2-22222-2-2200000000000000000000000000002−2−222-2-222-22-22222-2-2-2-2-2-22-2-22222-2-2200000000000000000000000000002−2−22
χ222-2-222-22-22222-2-2-2-2-2-22-2-22222-2-220000000000000000000000000000−222−22-2-222-22-22222-2-2-2-2-2-22-2-22222-2-220000000000000000000000000000−222−2
χ23444444441-2-2-211-2-2-2-2-2-2-2-2-211111000000000000000000002200-1-1-1-10000444444441-2-2-211-2-2-2-2-2-2-2-2-211111000000000000000000002200-1-1-1-10000
χ24444444441-2-2-211-2-2-2-2-2-2-2-2-21111100000000000000000000-2-20011110000444444441-2-2-211-2-2-2-2-2-2-2-2-21111100000000000000000000-2-20011110000
χ2544444444-2111-2-2111111111-2-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-10000000000000044444444-2111-2-2111111111-2-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ2644444444-2111-2-2111111111-2-2-2-2-2-2-2-2-2-2-21111111111110000000000000044444444-2111-2-2111111111-2-2-2-2-2-2-2-2-2-2-211111111111100000000000000
χ274444-2-2-2-2-21−1−3i32−1+3i32-2-21−1−3i32−1+3i3211−1−3i32−1+3i32−1−3i32−1+3i32-2111122−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000004444-2-2-2-2-21−1−3i32−1+3i32-2-21−1−3i32−1+3i3211−1−3i32−1+3i32−1−3i32−1+3i32-2111122−1−i3−1+i3−1−i3−1+i3-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i3200000000000000
χ284444-2-2-2-2-21−1−3i32−1+3i32-2-21−1−3i32−1+3i3211−1−3i32−1+3i32−1−3i32−1+3i32-21111-2-21+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000004444-2-2-2-2-21−1−3i32−1+3i32-2-21−1−3i32−1+3i3211−1−3i32−1+3i32−1−3i32−1+3i32-21111-2-21+i31−i31+i31−i311−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i3200000000000000
χ294444-2-2-2-2-21−1+3i32−1−3i32-2-21−1+3i32−1−3i3211−1+3i32−1−3i32−1+3i32−1−3i32-2111122−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000000004444-2-2-2-2-21−1+3i32−1−3i32-2-21−1+3i32−1−3i3211−1+3i32−1−3i32−1+3i32−1−3i32-2111122−1+i3−1−i3−1+i3−1−i3-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i3200000000000000
χ304444-2-2-2-2-21−1+3i32−1−3i32-2-21−1+3i32−1−3i3211−1+3i32−1−3i32−1+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−i32000000000000004444-2-2-2-2-21−1+3i32−1−3i32-2-21−1+3i32−1−3i3211−1+3i32−1−3i32−1+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
χ3144-4-444-4-41-2-2-2-11222-22-2-222-11-11-10000000000000000000000003−33−3000044-4-444-4-41-2-2-2-11222-22-2-222-11-11-10000000000000000000000003−33−30000
χ3244-4-444-4-41-2-2-2-11222-22-2-222-11-11-1000000000000000000000000−33−33000044-4-444-4-41-2-2-2-11222-22-2-222-11-11-1000000000000000000000000−33−330000
χ3344-4-444-4-4-21112-2-1-1-11-111-1-12-22-22000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000000000000044-4-444-4-4-21112-2-1-1-11-111-1-12-22-22000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300000000000000
χ3444-4-444-4-4-21112-2-1-1-11-111-1-12-22-22000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000000000000044-4-444-4-4-21112-2-1-1-11-111-1-12-22-22000000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300000000000000
χ3544-4-4-2-22244-2-2-44-4224-4-2-222-4-22-220000000000000000000000000000000044-4-4-2-22244-2-2-44-4224-4-2-222-4-22-2200000000000000000000000000000000
χ3644-4-4-2-222-21−1−3i32−1+3i322-2-11+3i321−3i321-1−1−3i32−1+3i321+3i321−3i3221-11-1000000−i3i3−3+i323−i323+i32−3−i32−i3i3−3+i323−i323+i32−3−i320000000000000044-4-4-2-222-21−1−3i32−1+3i322-2-11+3i321−3i321-1−1−3i32−1+3i321+3i321−3i3221-11-1000000−i3i3−3+i323−i323+i32−3−i32−i3i3−3+i323−i323+i32−3−i3200000000000000
χ3744-4-4-2-222-21−1−3i32−1+3i322-2-11+3i321−3i321-1−1−3i32−1+3i321+3i321−3i3221-11-1000000i3−i33−i32−3+i32−3−i323+i32i3−i33−i32−3+i32−3−i323+i320000000000000044-4-4-2-222-21−1−3i32−1+3i322-2-11+3i321−3i321-1−1−3i32−1+3i321+3i321−3i3221-11-1000000i3−i33−i32−3+i32−3−i323+i32i3−i33−i32−3+i32−3−i323+i3200000000000000
χ3844-4-4-2-222-21−1+3i32−1−3i322-2-11−3i321+3i321-1−1+3i32−1−3i321−3i321+3i3221-11-1000000−i3i33+i32−3−i32−3+i323−i32−i3i33+i32−3−i32−3+i323−i320000000000000044-4-4-2-222-21−1+3i32−1−3i322-2-11−3i321+3i321-1−1+3i32−1−3i321−3i321+3i3221-11-1000000−i3i33+i32−3−i32−3+i323−i32−i3i33+i32−3−i32−3+i323−i3200000000000000
χ3944-4-4-2-222-21−1+3i32−1−3i322-2-11−3i321+3i321-1−1+3i32−1−3i321−3i321+3i3221-11-1000000i3−i3−3−i323+i323−i32−3+i32i3−i3−3−i323+i323−i32−3+i320000000000000044-4-4-2-222-21−1+3i32−1−3i322-2-11−3i321+3i321-1−1+3i32−1−3i321−3i321+3i3221-11-1000000i3−i3−3−i323+i323−i32−3+i32i3−i3−3−i323+i323−i32−3+i3200000000000000
χ404-44-44-4-441-2-2-21-1-2-2-2222222-111-1-1000000000000000000002i−2i00−i−iii00004-44-44-4-441-2-2-21-1-2-2-2222222-111-1-1000000000000000000002i−2i00−i−iii0000
χ414-44-44-4-441-2-2-21-1-2-2-2222222-111-1-100000000000000000000−2i2i00ii−i−i00004-44-44-4-441-2-2-21-1-2-2-2222222-111-1-100000000000000000000−2i2i00ii−i−i0000
χ424-44-44-4-44-2111-22111-1-1-1-1-1-12-2-2222-222-2-2-1-1-1-1-1-1111111000000000000004-44-44-4-44-2111-22111-1-1-1-1-1-12-2-2222-222-2-2-1-1-1-1-1-111111100000000000000
χ434-44-44-4-44-2111-22111-1-1-1-1-1-12-2-222-22-2-222111111-1-1-1-1-1-1000000000000004-44-44-4-44-2111-22111-1-1-1-1-1-12-2-222-22-2-222111111-1-1-1-1-1-100000000000000
χ444-44-4-222-2-21−1−3i32−1+3i32-221−1−3i32−1+3i32-1-11+3i321−3i321+3i321−3i32211-1-12-2−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000004-44-4-222-2-21−1−3i32−1+3i32-221−1−3i32−1+3i32-1-11+3i321−3i321+3i321−3i32211-1-12-2−1−i3−1+i31+i31−i3-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i3200000000000000
χ454-44-4-222-2-21−1−3i32−1+3i32-221−1−3i32−1+3i32-1-11+3i321−3i321+3i321−3i32211-1-1-221+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000004-44-4-222-2-21−1−3i32−1+3i32-221−1−3i32−1+3i32-1-11+3i321−3i321+3i321−3i32211-1-1-221+i31−i3−1−i3−1+i311−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i3200000000000000
χ464-44-4-222-2-21−1+3i32−1−3i32-221−1+3i32−1−3i32-1-11−3i321+3i321−3i321+3i32211-1-12-2−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000004-44-4-222-2-21−1+3i32−1−3i32-221−1+3i32−1−3i32-1-11−3i321+3i321−3i321+3i32211-1-12-2−1+i3−1−i31−i31+i3-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i3200000000000000
χ474-44-4-222-2-21−1+3i32−1−3i32-221−1+3i32−1−3i32-1-11−3i321+3i321−3i321+3i32211-1-1-221−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000004-44-4-222-2-21−1+3i32−1−3i32-221−1+3i32−1−3i32-1-11−3i321+3i321−3i321+3i32211-1-1-221−i31+i3−1+i3−1−i311−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i3200000000000000
χ484-4-444-44-41-2-2-2-1-12222-222-2-211-1-11000000000000000000000000−i3i3i3−i300004-4-444-44-41-2-2-2-1-12222-222-2-211-1-11000000000000000000000000−i3i3i3−i30000
χ494-4-444-44-41-2-2-2-1-12222-222-2-211-1-11000000000000000000000000i3−i3−i3i300004-4-444-44-41-2-2-2-1-12222-222-2-211-1-11000000000000000000000000i3−i3−i3i30000
χ504-4-444-44-4-211122-1-1-1-11-1-111-2-222-2000000−i3i3−i3i3−i3i3i3−i3i3−i3i3−i3000000000000004-4-444-44-4-211122-1-1-1-11-1-111-2-222-2000000−i3i3−i3i3−i3i3i3−i3i3−i3i3−i300000000000000
χ514-4-444-44-4-211122-1-1-1-11-1-111-2-222-2000000i3−i3i3−i3i3−i3−i3i3−i3i3−i3i3000000000000004-4-444-44-4-211122-1-1-1-11-1-111-2-222-2000000i3−i3i3−i3i3−i3−i3i3−i3i3−i3i300000000000000
χ524-4-44-22-2244-2-2-4-4-422-4422-2-24-222-2000000000000000000000000000000004-4-44-22-2244-2-2-4-4-422-4422-2-24-222-200000000000000000000000000000000
χ534-4-44-22-22-21−1−3i32−1+3i3222-11+3i321−3i32-111+3i321−3i32−1−3i32−1+3i32-21-1-11000000−i3i3−3+i323−i323+i32−3−i32i3−i33−i32−3+i32−3−i323+i32000000000000004-4-44-22-22-21−1−3i32−1+3i3222-11+3i321−3i32-111+3i321−3i32−1−3i32−1+3i32-21-1-11000000−i3i3−3+i323−i323+i32−3−i32i3−i33−i32−3+i32−3−i323+i3200000000000000
χ544-4-44-22-22-21−1−3i32−1+3i3222-11+3i321−3i32-111+3i321−3i32−1−3i32−1+3i32-21-1-11000000i3−i33−i32−3+i32−3−i323+i32−i3i3−3+i323−i323+i32−3−i32000000000000004-4-44-22-22-21−1−3i32−1+3i3222-11+3i321−3i32-111+3i321−3i32−1−3i32−1+3i32-21-1-11000000i3−i33−i32−3+i32−3−i323+i32−i3i3−3+i323−i323+i32−3−i3200000000000000
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χ1144-4-44-22-22-21−1−3i32−1+3i3222-11+3i321−3i32-111+3i321−3i32−1−3i32−1+3i32-21-1-11000000i3−i33−i32−3+i32−3−i323+i32−i3i3−3+i323−i323+i32−3−i3200000000000000-444-42-22-22-11+3i321−3i32-2-21−1−3i32−1+3i321-1−1−3i32−1+3i321+3i321−3i322-111-1000000−i3i3−3+i323−i323+i32−3−i32i3−i33−i32−3+i32−3−i323+i3200000000000000
χ1154-4-44-22-22-21−1+3i32−1−3i3222-11−3i321+3i32-111−3i321+3i32−1+3i32−1−3i32-21-1-11000000−i3i33+i32−3−i32−3+i323−i32i3−i3−3−i323+i323−i32−3+i3200000000000000-444-42-22-22-11−3i321+3i32-2-21−1+3i32−1−3i321-1−1+3i32−1−3i321−3i321+3i322-111-1000000i3−i3−3−i323+i323−i32−3+i32−i3i33+i32−3−i32−3+i323−i3200000000000000
χ1164-4-44-22-22-21−1+3i32−1−3i3222-11−3i321+3i32-111−3i321+3i32−1+3i32−1−3i32-21-1-11000000i3−i3−3−i323+i323−i32−3+i32−i3i33+i32−3−i32−3+i323−i3200000000000000-444-42-22-22-11−3i321+3i32-2-21−1+3i32−1−3i321-1−1+3i32−1−3i321−3i321+3i322-111-1000000−i3i33+i32−3−i32−3+i323−i32i3−i3−3−i323+i323−i32−3+i3200000000000000
χ1178888-4-4-4-42-42222-422-4-422222-1-1-1-100000000000000000000000000000000-8-8-8-84444-24-2-2-2-24-2-244-2-2-2-2-2111100000000000000000000000000000000
χ11888-8-8-4-4442-422-224-2-2-4422-2-2-2-11-1100000000000000000000000000000000-8-88844-4-4-24-2-22-2-4224-4-2-22221-11-100000000000000000000000000000000
χ1198-88-8-444-42-4222-2-42244-2-2-2-2-2-1-11100000000000000000000000000000000-88-884-4-44-24-2-2-224-2-2-4-42222211-1-100000000000000000000000000000000
χ1208-8-88-44-442-422-2-24-2-24-4-2-2222-111-100000000000000000000000000000000-888-84-44-4-24-2-222-422-4422-2-2-21-1-1100000000000000000000000000000000

Here i is the imaginary unit (i² = −1).