Finite Group Databasebeta

← Group #13167306

Character table — Group #13167306

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222224444444444444444444444444444888888888812121212121212121212121212121212121212121212121212121212121212121212121218183636363636727272727272108108108108
order1222223666666633336666666666666666666666663666666666444412121212121212121212121212121212121212121212121212121212121212124441212121244121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111
χ51111-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11-111-1-111-1-1
χ61111-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-11-1-111-1-111
χ71111-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-111-1-11-111-1-1-1-111
χ81111-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-111-1-1-11-1-11111-1-1
χ92222222222222222222222222222222222222222222222222222000000000000000000000000000000000000-2-2-2-2-2-2-20000000000
χ10222222-1-1-1-1-1-1-1-122-1-1222-1-1-1-12222-1-1-1-1-1-1-1-12-1-122-122-1-1-1-1-1-1-10000−i3−i3i3i3−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i3-2-2-211110000000000
χ11222222-1-1-1-1-1-1-1-122-1-1222-1-1-1-12222-1-1-1-1-1-1-1-12-1-122-122-1-1-1-1-1-1-10000i3i3−i3−i3i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i3-2-2-211110000000000
χ12222222-1-1-1-1-1-1-1-122-1-1222-1-1-1-12222-1-1-1-1-1-1-1-12-1-122-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-10000000000
χ13222222-1-1-1-1-1-1-1-122-1-1222-1-1-1-12222-1-1-1-1-1-1-1-12-1-122-122-1-1-1-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-211111111222-1-1-1-10000000000
χ142222-2-222-2-2-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2222-2-2-2-2000000000000000000000000000000000000-2-22-2-2220000000000
χ152222-2-2-1-11111-1-122-1-1222-1-1-1-1-2-2-2-2111111112-1-122-1-2-2-1-1-111110000−i3−i3i3i3i3i3−i3−i30000−i3−i3−i3−i3i3i3i3i30000i3i3i3i3−i3−i3−i3−i3-2-2211-1-10000000000
χ162222-2-2-1-11111-1-122-1-1222-1-1-1-1-2-2-2-2111111112-1-122-1-2-2-1-1-111110000i3i3−i3−i3−i3−i3i3i30000i3i3i3i3−i3−i3−i3−i30000−i3−i3−i3−i3i3i3i3i3-2-2211-1-10000000000
χ172222-2-2-1-11111-1-122-1-1222-1-1-1-1-2-2-2-2111111112-1-122-1-2-2-1-1-1111122-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-21111111122-2-1-1110000000000
χ182222-2-2-1-11111-1-122-1-1222-1-1-1-1-2-2-2-2111111112-1-122-1-2-2-1-1-11111-2-2221111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-122-2-1-1110000000000
χ1922-2-22-22222-2-2-2-2222222-222-2-222-2-22222-2-2-2-2-2-2-2-2-222-22-2-222-2-200000000000000000000000000000000000000000000000002−22−2
χ2022-2-22-22222-2-2-2-2222222-222-2-222-2-22222-2-2-2-2-2-2-2-2-222-22-2-222-2-20000000000000000000000000000000000000000000000000−22−22
χ2122-2-2-2222-2-222-2-2222222-222-2-2-2-222-2-2-2-22222-2-2-2-2-22-222-2-2-2-22200000000000000000000000000000000000000000000000002−2−22
χ2222-2-2-2222-2-222-2-2222222-222-2-2-2-222-2-2-2-22222-2-2-2-2-22-222-2-2-2-2220000000000000000000000000000000000000000000000000−222−2
χ232-2-22002-20000-222222-2-22-2-222000000000000-2-2-22-2200-22-20000002i−2i00002i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2-202-2000000000000
χ242-2-22002-20000-222222-2-22-2-222000000000000-2-2-22-2200-22-2000000−2i2i0000−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i2-202-2000000000000
χ252-2-22002-20000-222222-2-22-2-222000000000000-2-2-22-2200-22-200002i−2i002i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000-220-22000000000000
χ262-2-22002-20000-222222-2-22-2-222000000000000-2-2-22-2200-22-20000−2i2i00−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000-220-22000000000000
χ272-2-2200-11−i3i3−i3i31-122-1-1-2-2211-1-10000−i3−i3i3i3−i3−i3i3i3-2112-2-1001-11−i3i3−i3i3002i−2i3−3−33−ii−ii000033−3−3−3−3332i2i−2i−2i−i−iii−i−iii2-20-11−i3i30000000000
χ282-2-2200-11−i3i3−i3i31-122-1-1-2-2211-1-10000−i3−i3i3i3−i3−i3i3i3-2112-2-1001-11−i3i3−i3i300−2i2i−333−3i−ii−i0000−3−33333−3−3−2i−2i2i2iii−i−iii−i−i2-20-11−i3i30000000000
χ292-2-2200-11−i3i3−i3i31-122-1-1-2-2211-1-10000−i3−i3i3i3−i3−i3i3i3-2112-2-1001-11−i3i3−i3i32i−2i00−ii−ii3−3−332i2i−2i−2i−i−iii−i−iii000033−3−3−3−333-2201-1i3−i30000000000
χ302-2-2200-11−i3i3−i3i31-122-1-1-2-2211-1-10000−i3−i3i3i3−i3−i3i3i3-2112-2-1001-11−i3i3−i3i3−2i2i00i−ii−i−333−3−2i−2i2i2iii−i−iii−i−i0000−3−33333−3−3-2201-1i3−i30000000000
χ312-2-2200-11i3−i3i3−i31-122-1-1-2-2211-1-10000i3i3−i3−i3i3i3−i3−i3-2112-2-1001-11i3−i3i3−i3002i−2i−333−3−ii−ii0000−3−33333−3−32i2i−2i−2i−i−iii−i−iii2-20-11i3−i30000000000
χ322-2-2200-11i3−i3i3−i31-122-1-1-2-2211-1-10000i3i3−i3−i3i3i3−i3−i3-2112-2-1001-11i3−i3i3−i300−2i2i3−3−33i−ii−i000033−3−3−3−333−2i−2i2i2iii−i−iii−i−i2-20-11i3−i30000000000
χ332-2-2200-11i3−i3i3−i31-122-1-1-2-2211-1-10000i3i3−i3−i3i3i3−i3−i3-2112-2-1001-11i3−i3i3−i32i−2i00−ii−ii−333−32i2i−2i−2i−i−iii−i−iii0000−3−33333−3−3-2201-1−i3i30000000000
χ342-2-2200-11i3−i3i3−i31-122-1-1-2-2211-1-10000i3i3−i3−i3i3i3−i3−i3-2112-2-1001-11i3−i3i3−i3−2i2i00i−ii−i3−3−33−2i−2i2i2iii−i−iii−i−i000033−3−3−3−333-2201-1−i3i30000000000
χ35444444444444441-2111-211111111111111111111-2-2-2-2-2-2-2-2-2-2-2-2222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000
χ36444444444444441-2111-211111111111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111111111111111111100000000000000000
χ3744444444444444-21-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000000000022-1-1-1-10000
χ3844444444444444-21-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111111110000000000000000000000000000000000000000000-2-211110000
χ39444444-2-2-2-2-2-2-2-21-2−1−3i32−1+3i321-21−1−3i32−1+3i32−1−3i32−1+3i321111−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i321−1−3i32−1+3i32-2-21-2-211111112222−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3200000000000000000
χ40444444-2-2-2-2-2-2-2-21-2−1−3i32−1+3i321-21−1−3i32−1+3i32−1−3i32−1+3i321111−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i321−1−3i32−1+3i32-2-21-2-21111111-2-2-2-21+i31+i31−i31−i31+i31+i31−i31−i31111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3200000000000000000
χ41444444-2-2-2-2-2-2-2-21-2−1+3i32−1−3i321-21−1+3i32−1−3i32−1+3i32−1−3i321111−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i321−1+3i32−1−3i32-2-21-2-211111112222−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3200000000000000000
χ42444444-2-2-2-2-2-2-2-21-2−1+3i32−1−3i321-21−1+3i32−1−3i32−1+3i32−1−3i321111−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i321−1+3i32−1−3i32-2-21-2-21111111-2-2-2-21−i31−i31+i31+i31−i31−i31+i31+i31111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3200000000000000000
χ434444-4-444-4-4-4-4441-2111-211111-1-1-1-1-1-1-1-1-1-1-1-1111-2-2-222-2-2-2222222-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000000000000
χ444444-4-444-4-4-4-4441-2111-211111-1-1-1-1-1-1-1-1-1-1-1-1111-2-2-222-2-2-22222-2-222-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-1-1-1-100000000000000000
χ454444-4-444-4-4-4-444-21-2-2-21-2-2-2-2-2222222222222-2-2-2111-1-1111-1-1-1-100000000000000000000000000000000000000000002-2-1-1110000
χ464444-4-444-4-4-4-444-21-2-2-21-2-2-2-2-2222222222222-2-2-2111-1-1111-1-1-1-10000000000000000000000000000000000000000000-2211-1-10000
χ474444-4-4-2-22222-2-21-2−1−3i32−1+3i321-21−1−3i32−1+3i32−1−3i32−1+3i32-1-1-1-11+3i321−3i321+3i321−3i321+3i321−3i321+3i321−3i321−1−3i32−1+3i32-2-2122111-1-1-1-122-2-2−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3200000000000000000
χ484444-4-4-2-22222-2-21-2−1−3i32−1+3i321-21−1−3i32−1+3i32−1−3i32−1+3i32-1-1-1-11+3i321−3i321+3i321−3i321+3i321−3i321+3i321−3i321−1−3i32−1+3i32-2-2122111-1-1-1-1-2-2221+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i31111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3200000000000000000
χ494444-4-4-2-22222-2-21-2−1+3i32−1−3i321-21−1+3i32−1−3i32−1+3i32−1−3i32-1-1-1-11−3i321+3i321−3i321+3i321−3i321+3i321−3i321+3i321−1+3i32−1−3i32-2-2122111-1-1-1-122-2-2−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3200000000000000000
χ504444-4-4-2-22222-2-21-2−1+3i32−1−3i321-21−1+3i32−1−3i32−1+3i32−1−3i32-1-1-1-11−3i321+3i321−3i321+3i321−3i321+3i321−3i321+3i321−1+3i32−1−3i32-2-2122111-1-1-1-1-2-2221−i31−i31+i31+i3−1+i3−1+i3−1−i3−1−i31111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3200000000000000000
χ5144-4-44-44444-4-4-4-41-2111-2-111-1-111-1-11111-1-1-1-1-1-1-122-2-22-222-2-2220000000000003−33−33−33−33−33−33−33−33−33−33−33−300000000000000000
χ5244-4-44-44444-4-4-4-41-2111-2-111-1-111-1-11111-1-1-1-1-1-1-122-2-22-222-2-222000000000000−33−33−33−33−33−33−33−33−33−33−33−3300000000000000000
χ5344-4-44-44444-4-4-4-4-21-2-2-212-2-222-2-222-2-2-2-22222222-1-111-11-1-111-1-10000000000000000000000000000000000000000000003−33−30000
χ5444-4-44-44444-4-4-4-4-21-2-2-212-2-222-2-222-2-2-2-22222222-1-111-11-1-111-1-1000000000000000000000000000000000000000000000−33−330000
χ5544-4-44-4-2-2-2-222221-2−1−3i32−1+3i321-2-1−1−3i32−1+3i321+3i321−3i3211-1-1−1−3i32−1+3i32−1−3i32−1+3i321+3i321−3i321+3i321−3i32-11+3i321−3i32221-221-1-111-1-10000000000003−33−32ζ14+ζ22−2ζ14−ζ222ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22−ζ14−2ζ22ζ14+2ζ223−33−32ζ14+ζ22−2ζ14−ζ222ζ14+ζ22−2ζ14−ζ22−ζ14−2ζ22ζ14+2ζ22−ζ14−2ζ22ζ14+2ζ2200000000000000000
χ5644-4-44-4-2-2-2-222221-2−1−3i32−1+3i321-2-1−1−3i32−1+3i321+3i321−3i3211-1-1−1−3i32−1+3i32−1−3i32−1+3i321+3i321−3i321+3i321−3i32-11+3i321−3i32221-221-1-111-1-1000000000000−33−33−2ζ14−ζ222ζ14+ζ22−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22ζ14+2ζ22−ζ14−2ζ22−33−33−2ζ14−ζ222ζ14+ζ22−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22ζ14+2ζ22−ζ14−2ζ2200000000000000000
χ5744-4-44-4-2-2-2-222221-2−1+3i32−1−3i321-2-1−1+3i32−1−3i321−3i321+3i3211-1-1−1+3i32−1−3i32−1+3i32−1−3i321−3i321+3i321−3i321+3i32-11−3i321+3i32221-221-1-111-1-10000000000003−33−3−ζ14−2ζ22ζ14+2ζ22−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ222ζ14+ζ22−2ζ14−ζ223−33−3−ζ14−2ζ22ζ14+2ζ22−ζ14−2ζ22ζ14+2ζ222ζ14+ζ22−2ζ14−ζ222ζ14+ζ22−2ζ14−ζ2200000000000000000
χ5844-4-44-4-2-2-2-222221-2−1+3i32−1−3i321-2-1−1+3i32−1−3i321−3i321+3i3211-1-1−1+3i32−1−3i32−1+3i32−1−3i321−3i321+3i321−3i321+3i32-11−3i321+3i32221-221-1-111-1-1000000000000−33−33ζ14+2ζ22−ζ14−2ζ22ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22−2ζ14−ζ222ζ14+ζ22−33−33ζ14+2ζ22−ζ14−2ζ22ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22−2ζ14−ζ222ζ14+ζ2200000000000000000
χ5944-4-44-4-2-2-2-2222244-2-244-4-2-22244-4-4-2-2-2-22222-422-4-4-24-4-222-2-22200000000000000000000000000000000000000000000000000000
χ6044-4-4-4444-4-444-4-41-2111-2-111-1-1-1-111-1-1-1-11111-1-1-122-22-2-22222-2-20000000000003−33−33−33−33−33−3−33−33−33−33−33−3300000000000000000
χ6144-4-4-4444-4-444-4-41-2111-2-111-1-1-1-111-1-1-1-11111-1-1-122-22-2-22222-2-2000000000000−33−33−33−33−33−333−33−33−33−33−33−300000000000000000
χ6244-4-4-4444-4-444-4-4-21-2-2-212-2-22222-2-22222-2-2-2-2222-1-11-111-1-1-1-1110000000000000000000000000000000000000000000003−3−330000
χ6344-4-4-4444-4-444-4-4-21-2-2-212-2-22222-2-22222-2-2-2-2222-1-11-111-1-1-1-111000000000000000000000000000000000000000000000−333−30000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.