Finite Group Databasebeta

← Group #13167072

Character table — Group #13167072

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size111122222222224444444444444444444444444444888888888812121212121212121212121212121212121212121212121212121212121212121212121218183636363636727272727272108108108108
order12223446661212121233336666666666661212121212121212121212123666121212121212444412121212121212121212121212121212121212121212121212121212121212124441212121244121212128888
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
χ511111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11-1-1-11111-1-1
χ611111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1111-1-1-1-111
χ711111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-111-1-11-1-1-111-1-111
χ811111-1-1111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-111-1-1-1111-1-111-1-1
χ92222222222222222222222222222222222222222222222222222000000000000000000000000000000000000-2-2-2-2-2-2-20000000000
χ1022222-2-2222-2-2-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000-2-22-2-2220000000000
χ112222-122-1-1-1-1-1-1-122-1-122-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000−i3−i3i3i3−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i30000−i3−i3−i3−i3i3i3i3i3-2-2-211110000000000
χ122222-122-1-1-1-1-1-1-122-1-122-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000i3i3−i3−i3i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i30000i3i3i3i3−i3−i3−i3−i3-2-2-211110000000000
χ132222-122-1-1-1-1-1-1-122-1-122-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-10000000000
χ142222-122-1-1-1-1-1-1-122-1-122-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211111111-2-2-2-211111111-2-2-2-211111111222-1-1-1-10000000000
χ152222-1-2-2-1-1-1111122-1-122-1-122-1-1-1-122-2-2-2-211111111-1-1-1-1-2-211110000−i3−i3i3i3i3i3−i3−i30000−i3−i3−i3−i3i3i3i3i30000i3i3i3i3−i3−i3−i3−i3-2-2211-1-10000000000
χ162222-1-2-2-1-1-1111122-1-122-1-122-1-1-1-122-2-2-2-211111111-1-1-1-1-2-211110000i3i3−i3−i3−i3−i3i3i30000i3i3i3i3−i3−i3−i3−i30000−i3−i3−i3−i3i3i3i3i3-2-2211-1-10000000000
χ172222-1-2-2-1-1-1111122-1-122-1-122-1-1-1-122-2-2-2-211111111-1-1-1-1-2-2111122-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-21111111122-2-1-1110000000000
χ182222-1-2-2-1-1-1111122-1-122-1-122-1-1-1-122-2-2-2-211111111-1-1-1-1-2-21111-2-2221111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-122-2-1-1110000000000
χ1922-2-2200-22-2000022222-2-2-22-222-2-2-2-200000000000022-2-2000000002i−2i00002i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i-2202-2000000000000
χ2022-2-2200-22-2000022222-2-2-22-222-2-2-2-200000000000022-2-200000000−2i2i0000−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i-2202-2000000000000
χ2122-2-2200-22-2000022222-2-2-22-222-2-2-2-200000000000022-2-20000002-2002-22-2000022-2-222-2-222-2-20000000000002-20-22000000000000
χ2222-2-2200-22-2000022222-2-2-22-222-2-2-2-200000000000022-2-2000000-2200-22-220000-2-222-2-222-2-2220000000000002-20-22000000000000
χ2322-2-2-1001-1133−3−322-1-12-2112-2-1-111-2-200003333−3−3−3−3-1-1110033−3−3002i−2i−i3i3i3−i3−ii−ii0000−i3−i3i3i3i3i3−i3−i32i2i−2i−2i−i−iii−i−iii-220-113−30000000000
χ2422-2-2-1001-1133−3−322-1-12-2112-2-1-111-2-200003333−3−3−3−3-1-1110033−3−300−2i2ii3−i3−i3i3i−ii−i0000i3i3−i3−i3−i3−i3i3i3−2i−2i2i2iii−i−iii−i−i-220-113−30000000000
χ2522-2-2-1001-1133−3−322-1-12-2112-2-1-111-2-200003333−3−3−3−3-1-1110033−3−32-200-11-113−3−3322-2-2-1-111-1-111000033−3−3−3−3332-201-1−330000000000
χ2622-2-2-1001-1133−3−322-1-12-2112-2-1-111-2-200003333−3−3−3−3-1-1110033−3−3-22001-11-1−333−3-2-22211-1-111-1-10000−3−33333−3−32-201-1−330000000000
χ2722-2-2-1001-11−3−33322-1-12-2112-2-1-111-2-20000−3−3−3−33333-1-11100−3−333002i−2ii3−i3−i3i3−ii−ii0000i3i3−i3−i3−i3−i3i3i32i2i−2i−2i−i−iii−i−iii-220-11−330000000000
χ2822-2-2-1001-11−3−33322-1-12-2112-2-1-111-2-20000−3−3−3−33333-1-11100−3−33300−2i2i−i3i3i3−i3i−ii−i0000−i3−i3i3i3i3i3−i3−i3−2i−2i2i2iii−i−iii−i−i-220-11−330000000000
χ2922-2-2-1001-11−3−33322-1-12-2112-2-1-111-2-20000−3−3−3−33333-1-11100−3−3332-200-11-11−333−322-2-2-1-111-1-1110000−3−33333−3−32-201-13−30000000000
χ3022-2-2-1001-11−3−33322-1-12-2112-2-1-111-2-20000−3−3−3−33333-1-11100−3−333-22001-11-13−3−33-2-22211-1-111-1-1000033−3−3−3−3332-201-13−30000000000
χ312-2-2222i−2i-2-222i−2i2i−2i2222-2-2-2-2-22-2-2222-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2-22-22i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000002−2−i2i2
χ322-2-2222i−2i-2-222i−2i2i−2i2222-2-2-2-2-22-2-2222-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2-22-22i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000−22i2−i2
χ332-2-222−2i2i-2-22−2i2i−2i2i2222-2-2-2-2-22-2-2222-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i2-22-2−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000000002−2i2−i2
χ342-2-222−2i2i-2-22−2i2i−2i2i2222-2-2-2-2-22-2-2222-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i2-22-2−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000−22−i2i2
χ35444444444444441-211-2111111111-2-2111111111111-2-2-2-2-2-2-2-2-2-2222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000
χ36444444444444441-211-2111111111-2-2111111111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111111111111111111100000000000000000
χ3744444444444444-21-2-21-2-2-2-2-2-2-2-2-211-2-2-2-2-2-2-2-2-2-2-2-21111111111000000000000000000000000000000000000000000022-1-1-1-10000
χ3844444444444444-21-2-21-2-2-2-2-2-2-2-2-211-2-2-2-2-2-2-2-2-2-2-2-211111111110000000000000000000000000000000000000000000-2-211110000
χ3944444-4-4444-4-4-4-41-211-2111111111-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222222222-2-22222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111100000000000000000
χ4044444-4-4444-4-4-4-41-211-2111111111-2-2-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222222-2-222-2-2-2-22222111111111111-1-1-1-1-1-1-1-1-1-1-1-100000000000000000
χ4144444-4-4444-4-4-4-4-21-2-21-2-2-2-2-2-2-2-2-2112222222222221111-1-1-1-1-1-100000000000000000000000000000000000000000002-211-1-10000
χ4244444-4-4444-4-4-4-4-21-2-21-2-2-2-2-2-2-2-2-2112222222222221111-1-1-1-1-1-10000000000000000000000000000000000000000000-22-1-1110000
χ434444-244-2-2-2-2-2-2-21-2−1−3i32−1+3i32-21−1−3i32−1+3i3211−1−3i32−1+3i32−1−3i32−1+3i32-2-21111−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i321111-2-211112222−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i3200000000000000000
χ444444-244-2-2-2-2-2-2-21-2−1−3i32−1+3i32-21−1−3i32−1+3i3211−1−3i32−1+3i32−1−3i32−1+3i32-2-21111−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i321111-2-21111-2-2-2-21+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
χ454444-244-2-2-2-2-2-2-21-2−1+3i32−1−3i32-21−1+3i32−1−3i3211−1+3i32−1−3i32−1+3i32−1−3i32-2-21111−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i321111-2-211112222−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i3200000000000000000
χ464444-244-2-2-2-2-2-2-21-2−1+3i32−1−3i32-21−1+3i32−1−3i3211−1+3i32−1−3i32−1+3i32−1−3i32-2-21111−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i32−1+3i32−1−3i321111-2-21111-2-2-2-21−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
χ474444-2-4-4-2-2-222221-2−1−3i32−1+3i32-21−1−3i32−1+3i3211−1−3i32−1+3i32−1−3i32−1+3i32-2-2-1-1-1-11+3i321−3i321+3i321−3i321+3i321−3i321+3i321−3i32111122-1-1-1-122-2-2−1−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
χ484444-2-4-4-2-2-222221-2−1−3i32−1+3i32-21−1−3i32−1+3i3211−1−3i32−1+3i32−1−3i32−1+3i32-2-2-1-1-1-11+3i321−3i321+3i321−3i321+3i321−3i321+3i321−3i32111122-1-1-1-1-2-2221+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
χ494444-2-4-4-2-2-222221-2−1+3i32−1−3i32-21−1+3i32−1−3i3211−1+3i32−1−3i32−1+3i32−1−3i32-2-2-1-1-1-11−3i321+3i321−3i321+3i321−3i321+3i321−3i321+3i32111122-1-1-1-122-2-2−1+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
χ504444-2-4-4-2-2-222221-2−1+3i32−1−3i32-21−1+3i32−1−3i3211−1+3i32−1−3i32−1+3i32−1−3i32-2-2-1-1-1-11−3i321+3i321−3i321+3i321−3i321+3i321−3i321+3i32111122-1-1-1-1-2-2221−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
χ5144-4-4400-44-400001-211-2-1-1-11-111-1-1223i−3i3i−3i3i−3i3i−3i−3i3i−3i3i-2-2220000002-22i−2i2-22-22i−2i2i−2i-1-111-1-111-1-111−i−iii−i−iii−i−iii00000000000000000
χ5244-4-4400-44-400001-211-2-1-1-11-111-1-1223i−3i3i−3i3i−3i3i−3i−3i3i−3i3i-2-222000000-22−2i2i-22-22−2i2i−2i2i11-1-111-1-111-1-1ii−i−iii−i−iii−i−i00000000000000000
χ5344-4-4400-44-400001-211-2-1-1-11-111-1-122−3i3i−3i3i−3i3i−3i3i3i−3i3i−3i-2-2220000002-2−2i2i2-22-2−2i2i−2i2i-1-111-1-111-1-111ii−i−iii−i−iii−i−i00000000000000000
χ5444-4-4400-44-400001-211-2-1-1-11-111-1-122−3i3i−3i3i−3i3i−3i3i3i−3i3i−3i-2-222000000-222i−2i-22-222i−2i2i−2i11-1-111-1-111-1-1−i−iii−i−iii−i−iii00000000000000000
χ5544-4-4-2002-222323−23−231-2−1−3i32−1+3i32-2-11+3i321−3i321-1−1−3i32−1+3i321+3i321−3i32223i−3i3i−3iζ14+2ζ22−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22−ζ14−2ζ222ζ14+ζ2211-1-100−3−3332-22i−2i−1−i31+i3−1+i31−i32ζ22−2ζ222ζ14−2ζ14-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−i−iii−ζ22−ζ22ζ22ζ22−ζ14−ζ14ζ14ζ1400000000000000000
χ5644-4-4-2002-222323−23−231-2−1−3i32−1+3i32-2-11+3i321−3i321-1−1−3i32−1+3i321+3i321−3i32223i−3i3i−3iζ14+2ζ22−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22−ζ14−2ζ222ζ14+ζ2211-1-100−3−333-22−2i2i1+i3−1−i31−i3−1+i3−2ζ222ζ22−2ζ142ζ1411-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32ii−i−iζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ1400000000000000000
χ5744-4-4-2002-222323−23−231-2−1+3i32−1−3i32-2-11−3i321+3i321-1−1+3i32−1−3i321−3i321+3i3222−3i3i−3i3i−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ222ζ14+ζ22−ζ14−2ζ2211-1-100−3−3332-2−2i2i−1+i31−i3−1−i31+i3−2ζ142ζ14−2ζ222ζ22-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32ii−i−iζ14ζ14−ζ14−ζ14ζ22ζ22−ζ22−ζ2200000000000000000
χ5844-4-4-2002-222323−23−231-2−1+3i32−1−3i32-2-11−3i321+3i321-1−1+3i32−1−3i321−3i321+3i3222−3i3i−3i3i−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ222ζ14+ζ22−ζ14−2ζ2211-1-100−3−333-222i−2i1−i3−1+i31+i3−1−i32ζ14−2ζ142ζ22−2ζ2211-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−i−iii−ζ14−ζ14ζ14ζ14−ζ22−ζ22ζ22ζ2200000000000000000
χ5944-4-4-2002-22−23−2323231-2−1−3i32−1+3i32-2-11+3i321−3i321-1−1−3i32−1+3i321+3i321−3i3222−3i3i−3i3i−ζ14−2ζ222ζ14+ζ22−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ2211-1-10033−3−32-2−2i2i−1−i31+i3−1+i31−i3−2ζ222ζ22−2ζ142ζ14-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32ii−i−iζ22ζ22−ζ22−ζ22ζ14ζ14−ζ14−ζ1400000000000000000
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χ724-44-4-200-222−2i32i32i3−2i344-2-2-44-2-2-4-42222-440000−2i3−2i32i32i32i32i3−2i3−2i3-222-200−2i32i32i3−2i300000000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.