Finite Group Databasebeta

← Group #13167074

Character table — Group #13167074

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size111122224444444444444444444888888888888888812121212121212121212121218181818181818182424242424242424242424243636727272727272108108108108
order12223666333346666666666661212366612121212121212121212121244441212121212121212444412121212121212121212121212121212121244121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ5111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-1111-111-1-111-1-1
χ6111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-1-1-1-111-11-1-111-1-111
χ7111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111-111-1-1-1-111
χ8111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-11-1-11111-1-1
χ92222222222222222222222222222222222222222222000000000000-2-2-2-2-2-2-2-2000000000000-2-20000000000
χ10222222222222-2222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-200000000000022-2-22222000000000000-2-20000000000
χ112222-1-1-1-122-1-12222-1-12-1-12-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-10000−i3−i3i3i3−i3−i3i3i3-2-2-2-2111100−i3−i3i3i300−i3−i3i3i3110000000000
χ122222-1-1-1-122-1-12222-1-12-1-12-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-10000i3i3−i3−i3i3i3−i3−i3-2-2-2-2111100i3i3−i3−i300i3i3−i3−i3110000000000
χ132222-1-1-1-122-1-12222-1-12-1-12-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-10000000000
χ142222-1-1-1-122-1-12222-1-12-1-12-1-12-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-2-21111-2-21111-1-10000000000
χ152222-1-1-1-122-1-1-2222-1-12-1-12-1-1211-1-1-1-1-2-21111-2-211110000−i3−i3i3i3i3i3−i3−i322-2-2-1-1-1-100i3i3−i3−i300−i3−i3i3i3110000000000
χ162222-1-1-1-122-1-1-2222-1-12-1-12-1-1211-1-1-1-1-2-21111-2-211110000i3i3−i3−i3−i3−i3i3i322-2-2-1-1-1-100−i3−i3i3i300i3i3−i3−i3110000000000
χ172222-1-1-1-122-1-1-2222-1-12-1-12-1-1211-1-1-1-1-2-21111-2-2111122-2-21111-1-1-1-1-2-222111122-1-1-1-1-2-21111-1-10000000000
χ182222-1-1-1-122-1-1-2222-1-12-1-12-1-1211-1-1-1-1-2-21111-2-21111-2-222-1-1-1-11111-2-2221111-2-2111122-1-1-1-1-1-10000000000
χ1922-2-22-22-22222022-222-2-2-2-2-2-2-20022-2-20000000000000000000000002-20022-2-2000000000000000000002−22−2
χ2022-2-22-22-22222022-222-2-2-2-2-2-2-20022-2-20000000000000000000000002-20022-2-200000000000000000000−22−22
χ2122-2-22-22-22222022-222-2-2-2-2-2-2-20022-2-2000000000000000000000000-2200-2-222000000000000000000002−2−22
χ2222-2-22-22-22222022-222-2-2-2-2-2-2-20022-2-2000000000000000000000000-2200-2-22200000000000000000000−222−2
χ232-22-22-2-2222220-2-22-2-2222-2-2-2-2002-22-2000000000000002i−2i2i−2i2i−2i000000-2200000000002i−2i2i−2i2i−2i2-20000000000
χ242-22-22-2-2222220-2-22-2-2222-2-2-2-2002-22-200000000000000−2i2i−2i2i−2i2i000000-220000000000−2i2i−2i2i−2i2i2-20000000000
χ252-22-22-2-2222220-2-22-2-2222-2-2-2-2002-22-20000000000002-20000002-22-2002-200002-22-22-2000000-220000000000
χ262-22-22-2-2222220-2-22-2-2222-2-2-2-2002-22-2000000000000-22000000-22-22002-20000-22-22-22000000-220000000000
χ272-22-2-111-122-1-10-2-22112-1-1-211-23−3-11-110033−3−30033−3−3002i−2i−ii−ii−i3i3i3−i300-223−33−300−i3i3i3−i32i−2i−ii−ii-110000000000
χ282-22-2-111-122-1-10-2-22112-1-1-211-23−3-11-110033−3−30033−3−300−2i2ii−ii−ii3−i3−i3i300-223−33−300i3−i3−i3i3−2i2ii−ii−i-110000000000
χ292-22-2-111-122-1-10-2-22112-1-1-211-23−3-11-110033−3−30033−3−32-2003−3−33-11-11002-2−33−332-2-11-11003−3−331-10000000000
χ302-22-2-111-122-1-10-2-22112-1-1-211-23−3-11-110033−3−30033−3−3-2200−333−31-11-1002-2−33−33-221-11-100−333−31-10000000000
χ312-22-2-111-122-1-10-2-22112-1-1-211-2−33-11-1100−3−33300−3−333002i−2i−ii−iii3−i3−i3i300-22−33−3300i3−i3−i3i32i−2i−ii−ii-110000000000
χ322-22-2-111-122-1-10-2-22112-1-1-211-2−33-11-1100−3−33300−3−33300−2i2ii−ii−i−i3i3i3−i300-22−33−3300−i3i3i3−i3−2i2ii−ii−i-110000000000
χ332-22-2-111-122-1-10-2-22112-1-1-211-2−33-11-1100−3−33300−3−3332-200−333−3-11-11002-23−33−32-2-11-1100−333−31-10000000000
χ342-22-2-111-122-1-10-2-22112-1-1-211-2−33-11-1100−3−33300−3−333-22003−3−331-11-1002-23−33−3-221-11-1003−3−331-10000000000
χ35444444441-21141-2-211111111-244-2-2-2-2111111-2-2-2-2-2-222222222222200000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ36444444441-21141-2-211111111-244-2-2-2-2111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000111111111111000000000000
χ37444444441-211-41-2-211111111-2-4-4-2-2-2-2-1-1-1-1-1-122222222-2-2-2-2-2-2222200000000-1-1-1-1-1-1111111000000000000
χ38444444441-211-41-2-211111111-2-4-4-2-2-2-2-1-1-1-1-1-1222222-2-2222222-2-2-2-200000000111111-1-1-1-1-1-1000000000000
χ3944444444-21-2-24-211-2-2-2-2-2-2-2-21441111-2-2-2-2-2-2111111000000000000000000000000000000000022-1-1-1-10000
χ4044444444-21-2-24-211-2-2-2-2-2-2-2-21441111-2-2-2-2-2-21111110000000000000000000000000000000000-2-211110000
χ4144444444-21-2-2-4-211-2-2-2-2-2-2-2-21-4-41111222222-1-1-1-1-1-100000000000000000000000000000000002-2-1-1110000
χ4244444444-21-2-2-4-211-2-2-2-2-2-2-2-21-4-41111222222-1-1-1-1-1-10000000000000000000000000000000000-2211-1-10000
χ434444-2-2-2-21-2−1−3i32−1+3i3241-2-2−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32-2-211112222−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i300000000-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000
χ444444-2-2-2-21-2−1−3i32−1+3i3241-2-2−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32-2-21111-2-2-2-21+i31+i31−i31−i31+i31+i31−i31−i30000000011−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000
χ454444-2-2-2-21-2−1−3i32−1+3i32-41-2-2−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2221111-1-11+3i321−3i321+3i321−3i3222-1-1-1-122-2-21+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i300000000-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000
χ464444-2-2-2-21-2−1−3i32−1+3i32-41-2-2−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2221111-1-11+3i321−3i321+3i321−3i3222-1-1-1-1-2-222−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i30000000011−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000
χ474444-2-2-2-21-2−1+3i32−1−3i3241-2-2−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32-2-211112222−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i300000000-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000000
χ484444-2-2-2-21-2−1+3i32−1−3i3241-2-2−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32-2-21111-2-2-2-21−i31−i31+i31+i31−i31−i31+i31+i30000000011−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000
χ494444-2-2-2-21-2−1+3i32−1−3i32-41-2-2−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2221111-1-11−3i321+3i321−3i321+3i3222-1-1-1-122-2-21−i31−i31+i31+i3−1+i3−1+i3−1−i3−1−i300000000-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000
χ504444-2-2-2-21-2−1+3i32−1−3i32-41-2-2−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2221111-1-11−3i321+3i321−3i321+3i3222-1-1-1-1-2-222−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i30000000011−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000
χ5144-4-4-22-2244-2-2044-4-2-2-422-422-400-2-2220000000000000000000000004-400-2-222000000000000000000000000
χ5244-4-4-22-2244-2-2044-4-2-2-422-422-400-2-222000000000000000000000000-440022-2-2000000000000000000000000
χ534-44-44-4-441-2110-12-2-1-1111-1-1-1200-22-223i−3i3i−3i−3i3i0000002-22i−2i2i−2i2i−2i2-22-200000000-11-11-11−ii−ii−ii000000000000
χ544-44-44-4-441-2110-12-2-1-1111-1-1-1200-22-223i−3i3i−3i−3i3i000000-22−2i2i−2i2i−2i2i-22-22000000001-11-11-1i−ii−ii−i000000000000
χ554-44-44-4-441-2110-12-2-1-1111-1-1-1200-22-22−3i3i−3i3i3i−3i0000002-2−2i2i−2i2i−2i2i2-22-200000000-11-11-11i−ii−ii−i000000000000
χ564-44-44-4-441-2110-12-2-1-1111-1-1-1200-22-22−3i3i−3i3i3i−3i000000-222i−2i2i−2i2i−2i-22-22000000001-11-11-1−ii−ii−ii000000000000
χ574-44-4-222-21-2−1−3i32−1+3i320-12-21+3i321−3i321−1−3i32−1+3i32-11+3i321−3i32223−231-11-13i−3iζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ2200−3−3332-22i−2i2ζ22−2ζ222ζ14−2ζ14−1−i31+i3−1+i31−i300000000-111+i32−1−i321−i32−1+i32−ii−ζ22ζ22−ζ14ζ14000000000000
χ584-44-4-222-21-2−1−3i32−1+3i320-12-21+3i321−3i321−1−3i32−1+3i32-11+3i321−3i32223−231-11-13i−3iζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ2200−3−333-22−2i2i−2ζ222ζ22−2ζ142ζ141+i3−1−i31−i3−1+i3000000001-1−1−i321+i32−1+i321−i32i−iζ22−ζ22ζ14−ζ14000000000000
χ594-44-4-222-21-2−1−3i32−1+3i320-12-21+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322−23231-11-1−3i3i−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ220033−3−32-2−2i2i−2ζ222ζ22−2ζ142ζ14−1−i31+i3−1+i31−i300000000-111+i32−1−i321−i32−1+i32i−iζ22−ζ22ζ14−ζ14000000000000
χ604-44-4-222-21-2−1−3i32−1+3i320-12-21+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322−23231-11-1−3i3i−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ220033−3−3-222i−2i2ζ22−2ζ222ζ14−2ζ141+i3−1−i31−i3−1+i3000000001-1−1−i321+i32−1+i321−i32−ii−ζ22ζ22−ζ14ζ14000000000000
χ614-44-4-222-21-2−1+3i32−1−3i320-12-21−3i321+3i321−1+3i32−1−3i32-11−3i321+3i32223−231-11-1−3i3i−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ2200−3−3332-2−2i2i−2ζ142ζ14−2ζ222ζ22−1+i31−i3−1−i31+i300000000-111−i32−1+i321+i32−1−i32i−iζ14−ζ14ζ22−ζ22000000000000
χ624-44-4-222-21-2−1+3i32−1−3i320-12-21−3i321+3i321−1+3i32−1−3i32-11−3i321+3i32223−231-11-1−3i3i−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ2200−3−333-222i−2i2ζ14−2ζ142ζ22−2ζ221−i3−1+i31+i3−1−i3000000001-1−1+i321−i32−1−i321+i32−ii−ζ14ζ14−ζ22ζ22000000000000
χ634-44-4-222-21-2−1+3i32−1−3i320-12-21−3i321+3i321−1+3i32−1−3i32-11−3i321+3i322−23231-11-13i−3i2ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ220033−3−32-22i−2i2ζ14−2ζ142ζ22−2ζ22−1+i31−i3−1−i31+i300000000-111−i32−1+i321+i32−1−i32−ii−ζ14ζ14−ζ22ζ22000000000000
χ644-44-4-222-21-2−1+3i32−1−3i320-12-21−3i321+3i321−1+3i32−1−3i32-11−3i321+3i322−23231-11-13i−3i2ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ220033−3−3-22−2i2i−2ζ142ζ14−2ζ222ζ221−i3−1+i31+i3−1−i3000000001-1−1+i321−i32−1−i321+i32i−iζ14−ζ14ζ22−ζ22000000000000
χ654-4-4444-4-444440-4-4-4-4-4-4-4-44444004-4-4400000000000000000000000000000000000000000000000000000000
χ664-4-4444-4-4-21-2-202-1-122222-2-2-21001-1-110000003-33-33-3000000000000000000000000000000000000−i3i3−i3i30000
χ674-4-4444-4-4-21-2-202-1-122222-2-2-21001-1-110000003-33-33-3000000000000000000000000000000000000i3−i3i3−i30000
χ684-4-4444-4-4-21-2-202-1-122222-2-2-21001-1-11000000-33-33-33000000000000000000000000000000000000−i3i3i3−i30000
χ694-4-4444-4-4-21-2-202-1-122222-2-2-21001-1-11000000-33-33-33000000000000000000000000000000000000i3−i3−i3i30000
χ704-4-44-2-22244-2-20-4-4-422-4224-2-2400-222-2000000000000000000000000000023−23−2323000000000000000000000000
χ714-4-44-2-22244-2-20-4-4-422-4224-2-2400-222-20000000000000000000000000000−232323−23000000000000000000000000
χ728888-4-4-4-4-42228-42222-422-4222-4-4-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000
χ738888-4-4-4-4-4222-8-42222-422-422244-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000
χ7488-8-88-88-82-42202-4422-2-2-2-2-2-2400-4-44400000000000000000000000000000000000000000000000000000000
χ7588-8-88-88-8-42-4-40-42-2-4-4444444-20022-2-200000000000000000000000000000000000000000000000000000000
χ7688-8-8-44-442-4−1−3i3−1+3i302-44−1−3i3−1+3i3-21+3i31−3i3-21+3i31−3i340022-2-200000000000000000000000000000000000000000000000000000000
χ7788-8-8-44-442-4−1+3i3−1−3i302-44−1+3i3−1−3i3-21−3i31+3i3-21−3i31+3i340022-2-200000000000000000000000000000000000000000000000000000000
χ7888-8-8-44-44-42220-42-2224-2-24-2-2-200-1-1110000000033−33−333300000000000000000000000000000000000000000000
χ7988-8-8-44-44-42220-42-2224-2-24-2-2-200-1-11100000000−333333−3300000000000000000000000000000000000000000000
χ808-88-88-8-88-42-4-404-2244-4-4-4444-2002-22-200000000000000000000000000000000000000000000000000000000
χ818-88-8-444-4-422204-22-2-2-4224-2-2-243−43-11-1100−23−2323230033−3−300000000000000000000000000000000000000000000
χ828-88-8-444-4-422204-22-2-2-4224-2-2-2−4343-11-11002323−23−2300−3−33300000000000000000000000000000000000000000000
χ838-8-8888-8-82-4220-244-2-2-2-2-2222-400-444-400000000000000000000000000000000000000000000000000000000
χ848-8-88-4-4442-4−1−3i3−1+3i30-2441+3i31−3i3-21+3i31−3i32−1−3i3−1+3i3-4002-2-2200000000000000000000000000000000000000000000000000000000
χ858-8-88-4-4442-4−1+3i3−1−3i30-2441−3i31+3i3-21−3i31+3i32−1+3i3−1−3i3-4002-2-2200000000000000000000000000000000000000000000000000000000
χ868-8-88-4-444-422204-2-2-2-24-2-2-422200-111-10000006-6-33-3300000000000000000000000000000000000000000000
χ878-8-88-4-444-422204-2-2-2-24-2-2-422200-111-1000000-663-33-300000000000000000000000000000000000000000000

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