Finite Group Databasebeta

← Group #13167065

Character table — Group #13167065

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
χ5111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1111111111-111-1-111-1-1
χ6111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111111111-11-1-111-1-111
χ7111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-11-1-1-1-1111111-1-1-1-1-1-1111-111-1-1-1-111
χ8111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-11-1-1-1-1111111-1-1-1-1-1-111-11-1-11111-1-1
χ92222222222222222222222222222222222222222222000000000000-2-2-2-2-2-2-2-2000000000000-2-20000000000
χ10222222222222-2222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2000000000000-222-22222000000000000-2-20000000000
χ112222-1-1-1-122-1-1222-1-122-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000−i3−i3i3i3−i3−i3i3i3-2-2-2-2111100−i3−i3i3i300−i3−i3i3i3110000000000
χ122222-1-1-1-122-1-1222-1-122-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000i3i3−i3−i3i3i3−i3−i3-2-2-2-2111100i3i3−i3−i300i3i3−i3−i3110000000000
χ132222-1-1-1-122-1-1222-1-122-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-10000000000
χ142222-1-1-1-122-1-1222-1-122-1-12-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2111111112222-1-1-1-1-2-21111-2-21111-1-10000000000
χ152222-1-1-1-122-1-1-222-1-122-1-12-1-1211-1-1-1-1-2-2-2-2111111110000−i3−i3i3i3i3i3−i3−i3-222-2-1-1-1-100i3i3−i3−i300−i3−i3i3i3110000000000
χ162222-1-1-1-122-1-1-222-1-122-1-12-1-1211-1-1-1-1-2-2-2-2111111110000i3i3−i3−i3−i3−i3i3i3-222-2-1-1-1-100−i3−i3i3i300i3i3−i3−i3110000000000
χ172222-1-1-1-122-1-1-222-1-122-1-12-1-1211-1-1-1-1-2-2-2-21111111122-2-2-1-1-1-111112-2-221111-2-2111122-1-1-1-1-1-10000000000
χ182222-1-1-1-122-1-1-222-1-122-1-12-1-1211-1-1-1-1-2-2-2-211111111-2-2221111-1-1-1-12-2-22111122-1-1-1-1-2-21111-1-10000000000
χ192-22-22-2-22222202-2-2-2-2222-2-2-2-20022-2-2000000000000002-200002-22-2200-200002-22-22-20000002-20000000000
χ202-22-22-2-22222202-2-2-2-2222-2-2-2-20022-2-200000000000000-220000-22-22200-20000-22-22-220000002-20000000000
χ212-22-22-2-22222202-2-2-2-2222-2-2-2-20022-2-20000000000002i−2i002i−2i2i−2i0000-200200000000002i−2i2i−2i2i−2i-220000000000
χ222-22-22-2-22222202-2-2-2-2222-2-2-2-20022-2-2000000000000−2i2i00−2i2i−2i2i0000-20020000000000−2i2i−2i2i−2i2i-220000000000
χ232-22-2-111-122-1-102-211-22-1-1-211-23−3-1-111000033−3−333−3−3002-23−3−33-11-11200-233−3−32-2-11-11003−3−33-110000000000
χ242-22-2-111-122-1-102-211-22-1-1-211-23−3-1-111000033−3−333−3−300-22−333−31-11-1200-233−3−3-221-11-100−333−3-110000000000
χ252-22-2-111-122-1-102-211-22-1-1-211-23−3-1-111000033−3−333−3−32i−2i00−ii−ii−i3i3i3−i3-2002−3−33300−i3i3i3−i32i−2i−ii−ii1-10000000000
χ262-22-2-111-122-1-102-211-22-1-1-211-23−3-1-111000033−3−333−3−3−2i2i00i−ii−ii3−i3−i3i3-2002−3−33300i3−i3−i3i3−2i2ii−ii−i1-10000000000
χ272-22-2-111-122-1-102-211-22-1-1-211-2−33-1-1110000−3−333−3−333002-2−333−3-11-11200-2−3−3332-2-11-1100−333−3-110000000000
χ282-22-2-111-122-1-102-211-22-1-1-211-2−33-1-1110000−3−333−3−33300-223−3−331-11-1200-2−3−333-221-11-1003−3−33-110000000000
χ292-22-2-111-122-1-102-211-22-1-1-211-2−33-1-1110000−3−333−3−3332i−2i00−ii−iii3−i3−i3i3-200233−3−300i3−i3−i3i32i−2i−ii−ii1-10000000000
χ302-22-2-111-122-1-102-211-22-1-1-211-2−33-1-1110000−3−333−3−333−2i2i00i−ii−i−i3i3i3−i3-200233−3−300−i3i3i3−i3−2i2ii−ii−i1-10000000000
χ312-2-222-22-222220-2222-2-2-2-2-2-2-22002-22-200000000000000000000000002-202-22-200000000000000000000−i2i2−i2i2
χ322-2-222-22-222220-2222-2-2-2-2-2-2-22002-22-200000000000000000000000002-202-22-200000000000000000000i2−i2i2−i2
χ332-2-222-22-222220-2222-2-2-2-2-2-2-22002-22-20000000000000000000000000-220-22-2200000000000000000000−i2i2i2−i2
χ342-2-222-22-222220-2222-2-2-2-2-2-2-22002-22-20000000000000000000000000-220-22-2200000000000000000000i2−i2−i2i2
χ35444444441-2114-2111-2111111-244-2-2-2-2-2-2111111-2-2-2-222222222222200000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ36444444441-2114-2111-2111111-244-2-2-2-2-2-2111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000111111111111000000000000
χ37444444441-211-4-2111-2111111-2-4-4-2-2-2-222-1-1-1-1-1-1222222-2-22222-2-2-2-200000000111111-1-1-1-1-1-1000000000000
χ38444444441-211-4-2111-2111111-2-4-4-2-2-2-222-1-1-1-1-1-12222-2-222-2-2-2-2222200000000-1-1-1-1-1-1111111000000000000
χ3944444444-21-2-241-2-2-21-2-2-2-2-2-2144111111-2-2-2-2-2-21111000000000000000000000000000000000022-1-1-1-10000
χ4044444444-21-2-241-2-2-21-2-2-2-2-2-2144111111-2-2-2-2-2-211110000000000000000000000000000000000-2-211110000
χ4144444444-21-2-2-41-2-2-21-2-2-2-2-2-21-4-41111-1-1222222-1-1-1-100000000000000000000000000000000002-2-1-1110000
χ4244444444-21-2-2-41-2-2-21-2-2-2-2-2-21-4-41111-1-1222222-1-1-1-10000000000000000000000000000000000-2211-1-10000
χ434444-2-2-2-21-2−1−3i32−1+3i324-21−1−3i32−1+3i32-21−1−3i32−1+3i321−1−3i32−1+3i32-2-2-21111-2-211−1−3i32−1+3i32−1−3i32−1+3i3211112222−1−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+3i324-21−1−3i32−1+3i32-21−1−3i32−1+3i321−1−3i32−1+3i32-2-2-21111-2-211−1−3i32−1+3i32−1−3i32−1+3i321111-2-2-2-21+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+3i32-4-21−1−3i32−1+3i32-21−1−3i32−1+3i321−1−3i32−1+3i32-222111122-1-11+3i321−3i321+3i321−3i32-1-1-1-122-2-2−1−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
χ464444-2-2-2-21-2−1−3i32−1+3i32-4-21−1−3i32−1+3i32-21−1−3i32−1+3i321−1−3i32−1+3i32-222111122-1-11+3i321−3i321+3i321−3i32-1-1-1-1-2-2221+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
χ474444-2-2-2-21-2−1+3i32−1−3i324-21−1+3i32−1−3i32-21−1+3i32−1−3i321−1+3i32−1−3i32-2-2-21111-2-211−1+3i32−1−3i32−1+3i32−1−3i3211112222−1+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+3i32−1−3i324-21−1+3i32−1−3i32-21−1+3i32−1−3i321−1+3i32−1−3i32-2-2-21111-2-211−1+3i32−1−3i32−1+3i32−1−3i321111-2-2-2-21−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+3i32−1−3i32-4-21−1+3i32−1−3i32-21−1+3i32−1−3i321−1+3i32−1−3i32-222111122-1-11−3i321+3i321−3i321+3i32-1-1-1-122-2-2−1+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
χ504444-2-2-2-21-2−1+3i32−1−3i32-4-21−1+3i32−1−3i32-21−1+3i32−1−3i321−1+3i32−1−3i32-222111122-1-11−3i321+3i321−3i321+3i32-1-1-1-1-2-2221−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
χ5144-4-444-4-444440-4-4-4-44-4-4-4444-4004-4-4400000000000000000000000000000000000000000000000000000000
χ5244-4-444-4-4-21-2-20-12221222-2-2-2-1001-1-113-30000003-33-30000000000000000000000000000000000003−33−30000
χ5344-4-444-4-4-21-2-20-12221222-2-2-2-1001-1-113-30000003-33-3000000000000000000000000000000000000−33−330000
χ5444-4-444-4-4-21-2-20-12221222-2-2-2-1001-1-11-33000000-33-330000000000000000000000000000000000003−3−330000
χ5544-4-444-4-4-21-2-20-12221222-2-2-2-1001-1-11-33000000-33-33000000000000000000000000000000000000−333−30000
χ5644-4-4-2-22244-2-20-4-4224-4224-2-2-400-222-2000000000000000000000000000023−23−2323000000000000000000000000
χ5744-4-4-2-22244-2-20-4-4224-4224-2-2-400-222-20000000000000000000000000000−232323−23000000000000000000000000
χ584-44-44-4-441-2110-2-1-1-12111-1-1-1200-2-222003i−3i3i−3i−3i3i00002i−2i2-22i−2i2i−2i2-22-200000000-11-11-11−ii−ii−ii000000000000
χ594-44-44-4-441-2110-2-1-1-12111-1-1-1200-2-222003i−3i3i−3i−3i3i0000−2i2i-22−2i2i−2i2i-22-22000000001-11-11-1i−ii−ii−i000000000000
χ604-44-44-4-441-2110-2-1-1-12111-1-1-1200-2-22200−3i3i−3i3i3i−3i00002i−2i-222i−2i2i−2i-22-22000000001-11-11-1−ii−ii−ii000000000000
χ614-44-44-4-441-2110-2-1-1-12111-1-1-1200-2-22200−3i3i−3i3i3i−3i0000−2i2i2-2−2i2i−2i2i2-22-200000000-11-11-11i−ii−ii−i000000000000
χ624-44-4-222-21-2−1−3i32−1+3i320-2-11+3i321−3i3221−1−3i32−1+3i32-11+3i321−3i32223−2311-1-1003i−3iζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22−3−3332i−2i2-22ζ22−2ζ222ζ14−2ζ14−1−i31+i3−1+i31−i300000000-111+i32−1−i321−i32−1+i32−ii−ζ22ζ22−ζ14ζ14000000000000
χ634-44-4-222-21-2−1−3i32−1+3i320-2-11+3i321−3i3221−1−3i32−1+3i32-11+3i321−3i32223−2311-1-1003i−3iζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22−3−333−2i2i-22−2ζ222ζ22−2ζ142ζ141+i3−1−i31−i3−1+i3000000001-1−1−i321+i32−1+i321−i32i−iζ22−ζ22ζ14−ζ14000000000000
χ644-44-4-222-21-2−1−3i32−1+3i320-2-11+3i321−3i3221−1−3i32−1+3i32-11+3i321−3i322−232311-1-100−3i3i−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ2233−3−32i−2i-222ζ22−2ζ222ζ14−2ζ141+i3−1−i31−i3−1+i3000000001-1−1−i321+i32−1+i321−i32−ii−ζ22ζ22−ζ14ζ14000000000000
χ654-44-4-222-21-2−1−3i32−1+3i320-2-11+3i321−3i3221−1−3i32−1+3i32-11+3i321−3i322−232311-1-100−3i3i−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ2233−3−3−2i2i2-2−2ζ222ζ22−2ζ142ζ14−1−i31+i3−1+i31−i300000000-111+i32−1−i321−i32−1+i32i−iζ22−ζ22ζ14−ζ14000000000000
χ664-44-4-222-21-2−1+3i32−1−3i320-2-11−3i321+3i3221−1+3i32−1−3i32-11−3i321+3i32223−2311-1-100−3i3i−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ22−3−3332i−2i-222ζ14−2ζ142ζ22−2ζ221−i3−1+i31+i3−1−i3000000001-1−1+i321−i32−1−i321+i32−ii−ζ14ζ14−ζ22ζ22000000000000
χ674-44-4-222-21-2−1+3i32−1−3i320-2-11−3i321+3i3221−1+3i32−1−3i32-11−3i321+3i32223−2311-1-100−3i3i−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ22−3−333−2i2i2-2−2ζ142ζ14−2ζ222ζ22−1+i31−i3−1−i31+i300000000-111−i32−1+i321+i32−1−i32i−iζ14−ζ14ζ22−ζ22000000000000
χ684-44-4-222-21-2−1+3i32−1−3i320-2-11−3i321+3i3221−1+3i32−1−3i32-11−3i321+3i322−232311-1-1003i−3i2ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ2233−3−32i−2i2-22ζ14−2ζ142ζ22−2ζ22−1+i31−i3−1−i31+i300000000-111−i32−1+i321+i32−1−i32−ii−ζ14ζ14−ζ22ζ22000000000000
χ694-44-4-222-21-2−1+3i32−1−3i320-2-11−3i321+3i3221−1+3i32−1−3i32-11−3i321+3i322−232311-1-1003i−3i2ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ2233−3−3−2i2i-22−2ζ142ζ14−2ζ222ζ221−i3−1+i31+i3−1−i3000000001-1−1+i321−i32−1−i321+i32i−iζ14−ζ14ζ22−ζ22000000000000
χ704-4-44-22-2244-2-20-44-2-2-4-422-422400-22-2200000000000000000000000004-40-22-22000000000000000000000000
χ714-4-44-22-2244-2-20-44-2-2-4-422-422400-22-220000000000000000000000000-4402-22-2000000000000000000000000
χ728888-4-4-4-4-422282-4222-422-4222-4-4-1-1-1-122-4-42222-1-1-1-100000000000000000000000000000000000000000000
χ738888-4-4-4-4-4222-82-4222-422-422244-1-1-1-1-2-244-2-2-2-2111100000000000000000000000000000000000000000000
χ7488-8-888-8-82-42204-2-2-2-4-2-2-2222400-444-400000000000000000000000000000000000000000000000000000000
χ7588-8-8-4-4442-4−1−3i3−1+3i304-21+3i31−3i3-4-21+3i31−3i32−1−3i3−1+3i34002-2-2200000000000000000000000000000000000000000000000000000000
χ7688-8-8-4-4442-4−1+3i3−1−3i304-21−3i31+3i3-4-21−3i31+3i32−1+3i3−1−3i34002-2-2200000000000000000000000000000000000000000000000000000000
χ7788-8-8-4-444-42220-24-2-224-2-2-422-200-111-16-6000000-33-3300000000000000000000000000000000000000000000
χ7888-8-8-4-444-42220-24-2-224-2-2-422-200-111-1-660000003-33-300000000000000000000000000000000000000000000
χ798-88-88-8-88-42-4-402444-2-4-4-4444-20022-2-200000000000000000000000000000000000000000000000000000000
χ808-88-8-444-4-4222024-2-2-2-4224-2-2-243−43-1-1110000−23−23232333−3−300000000000000000000000000000000000000000000
χ818-88-8-444-4-4222024-2-2-2-4224-2-2-2−4343-1-11100002323−23−23−3−33300000000000000000000000000000000000000000000
χ828-8-888-88-82-422042224-2-2-2-2-2-2-400-44-4400000000000000000000000000000000000000000000000000000000
χ838-8-888-88-8-42-4-40-2-4-4-4-24444442002-22-200000000000000000000000000000000000000000000000000000000
χ848-8-88-44-442-4−1−3i3−1+3i3042−1−3i3−1+3i34-21+3i31−3i3-21+3i31−3i3-4002-22-200000000000000000000000000000000000000000000000000000000
χ858-8-88-44-442-4−1+3i3−1−3i3042−1+3i3−1−3i34-21−3i31+3i3-21−3i31+3i3-4002-22-200000000000000000000000000000000000000000000000000000000
χ868-8-88-44-44-42220-2-422-24-2-24-2-2200-11-110000000033−33−333300000000000000000000000000000000000000000000
χ878-8-88-44-44-42220-2-422-24-2-24-2-2200-11-1100000000−333333−3300000000000000000000000000000000000000000000

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