Finite Group Databasebeta

← Group #13167086

Character table — Group #13167086

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
χ5111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111-1-11-1-1-1-1111111-1-1-1-1-1-1111-1-1-11111-1-1
χ6111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111-1-11-1-1-1-1111111-1-1-1-1-1-111-1111-1-1-1-111
χ7111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-111
χ8111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111111111-1111-1-111-1-1
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
χ112222-1-1-1-122-1-1222-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-10000−i3−i3i3i3−i3−i3i3i3-2-2-2-2111100−i3−i3i3i300−i3−i3i3i3110000000000
χ122222-1-1-1-122-1-1222-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-10000i3i3−i3−i3i3i3−i3−i3-2-2-2-2111100i3i3−i3−i300i3i3−i3−i3110000000000
χ132222-1-1-1-122-1-1222-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-122-1-1-1-122-1-1-1-1-1-10000000000
χ142222-1-1-1-122-1-1222-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-2111111112222-1-1-1-1-2-21111-2-21111-1-10000000000
χ152222-1-1-1-122-1-1-222-1-12-1-12-1-12211-1-1-1-1-2-21111-2-211110000−i3−i3i3i3i3i3−i3−i3-222-2-1-1-1-100i3i3−i3−i300−i3−i3i3i3110000000000
χ162222-1-1-1-122-1-1-222-1-12-1-12-1-12211-1-1-1-1-2-21111-2-211110000i3i3−i3−i3−i3−i3i3i3-222-2-1-1-1-100−i3−i3i3i300i3i3−i3−i3110000000000
χ172222-1-1-1-122-1-1-222-1-12-1-12-1-12211-1-1-1-1-2-21111-2-2111122-2-21111-1-1-1-12-2-22111122-1-1-1-1-2-21111-1-10000000000
χ182222-1-1-1-122-1-1-222-1-12-1-12-1-12211-1-1-1-1-2-21111-2-21111-2-222-1-1-1-111112-2-221111-2-2111122-1-1-1-1-1-10000000000
χ1922-2-22-2-22222202-2-2-2222-2-2-2-2-20022-2-2000000000000002i−2i2i−2i2i−2i0000-200200000000002i−2i2i−2i2i−2i2-20000000000
χ2022-2-22-2-22222202-2-2-2222-2-2-2-2-20022-2-200000000000000−2i2i−2i2i−2i2i0000-20020000000000−2i2i−2i2i−2i2i2-20000000000
χ2122-2-22-2-22222202-2-2-2222-2-2-2-2-20022-2-20000000000002-20000002-22-2200-200002-22-22-2000000-220000000000
χ2222-2-22-2-22222202-2-2-2222-2-2-2-2-20022-2-2000000000000-22000000-22-22200-20000-22-22-22000000-220000000000
χ2322-2-2-111-122-1-102-2112-1-1-211-2-23−3-1-1110033−3−30033−3−3002i−2i−ii−ii−i3i3i3−i3-200233−3−300−i3i3i3−i32i−2i−ii−ii-110000000000
χ2422-2-2-111-122-1-102-2112-1-1-211-2-23−3-1-1110033−3−30033−3−300−2i2ii−ii−ii3−i3−i3i3-200233−3−300i3−i3−i3i3−2i2ii−ii−i-110000000000
χ2522-2-2-111-122-1-102-2112-1-1-211-2-23−3-1-1110033−3−30033−3−32-2003−3−33-11-11200-2−3−3332-2-11-11003−3−331-10000000000
χ2622-2-2-111-122-1-102-2112-1-1-211-2-23−3-1-1110033−3−30033−3−3-2200−333−31-11-1200-2−3−333-221-11-100−333−31-10000000000
χ2722-2-2-111-122-1-102-2112-1-1-211-2-2−33-1-11100−3−33300−3−333002i−2i−ii−iii3−i3−i3i3-2002−3−33300i3−i3−i3i32i−2i−ii−ii-110000000000
χ2822-2-2-111-122-1-102-2112-1-1-211-2-2−33-1-11100−3−33300−3−33300−2i2ii−ii−i−i3i3i3−i3-2002−3−33300−i3i3i3−i3−2i2ii−ii−i-110000000000
χ2922-2-2-111-122-1-102-2112-1-1-211-2-2−33-1-11100−3−33300−3−3332-200−333−3-11-11200-233−3−32-2-11-1100−333−31-10000000000
χ3022-2-2-111-122-1-102-2112-1-1-211-2-2−33-1-11100−3−33300−3−333-22003−3−331-11-1200-233−3−3-221-11-1003−3−331-10000000000
χ312-22-222-2-222220-2-2-2-2-2-2-2222-22002-2-2200000000000000000000000002i−2i02i−2i2i−2i00000000000000000000−i2i22−2
χ322-22-222-2-222220-2-2-2-2-2-2-2222-22002-2-2200000000000000000000000002i−2i02i−2i2i−2i00000000000000000000i2−i2−22
χ332-22-222-2-222220-2-2-2-2-2-2-2222-22002-2-220000000000000000000000000−2i2i0−2i2i−2i2i00000000000000000000−i2i2−22
χ342-22-222-2-222220-2-2-2-2-2-2-2222-22002-2-220000000000000000000000000−2i2i0−2i2i−2i2i00000000000000000000i2−i22−2
χ35444444441-2114-2111111111-2-244-2-2-2-2111111-2-2-2-2-2-222222222222200000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ36444444441-2114-2111111111-2-244-2-2-2-2111111-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000111111111111000000000000
χ37444444441-211-4-2111111111-2-2-4-4-2-2-2-2-1-1-1-1-1-122222222-2-2-2-2-2-2222200000000-1-1-1-1-1-1111111000000000000
χ38444444441-211-4-2111111111-2-2-4-4-2-2-2-2-1-1-1-1-1-1222222-2-2222222-2-2-2-200000000111111-1-1-1-1-1-1000000000000
χ3944444444-21-2-241-2-2-2-2-2-2-2-2-211441111-2-2-2-2-2-2111111000000000000000000000000000000000022-1-1-1-10000
χ4044444444-21-2-241-2-2-2-2-2-2-2-2-211441111-2-2-2-2-2-21111110000000000000000000000000000000000-2-211110000
χ4144444444-21-2-2-41-2-2-2-2-2-2-2-2-211-4-41111222222-1-1-1-1-1-100000000000000000000000000000000002-211-1-10000
χ4244444444-21-2-2-41-2-2-2-2-2-2-2-2-211-4-41111222222-1-1-1-1-1-10000000000000000000000000000000000-22-1-1110000
χ434444-2-2-2-21-2−1−3i32−1+3i324-21−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2-2111111−1−3i32−1+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+3i324-21−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2-2-2111111−1−3i32−1+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+3i32-4-21−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2221111-1-11+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+3i32-4-21−1−3i32−1+3i321−1−3i32−1+3i321−1−3i32−1+3i32-2-2221111-1-11+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+3i32−1−3i324-21−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2-2111111−1+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+3i32−1−3i324-21−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2-2-2111111−1+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+3i32−1−3i32-4-21−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2221111-1-11−3i321+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+3i32−1−3i32-4-21−1+3i32−1−3i321−1+3i32−1−3i321−1+3i32−1−3i32-2-2221111-1-11−3i321+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
χ5144-4-44-4-441-2110-2-1-1-1111-1-1-12200-2-2223i−3i3i−3i−3i3i0000002-22i−2i2i−2i2i−2i2-22-200000000-11-11-11−ii−ii−ii000000000000
χ5244-4-44-4-441-2110-2-1-1-1111-1-1-12200-2-2223i−3i3i−3i−3i3i000000-22−2i2i−2i2i−2i2i-22-22000000001-11-11-1i−ii−ii−i000000000000
χ5344-4-44-4-441-2110-2-1-1-1111-1-1-12200-2-222−3i3i−3i3i3i−3i0000002-2−2i2i−2i2i−2i2i2-22-200000000-11-11-11i−ii−ii−i000000000000
χ5444-4-44-4-441-2110-2-1-1-1111-1-1-12200-2-222−3i3i−3i3i3i−3i000000-222i−2i2i−2i2i−2i-22-22000000001-11-11-1−ii−ii−ii000000000000
χ5544-4-4-222-21-2−1−3i32−1+3i320-2-11+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322223−2311-1-13i−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
χ5644-4-4-222-21-2−1−3i32−1+3i320-2-11+3i321−3i321−1−3i32−1+3i32-11+3i321−3i322223−2311-1-13i−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
χ5744-4-4-222-21-2−1−3i32−1+3i320-2-11+3i321−3i321−1−3i32−1+3i32-11+3i321−3i3222−232311-1-1−3i3i−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
χ5844-4-4-222-21-2−1−3i32−1+3i320-2-11+3i321−3i321−1−3i32−1+3i32-11+3i321−3i3222−232311-1-1−3i3i−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
χ5944-4-4-222-21-2−1+3i32−1−3i320-2-11−3i321+3i321−1+3i32−1−3i32-11−3i321+3i322223−2311-1-1−3i3i−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
χ6044-4-4-222-21-2−1+3i32−1−3i320-2-11−3i321+3i321−1+3i32−1−3i32-11−3i321+3i322223−2311-1-1−3i3i−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
χ6144-4-4-222-21-2−1+3i32−1−3i320-2-11−3i321+3i321−1+3i32−1−3i32-11−3i321+3i3222−232311-1-13i−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
χ6244-4-4-222-21-2−1+3i32−1−3i320-2-11−3i321+3i321−1+3i32−1−3i32-11−3i321+3i3222−232311-1-13i−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
χ634-44-4-2-22244-2-20-4-422-4224-2-2-4400-222-200000000000000000000000004i−4i0−2i2i−2i2i000000000000000000000000
χ644-44-4-2-22244-2-20-4-422-4224-2-2-4400-222-20000000000000000000000000−4i4i02i−2i2i−2i000000000000000000000000
χ654-4-444-44-444440-4444-4-4-4-4-4-44-4004-44-400000000000000000000000000000000000000000000000000000000
χ664-4-444-44-4-21-2-20-1-2-2-22222221-1001-11-10000003i−3i3i−3i3i−3i000000000000000000000000000000000000−i3i33−30000
χ674-4-444-44-4-21-2-20-1-2-2-22222221-1001-11-10000003i−3i3i−3i3i−3i000000000000000000000000000000000000i3−i3−330000
χ684-4-444-44-4-21-2-20-1-2-2-22222221-1001-11-1000000−3i3i−3i3i−3i3i000000000000000000000000000000000000−i3i3−330000
χ694-4-444-44-4-21-2-20-1-2-2-22222221-1001-11-1000000−3i3i−3i3i−3i3i000000000000000000000000000000000000i3−i33−30000
χ704-4-44-22-2244-2-20-44-2-2-422-4224-400-22-220000000000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ714-4-44-22-2244-2-20-44-2-2-422-4224-400-22-2200000000000000000000000000002i3−2i3−2i32i3000000000000000000000000
χ728888-4-4-4-4-422282-422-422-42222-4-4-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000
χ738888-4-4-4-4-4222-82-422-422-4222244-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000
χ7488-8-88-8-88-42-4-402444-4-4-4444-2-20022-2-200000000000000000000000000000000000000000000000000000000
χ7588-8-8-444-4-4222024-2-2-4224-2-2-2-243−43-1-11100−23−2323230033−3−300000000000000000000000000000000000000000000
χ7688-8-8-444-4-4222024-2-2-4224-2-2-2-2−4343-1-111002323−23−2300−3−33300000000000000000000000000000000000000000000
χ778-88-888-8-82-42204-2-2-2-2-2-22224-400-444-400000000000000000000000000000000000000000000000000000000
χ788-88-888-8-8-42-4-40-2444444-4-4-4-22002-2-2200000000000000000000000000000000000000000000000000000000
χ798-88-8-4-4442-4−1−3i3−1+3i304-21+3i31−3i3-21+3i31−3i32−1−3i3−1+3i34-4002-2-2200000000000000000000000000000000000000000000000000000000
χ808-88-8-4-4442-4−1+3i3−1−3i304-21−3i31+3i3-21−3i31+3i32−1+3i3−1−3i34-4002-2-2200000000000000000000000000000000000000000000000000000000
χ818-88-8-4-444-42220-24-2-24-2-2-422-2200-111-100000000−3i33i33i3−3i300000000000000000000000000000000000000000000
χ828-88-8-4-444-42220-24-2-24-2-2-422-2200-111-1000000003i3−3i3−3i33i300000000000000000000000000000000000000000000
χ838-8-888-88-82-42204222-2-2-2-2-2-2-4400-44-4400000000000000000000000000000000000000000000000000000000
χ848-8-88-44-442-4−1−3i3−1+3i3042−1−3i3−1+3i3-21+3i31−3i3-21+3i31−3i3-44002-22-200000000000000000000000000000000000000000000000000000000
χ858-8-88-44-442-4−1+3i3−1−3i3042−1+3i3−1−3i3-21−3i31+3i3-21−3i31+3i3-44002-22-200000000000000000000000000000000000000000000000000000000
χ868-8-88-44-44-42220-2-4224-2-24-2-22-200-11-110000006i−6i−3i3i−3i3i00000000000000000000000000000000000000000000
χ878-8-88-44-44-42220-2-4224-2-24-2-22-200-11-11000000−6i6i3i−3i3i−3i00000000000000000000000000000000000000000000

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