Finite Group Databasebeta

← Group #13167219

Character table — Group #13167219

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222444444444444444444488888888888888889999121212121212121212121212181818182424242424242424242424243636363636363672727272108108108108
order12223666333346666666666661212366612121212121212121212121222222244666612121212666666666612121212121222224121266664444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111
χ5111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-111-1-111-1-1
χ6111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-111
χ7111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-111-1-1-1-111
χ8111111111111-1111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1111111-1-111-1-1-1-1-11111-1-1
χ92222222222222222222222222222222222222222222-2-2-2-2000000000000-2-2-2-20000000000000000-2-2-200000000
χ10222222222222-2222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000-2-2-2-2000000000000000022200000000
χ112222-1-1-1-12-1-1222-1-1222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100002-1-100000000
χ122222-1-1-1-12-1-1222-1-1222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-2-21111-2-2111100002-1-100000000
χ132222-1-1-1-12-1-1222-1-1222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-20000−i3−i3i3i3−i3−i3i3i3111100−i3−i3i3i300−i3−i3i3i30000-21100000000
χ142222-1-1-1-12-1-1222-1-1222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-20000i3i3−i3−i3i3i3−i3−i3111100i3i3−i3−i300i3i3−i3−i30000-21100000000
χ152222-1-1-1-12-1-12-22-1-1222-1-122-1-111-1-1-1-1-2-2-2-211111111222222-2-2-1-1-1-11111-1-1-1-122-1-1-1-1-2-211110000-21100000000
χ162222-1-1-1-12-1-12-22-1-1222-1-122-1-111-1-1-1-1-2-2-2-2111111112222-2-2221111-1-1-1-1-1-1-1-1-2-2111122-1-1-1-10000-21100000000
χ172222-1-1-1-12-1-12-22-1-1222-1-122-1-111-1-1-1-1-2-2-2-211111111-2-2-2-20000−i3−i3i3i3i3i3−i3−i3111100−i3−i3i3i300i3i3−i3−i300002-1-100000000
χ182222-1-1-1-12-1-12-22-1-1222-1-122-1-111-1-1-1-1-2-2-2-211111111-2-2-2-20000i3i3−i3−i3−i3−i3i3i3111100i3i3−i3−i300−i3−i3i3i300002-1-100000000
χ1922-2-222-2-2222202222-2-2-2-2-2-2-2-20022-2-200000000000022-2-2002i−2i00002i−2i2i−2i22-2-20000002i−2i2i−2i2i−2i000000000000000
χ2022-2-222-2-2222202222-2-2-2-2-2-2-2-20022-2-200000000000022-2-200−2i2i0000−2i2i−2i2i22-2-2000000−2i2i−2i2i−2i2i000000000000000
χ2122-2-222-2-2222202222-2-2-2-2-2-2-2-20022-2-2000000000000-2-2222-2002-22-20000-2-2222-22-22-2000000000000000000000
χ2222-2-222-2-2222202222-2-2-2-2-2-2-2-20022-2-2000000000000-2-222-2200-22-220000-2-222-22-22-22000000000000000000000
χ2322-2-2-1-1112-1-1202-1-12-2-211-2-2113−3-1-111000033−3−333−3−322-2-2002i−2i−i3i3i3−i3−ii−ii-1-11100−i3i3i3−i32i−2i−ii−ii000003−300000000
χ2422-2-2-1-1112-1-1202-1-12-2-211-2-2113−3-1-111000033−3−333−3−322-2-200−2i2ii3−i3−i3i3i−ii−i-1-11100i3−i3−i3i3−2i2ii−ii−i000003−300000000
χ2522-2-2-1-1112-1-1202-1-12-2-211-2-2113−3-1-111000033−3−333−3−3-2-2222-200-11-113−3−3311-1-12-2-11-11003−3−3300000−3300000000
χ2622-2-2-1-1112-1-1202-1-12-2-211-2-2113−3-1-111000033−3−333−3−3-2-222-22001-11-1−333−311-1-1-221-11-100−333−300000−3300000000
χ2722-2-2-1-1112-1-1202-1-12-2-211-2-211−33-1-1110000−3−333−3−33322-2-2002i−2ii3−i3−i3i3−ii−ii-1-11100i3−i3−i3i32i−2i−ii−ii00000−3300000000
χ2822-2-2-1-1112-1-1202-1-12-2-211-2-211−33-1-1110000−3−333−3−33322-2-200−2i2i−i3i3i3−i3i−ii−i-1-11100−i3i3i3−i3−2i2ii−ii−i00000−3300000000
χ2922-2-2-1-1112-1-1202-1-12-2-211-2-211−33-1-1110000−3−333−3−333-2-2222-200-11-11−333−311-1-12-2-11-1100−333−3000003−300000000
χ3022-2-2-1-1112-1-1202-1-12-2-211-2-211−33-1-1110000−3−333−3−333-2-222-22001-11-13−3−3311-1-1-221-11-1003−3−33000003−300000000
χ312-22-22-22-222220-2-2-2-22-2-2-2-2222002-22-20000000000002-22-20000000000002-22-200000000000000000000000002-2
χ322-22-22-22-222220-2-2-2-22-2-2-2-2222002-22-20000000000002-22-20000000000002-22-20000000000000000000000000-22
χ332-22-22-22-222220-2-2-2-22-2-2-2-2222002-22-2000000000000-22-22000000000000-22-22000000000000000000000002-200
χ342-22-22-22-222220-2-2-2-22-2-2-2-2222002-22-2000000000000-22-22000000000000-22-2200000000000000000000000-2200
χ352-2-222-2-2222220-2-2-2-2-22222-2-2-2002-2-220000000000002-2-220000000000002-2-220000000000002-2000002-2000000
χ362-2-222-2-2222220-2-2-2-2-22222-2-2-2002-2-220000000000002-2-220000000000002-2-22000000000000-2200000-22000000
χ372-2-222-2-2222220-2-2-2-2-22222-2-2-2002-2-22000000000000-222-2000000000000-222-2000000000000002-2000002-20000
χ382-2-222-2-2222220-2-2-2-2-22222-2-2-2002-2-22000000000000-222-2000000000000-222-200000000000000-2200000-220000
χ3944444444111-24111-2-2111-211144-2-2-2-211-2-21111-2-2-2-200002222222222220000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000
χ4044444444111-24111-2-2111-211144-2-2-2-211-2-21111-2-2-2-20000-2-2-2-2-2-2-2-2-2-2-2-20000111111111111000000000000000
χ4144444444111-2-4111-2-2111-2111-4-4-2-2-2-2-1-122-1-1-1-12222000022-2-22222-2-2-2-20000-1-1-1-1-1-1111111000000000000000
χ4244444444111-2-4111-2-2111-2111-4-4-2-2-2-2-1-122-1-1-1-122220000-2-222-2-2-2-222220000111111-1-1-1-1-1-1000000000000000
χ4344444444-2-2-214-2-2-211-2-2-21-2-2-2441111-2-211-2-2-2-21111000000000000000000000000000000002222000-1-1-1-10000
χ4444444444-2-2-214-2-2-211-2-2-21-2-2-2441111-2-211-2-2-2-2111100000000000000000000000000000000-2-2-2-200011110000
χ4544444444-2-2-21-4-2-2-211-2-2-21-2-2-2-4-4111122-1-12222-1-1-1-10000000000000000000000000000000022-2-2000-1-1110000
χ4644444444-2-2-21-4-2-2-211-2-2-21-2-2-2-4-4111122-1-12222-1-1-1-100000000000000000000000000000000-2-22200011-1-10000
χ474444-2-2-2-21−1−3i32−1+3i32-241−1−3i32−1+3i32-2-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-2111111-2-2−1−3i32−1+3i32−1−3i32−1+3i32111100002222−1−i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1+i30000-1-11+i321+i321−i321−i32-1-11+i321+i321−i321−i32000000000000000
χ484444-2-2-2-21−1−3i32−1+3i32-241−1−3i32−1+3i32-2-21−1−3i32−1+3i32-21−1−3i32−1+3i32-2-2111111-2-2−1−3i32−1+3i32−1−3i32−1+3i3211110000-2-2-2-21+i31+i31−i31−i31+i31+i31−i31−i3000011−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32000000000000000
χ494444-2-2-2-21−1−3i32−1+3i32-2-41−1−3i32−1+3i32-2-21−1−3i32−1+3i32-21−1−3i32−1+3i32221111-1-1221+3i321−3i321+3i321−3i32-1-1-1-1000022-2-2−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i30000-1-11+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i32000000000000000
χ504444-2-2-2-21−1−3i32−1+3i32-2-41−1−3i32−1+3i32-2-21−1−3i32−1+3i32-21−1−3i32−1+3i32221111-1-1221+3i321−3i321+3i321−3i32-1-1-1-10000-2-2221+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i3000011−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i32000000000000000
χ514444-2-2-2-21−1+3i32−1−3i32-241−1+3i32−1−3i32-2-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-2111111-2-2−1+3i32−1−3i32−1+3i32−1−3i32111100002222−1+i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1−i30000-1-11−i321−i321+i321+i32-1-11−i321−i321+i321+i32000000000000000
χ524444-2-2-2-21−1+3i32−1−3i32-241−1+3i32−1−3i32-2-21−1+3i32−1−3i32-21−1+3i32−1−3i32-2-2111111-2-2−1+3i32−1−3i32−1+3i32−1−3i3211110000-2-2-2-21−i31−i31+i31+i31−i31−i31+i31+i3000011−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32000000000000000
χ534444-2-2-2-21−1+3i32−1−3i32-2-41−1+3i32−1−3i32-2-21−1+3i32−1−3i32-21−1+3i32−1−3i32221111-1-1221−3i321+3i321−3i321+3i32-1-1-1-1000022-2-2−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i30000-1-11−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i32000000000000000
χ544444-2-2-2-21−1+3i32−1−3i32-2-41−1+3i32−1−3i32-2-21−1+3i32−1−3i32-21−1+3i32−1−3i32221111-1-1221−3i321+3i321−3i321+3i32-1-1-1-10000-2-2221−i31−i31+i31+i3−1+i3−1+i3−1−i3−1−i3000011−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i32000000000000000
χ5544-4-444-4-4111-20111-22-1-1-12-1-1-100-2-2223i−3i003i−3i−3i3i000000002-22i−2i2-22-22i−2i2i−2i0000-11-11-11−ii−ii−ii000000000000000
χ5644-4-444-4-4111-20111-22-1-1-12-1-1-100-2-2223i−3i003i−3i−3i3i00000000-22−2i2i-22-22−2i2i−2i2i00001-11-11-1i−ii−ii−i000000000000000
χ5744-4-444-4-4111-20111-22-1-1-12-1-1-100-2-222−3i3i00−3i3i3i−3i000000002-2−2i2i2-22-2−2i2i−2i2i0000-11-11-11i−ii−ii−i000000000000000
χ5844-4-444-4-4111-20111-22-1-1-12-1-1-100-2-222−3i3i00−3i3i3i−3i00000000-222i−2i-22-222i−2i2i−2i00001-11-11-1−ii−ii−ii000000000000000
χ5944-4-4-2-2221−1−3i32−1+3i32-201−1−3i32−1+3i32-22-11+3i321−3i322-11+3i321−3i3223−2311-1-13i−3i00ζ7+2ζ11−2ζ7−ζ11−ζ7−2ζ112ζ7+ζ11−3−33300002-22i−2i−1−i31+i3−1+i31−i32ζ11−2ζ112ζ7−2ζ70000-111+i32−1−i321−i32−1+i32−ii−ζ11ζ11−ζ7ζ7000000000000000
χ6044-4-4-2-2221−1−3i32−1+3i32-201−1−3i32−1+3i32-22-11+3i321−3i322-11+3i321−3i3223−2311-1-13i−3i00ζ7+2ζ11−2ζ7−ζ11−ζ7−2ζ112ζ7+ζ11−3−3330000-22−2i2i1+i3−1−i31−i3−1+i3−2ζ112ζ11−2ζ72ζ700001-1−1−i321+i32−1+i321−i32i−iζ11−ζ11ζ7−ζ7000000000000000
χ6144-4-4-2-2221−1−3i32−1+3i32-201−1−3i32−1+3i32-22-11+3i321−3i322-11+3i321−3i32−232311-1-1−3i3i00−ζ7−2ζ112ζ7+ζ11ζ7+2ζ11−2ζ7−ζ1133−3−300002-2−2i2i−1−i31+i3−1+i31−i3−2ζ112ζ11−2ζ72ζ70000-111+i32−1−i321−i32−1+i32i−iζ11−ζ11ζ7−ζ7000000000000000
χ6244-4-4-2-2221−1−3i32−1+3i32-201−1−3i32−1+3i32-22-11+3i321−3i322-11+3i321−3i32−232311-1-1−3i3i00−ζ7−2ζ112ζ7+ζ11ζ7+2ζ11−2ζ7−ζ1133−3−30000-222i−2i1+i3−1−i31−i3−1+i32ζ11−2ζ112ζ7−2ζ700001-1−1−i321+i32−1+i321−i32−ii−ζ11ζ11−ζ7ζ7000000000000000
χ6344-4-4-2-2221−1+3i32−1−3i32-201−1+3i32−1−3i32-22-11−3i321+3i322-11−3i321+3i3223−2311-1-1−3i3i00−2ζ7−ζ11ζ7+2ζ112ζ7+ζ11−ζ7−2ζ11−3−33300002-2−2i2i−1+i31−i3−1−i31+i3−2ζ72ζ7−2ζ112ζ110000-111−i32−1+i321+i32−1−i32i−iζ7−ζ7ζ11−ζ11000000000000000
χ6444-4-4-2-2221−1+3i32−1−3i32-201−1+3i32−1−3i32-22-11−3i321+3i322-11−3i321+3i3223−2311-1-1−3i3i00−2ζ7−ζ11ζ7+2ζ112ζ7+ζ11−ζ7−2ζ11−3−3330000-222i−2i1−i3−1+i31+i3−1−i32ζ7−2ζ72ζ11−2ζ1100001-1−1+i321−i32−1−i321+i32−ii−ζ7ζ7−ζ11ζ11000000000000000
χ6544-4-4-2-2221−1+3i32−1−3i32-201−1+3i32−1−3i32-22-11−3i321+3i322-11−3i321+3i32−232311-1-13i−3i002ζ7+ζ11−ζ7−2ζ11−2ζ7−ζ11ζ7+2ζ1133−3−300002-22i−2i−1+i31−i3−1−i31+i32ζ7−2ζ72ζ11−2ζ110000-111−i32−1+i321+i32−1−i32−ii−ζ7ζ7−ζ11ζ11000000000000000
χ6644-4-4-2-2221−1+3i32−1−3i32-201−1+3i32−1−3i32-22-11−3i321+3i322-11−3i321+3i32−232311-1-13i−3i002ζ7+ζ11−ζ7−2ζ11−2ζ7−ζ11ζ7+2ζ1133−3−30000-22−2i2i1−i3−1+i31+i3−1−i3−2ζ72ζ7−2ζ112ζ1100001-1−1+i321−i32−1−i321+i32i−iζ7−ζ7ζ11−ζ11000000000000000
χ674-44-4-22-224-2-240-422-44-422-44-2-200-22-220000000000004-44-4000000000000-22-22000000000000000000000000000
χ684-44-4-22-224-2-240-422-44-422-44-2-200-22-22000000000000-44-440000000000002-22-2000000000000000000000000000
χ694-4-444-4-44-2-2-210222-1-1-2-2-21222001-1-11003-300003-33-3000000000000000000000000000000002-22-2000-11-110000
χ704-4-444-4-44-2-2-210222-1-1-2-2-21222001-1-11003-300003-33-300000000000000000000000000000000-22-220001-11-10000
χ714-4-444-4-44-2-2-210222-1-1-2-2-21222001-1-1100-330000-33-33000000000000000000000000000000002-2-22000-111-10000
χ724-4-444-4-44-2-2-210222-1-1-2-2-21222001-1-1100-330000-33-3300000000000000000000000000000000-222-20001-1-110000
χ734-4-44-222-24-2-240-422-4-44-2-24-42200-222-20000000000004-4-44000000000000-222-2000000000000000000000000000
χ744-4-44-222-24-2-240-422-4-44-2-24-42200-222-2000000000000-444-40000000000002-2-22000000000000000000000000000
χ758888-4-4-4-4-42228-42222-4222-422-4-4-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000000
χ768888-4-4-4-4-4222-8-42222-4222-42244-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000000
χ7788-8-888-8-8-4-4-420-4-4-42-2444-24440022-2-200000000000000000000000000000000000000000000000000000000000
χ7888-8-8-4-444-42220-4222-24-2-2-24-2-243−43-1-1110000−23−23232333−3−300000000000000000000000000000000000000000000000
χ7988-8-8-4-444-42220-4222-24-2-2-24-2-2−4343-1-11100002323−23−23−3−33300000000000000000000000000000000000000000000000
χ808-88-88-88-8222-40-2-2-24-4-2-2-2422200-44-4400000000000000000000000000000000000000000000000000000000000
χ818-88-88-88-8-4-4-420444-22444-2-4-4-4002-22-200000000000000000000000000000000000000000000000000000000000
χ828-88-8-44-442−1−3i3−1+3i3-40-21+3i31−3i34-4-21+3i31−3i342−1−3i3−1+3i3002-22-200000000000000000000000000000000000000000000000000000000000
χ838-88-8-44-442−1+3i3−1−3i3-40-21−3i31+3i34-4-21−3i31+3i342−1+3i3−1−3i3002-22-200000000000000000000000000000000000000000000000000000000000
χ848-88-8-44-44-422204-2-2-224-2-2-2-42200-11-110000000033−33−333300000000000000000000000000000000000000000000000
χ858-88-8-44-44-422204-2-2-224-2-2-2-42200-11-1100000000−333333−3300000000000000000000000000000000000000000000000
χ868-8-888-8-88222-40-2-2-244222-4-2-2-200-444-400000000000000000000000000000000000000000000000000000000000
χ878-8-88-444-42−1−3i3−1+3i3-40-21+3i31−3i3442−1−3i3−1+3i3-4-21+3i31−3i3002-2-2200000000000000000000000000000000000000000000000000000000000
χ888-8-88-444-42−1+3i3−1−3i3-40-21−3i31+3i3442−1+3i3−1−3i3-4-21−3i31+3i3002-2-2200000000000000000000000000000000000000000000000000000000000
χ898-8-88-444-4-422204-2-2-2-2-42224-2-200-111-1006-60000-33-3300000000000000000000000000000000000000000000000
χ908-8-88-444-4-422204-2-2-2-2-42224-2-200-111-100-6600003-33-300000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.