Finite Group Databasebeta

← Group #72222927

Character table — Group #72222927

Order 2592.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11222233446666666666666661212121212121212121212121212181818181818181818181818181824242424242424244848484854545454727272727272727272727272162216216
order1233662236236666666666666333666666666662466666666661212333366663366241212666666121212121212266
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-11111111111-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111−1−i32−1+i32111111111−1−i32−1+i3211111111111111−1−i32−1+i32−1−i32−1+i32−1−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+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32
χ411111111111111111111111111−1−i32−1+i32111111111−1−i32−1+i321-11111111111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i321−i321−i32-11+i321−i32
χ511111111111111111111111111−1+i32−1−i32111111111−1+i32−1−i3211111111111111−1+i32−1−i32−1+i32−1−i32−1+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−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32
χ611111111111111111111111111−1+i32−1−i32111111111−1+i32−1−i321-11111111111-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i321+i321+i32-11−i321+i32
χ71111111111-111111-1-1111111111111111111111-11-1-1-1-1-1-1-1-1-1-111111111111111-1111-1-1-1-1-1-1111111-1-1-1
χ81111111111-111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ91111111111-111111-1-111111111−1−i32−1+i32111111111−1−i32−1+i32-11-1-1-1-1-1-1-1-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-11111+i321−i321+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11+i321−i32
χ101111111111-111111-1-111111111−1−i32−1+i32111111111−1−i32−1+i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321-1-1-11+i321−i321+i321+i321−i321−i321+i321−i321+i321+i321−i321−i321−1−i32−1+i32
χ111111111111-111111-1-111111111−1+i32−1−i32111111111−1+i32−1−i32-11-1-1-1-1-1-1-1-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-11111−i321+i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11−i321+i32
χ121111111111-111111-1-111111111−1+i32−1−i32111111111−1+i32−1−i32-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321-1-1-11−i321+i321−i321−i321+i321+i321−i321+i321−i321−i321+i321+i321−1+i32−1−i32
χ1322222222222-1222222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1222022-1-1-1-1-1-1-1-10022-1-1-1-122-1-1-1-1000022-1-1-1-1000000000
χ1422222222222-1222222-1-1-1-1-1-1-1-1−1−i3−1+i322-1-1-1-1-1-1-1−1−i3−1+i32022-1-1-1-1-1-1-1-100−1−i3−1+i31+i321−i321+i321−i32−1−i3−1+i31+i321−i321+i321−i320000−1−i3−1+i31+i321+i321−i321−i32000000000
χ1522222222222-1222222-1-1-1-1-1-1-1-1−1+i3−1−i322-1-1-1-1-1-1-1−1+i3−1−i32022-1-1-1-1-1-1-1-100−1+i3−1−i31−i321+i321−i321+i32−1+i3−1−i31−i321+i321−i321+i320000−1+i3−1−i31−i321−i321+i321+i32000000000
χ162222222222-2-12222-2-2-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-122-20-2-2111111110022-1-1-1-122-1-1-1-10000-2-21111000000000
χ172222222222-2-12222-2-2-1-1-1-1-1-1-1-1−1−i3−1+i322-1-1-1-1-1-1-1−1−i3−1+i3-20-2-21111111100−1−i3−1+i31+i321−i321+i321−i32−1−i3−1+i31+i321−i321+i321−i3200001+i31−i3−1−i32−1−i32−1+i32−1+i32000000000
χ182222222222-2-12222-2-2-1-1-1-1-1-1-1-1−1+i3−1−i322-1-1-1-1-1-1-1−1+i3−1−i3-20-2-21111111100−1+i3−1−i31−i321+i321−i321+i32−1+i3−1−i31−i321+i321−i321+i3200001−i31+i3−1+i32−1+i32−1−i32−1−i32000000000
χ1922-122-122-1-102-1-122002222222-122-1-1-1-1-1-1-1-1-122020000000000-1-1-1-12222-1-1-1-1-1-102-1-100000022-1-1-1-1000
χ2022-122-122-1-102-1-122002222222-122-1-1-1-1-1-1-1-1-1220-2000000000011-1-12222-1-1-1-1-1-10-211000000-2-21111000
χ2122-122-122-1-102-1-122002222222-1−1−i3−1+i3-1-1-1-1-1-1-1-1-1−1−i3−1+i3020000000000-1-11+i321−i32−1−i3−1+i3−1−i3−1+i31+i321−i321+i321−i321+i321−i3202-1-1000000−1−i3−1+i31+i321+i321−i321−i32000
χ2222-122-122-1-102-1-122002222222-1−1−i3−1+i3-1-1-1-1-1-1-1-1-1−1−i3−1+i30-20000000000111+i321−i32−1−i3−1+i3−1−i3−1+i31+i321−i321+i321−i321+i321−i320-2110000001+i31−i3−1−i32−1−i32−1+i32−1+i32000
χ2322-122-122-1-102-1-122002222222-1−1+i3−1−i3-1-1-1-1-1-1-1-1-1−1+i3−1−i3020000000000-1-11−i321+i32−1+i3−1−i3−1+i3−1−i31−i321+i321−i321+i321−i321+i3202-1-1000000−1+i3−1−i31−i321−i321+i321+i32000
χ2422-122-122-1-102-1-122002222222-1−1+i3−1−i3-1-1-1-1-1-1-1-1-1−1+i3−1−i30-20000000000111−i321+i32−1+i3−1−i3−1+i3−1−i31−i321+i321−i321+i321−i321+i320-2110000001−i31+i3−1+i32−1+i32−1−i32−1−i32000
χ252-222-2-22-22-2022-22-200222-2-2-2-22222-2222-2-2-2-2-2-2000000000000002222-2-2-2-222-2-20000000000000000000
χ262-222-2-22-22-2022-22-200222-2-2-2-22−1−i3−1+i32-2222-2-2-2-21+i31−i300000000000000−1−i3−1+i3−1−i3−1+i31+i31−i31+i31−i3−1−i3−1+i31+i31−i30000000000000000000
χ272-222-2-22-22-2022-22-200222-2-2-2-22−1+i3−1−i32-2222-2-2-2-21−i31+i300000000000000−1+i3−1−i3−1+i3−1−i31−i31+i31−i31+i3−1+i3−1−i31−i31+i30000000000000000000
χ282-222-2-22-22-20-12-22-200-1-1-11111-1222-2-1-1-11111-2-20000−i3−i3−i3−i3i3i3i3i30022-1-111-2-2-1-111000000−i3i3−i3i3000000000
χ292-222-2-22-22-20-12-22-200-1-1-11111-1222-2-1-1-11111-2-20000i3i3i3i3−i3−i3−i3−i30022-1-111-2-2-1-111000000i3−i3i3−i3000000000
χ302-222-2-22-22-20-12-22-200-1-1-11111-1−1−i3−1+i32-2-1-1-111111+i31−i30000−i3−i3−i3−i3i3i3i3i300−1−i3−1+i31+i321−i32−1−i32−1+i321+i31−i31+i321−i32−1−i32−1+i32000000−3+i323−i323+i32−3−i32000000000
χ312-222-2-22-22-20-12-22-200-1-1-11111-1−1−i3−1+i32-2-1-1-111111+i31−i30000i3i3i3i3−i3−i3−i3−i300−1−i3−1+i31+i321−i32−1−i32−1+i321+i31−i31+i321−i32−1−i32−1+i320000003−i32−3+i32−3−i323+i32000000000
χ322-222-2-22-22-20-12-22-200-1-1-11111-1−1+i3−1−i32-2-1-1-111111−i31+i30000−i3−i3−i3−i3i3i3i3i300−1+i3−1−i31−i321+i32−1+i32−1−i321−i31+i31−i321+i32−1+i32−1−i320000003+i32−3−i32−3+i323−i32000000000
χ332-222-2-22-22-20-12-22-200-1-1-11111-1−1+i3−1−i32-2-1-1-111111−i31+i30000i3i3i3i3−i3−i3−i3−i300−1+i3−1−i31−i321+i32−1+i32−1−i321−i31+i31−i321+i32−1+i32−1−i32000000−3−i323+i323−i32−3+i32000000000
χ342-2-12-212-2-1102-112-200222-2-2-2-2-122-11-1-1-11111-2-20000000000003−3-1-122-2-211-1-111003−3000000003−33−3000
χ352-2-12-212-2-1102-112-200222-2-2-2-2-122-11-1-1-11111-2-2000000000000−33-1-122-2-211-1-11100−3300000000−33−33000
χ362-2-12-212-2-1102-112-200222-2-2-2-2-1−1−i3−1+i3-11-1-1-111111+i31−i30000000000003−31+i321−i32−1−i3−1+i31+i31−i3−1−i32−1+i321+i321−i32−1−i32−1+i32003−3000000002ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000
χ372-2-12-212-2-1102-112-200222-2-2-2-2-1−1−i3−1+i3-11-1-1-111111+i31−i3000000000000−331+i321−i32−1−i3−1+i31+i31−i3−1−i32−1+i321+i321−i32−1−i32−1+i3200−3300000000−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000
χ382-2-12-212-2-1102-112-200222-2-2-2-2-1−1+i3−1−i3-11-1-1-111111−i31+i30000000000003−31−i321+i32−1+i3−1−i31−i31+i3−1+i32−1−i321−i321+i32−1+i32−1−i32003−300000000−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000
χ392-2-12-212-2-1102-112-200222-2-2-2-2-1−1+i3−1−i3-11-1-1-111111−i31+i3000000000000−331−i321+i32−1+i3−1−i31−i31+i3−1+i32−1−i321−i321+i32−1+i32−1−i3200−3300000000ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000
χ40333333-1-13333-1-1-1-133-1-1-13-1-1-1300-1-1-1-1-13-1-1-100-13-1-13-1-1-13-1-1-1330000000000003-1-1-1000000000000-100
χ41333333-1-13333-1-1-1-133-1-1-13-1-1-1300-1-1-1-1-13-1-1-100-1-3-1-13-1-1-13-1-1-1-3-3000000000000-3111000000000000100
χ42333333-1-133-33-1-1-1-1-3-3-1-1-13-1-1-1300-1-1-1-1-13-1-1-1001311-3111-311133000000000000-3-1-1-1000000000000100
χ43333333-1-133-33-1-1-1-1-3-3-1-1-13-1-1-1300-1-1-1-1-13-1-1-1001-311-3111-3111-3-30000000000003111000000000000-100
χ4444-244-244-2-20-2-2-24400-2-2-2-2-2-2-2144-2-211111114400000000000000-2-2-2-2-2-2-2-211110000000000000000000
χ4544-244-244-2-20-2-2-24400-2-2-2-2-2-2-21−2−2i3−2+2i3-2-21111111−2−2i3−2+2i3000000000000001+i31−i31+i31−i31+i31−i31+i31−i3−1−i32−1+i32−1−i32−1+i320000000000000000000
χ4644-244-244-2-20-2-2-24400-2-2-2-2-2-2-21−2+2i3−2−2i3-2-21111111−2+2i3−2−2i3000000000000001−i31+i31−i31+i31−i31+i31−i31+i3−1+i32−1−i32−1+i32−1−i320000000000000000000
χ474-4-24-424-4-220-2-224-400-2-2-22222144-22111-1-1-1-1-4-400000000000000-2-2-2-2222211-1-10000000000000000000
χ484-4-24-424-4-220-2-224-400-2-2-222221−2−2i3−2+2i3-22111-1-1-1-12+2i32−2i3000000000000001+i31−i31+i31−i3−1−i3−1+i3−1−i3−1+i3−1−i32−1+i321+i321−i320000000000000000000
χ494-4-24-424-4-220-2-224-400-2-2-222221−2+2i3−2−2i3-22111-1-1-1-12−2i32+2i3000000000000001−i31+i31−i31+i3−1+i3−1−i3−1+i3−1−i3−1+i32−1−i321−i321+i320000000000000000000
χ50666666-2-2666-3-2-2-2-266111-3111-300-2-2111-311100-20-2-2-3111-3111000000000000000000000000000000000
χ51666666-2-266-6-3-2-2-2-2-6-6111-3111-300-2-2111-31110020223-1-1-13-1-1-1000000000000000000000000000000000
χ52666-3-3666-3-36066-3-3-3-30000000000-3-300000000060-3-300000000000000000000000000000000000000000
χ53666-3-3666-3-3-6066-3-3330000000000-3-3000000000-603300000000000000000000000000000000000000000
χ54666-3-36-2-2-3-360-2-211-3-34-2-204-2-2000114-2-204-2-200-201104-2-204-2-2000000000000000000000000000000000
χ55666-3-36-2-2-3-360-2-211-3-3-24-20-24-200011-24-20-24-200-20110-24-20-24-2000000000000000000000000000000000
χ56666-3-36-2-2-3-360-2-211-3-3-2-240-2-2400011-2-240-2-2400-20110-2-240-2-24000000000000000000000000000000000
χ57666-3-36-2-2-3-3-60-2-211334-2-204-2-2000114-2-204-2-20020-1-10-4220-422000000000000000000000000000000000
χ58666-3-36-2-2-3-3-60-2-21133-24-20-24-200011-24-20-24-20020-1-102-4202-42000000000000000000000000000000000
χ59666-3-36-2-2-3-3-60-2-21133-2-240-2-2400011-2-240-2-240020-1-1022-4022-4000000000000000000000000000000000
χ6066-366-3-2-2-3-30611-2-200-2-2-26-2-2-2-30011111-311100060000000000-3-30000000000000-211000000000000000
χ6166-366-3-2-2-3-30611-2-200-2-2-26-2-2-2-30011111-3111000-600000000003300000000000002-1-1000000000000000
χ626-666-6-6-226-606-22-2200-2-2-2-6222600-22-2-2-2-622200000000000000000000000000000000000000000000000
χ636-666-6-6-226-60-3-22-22001113-1-1-1-300-221113-1-1-1000000−3i3i3i3i33i3−i3−i3−i3000000000000000000000000000000000
χ646-666-6-6-226-60-3-22-22001113-1-1-1-300-221113-1-1-10000003i3−i3−i3−i3−3i3i3i3i3000000000000000000000000000000000
χ656-66-33-66-6-33006-6-33−3i33i30000000000-3300000000000−3i33i300000000000000000000000000000000000000000
χ666-66-33-66-6-33006-6-333i3−3i30000000000-33000000000003i3−3i300000000000000000000000000000000000000000
χ676-66-33-6-22-3300-221-1−3i33i34-2-20-4220001-14-2-20-4220000i3−i300−2i32i3002i3−2i3000000000000000000000000000000000
χ686-66-33-6-22-3300-221-1−3i33i3-24-202-420001-1-24-202-420000i3−i302i30−2i30−2i302i3000000000000000000000000000000000
χ696-66-33-6-22-3300-221-1−3i33i3-2-24022-40001-1-2-24022-40000i3−i30−2i32i3002i3−2i30000000000000000000000000000000000
χ706-66-33-6-22-3300-221-13i3−3i34-2-20-4220001-14-2-20-4220000−i3i3002i3−2i300−2i32i3000000000000000000000000000000000
χ716-66-33-6-22-3300-221-13i3−3i3-24-202-420001-1-24-202-420000−i3i30−2i302i302i30−2i3000000000000000000000000000000000
χ726-66-33-6-22-3300-221-13i3−3i3-2-24022-40001-1-2-24022-40000−i3i302i3−2i300−2i32i30000000000000000000000000000000000
χ736-6-36-63-22-33061-1-2200-2-2-2-6222-3001-11113-1-1-10000000000000033−3300000000000000−33000000000000000
χ746-6-36-63-22-33061-1-2200-2-2-2-6222-3001-11113-1-1-100000000000000−3333000000000000003−3000000000000000
χ751212-61212-6-4-4-6-60-622-4-400222-622230022-1-1-13-1-1-100000000000000000000000000000000000000000000000
χ761212-6-6-6-612123300-6-6-6-600000000000033000000000000000000000000000000000000000000000000000000
χ771212-6-6-6-6-4-433002222008-4-408-4-4000-1-1-4220-42200000000000000000000000000000000000000000000000
χ781212-6-6-6-6-4-43300222200-48-40-48-4000-1-12-4202-4200000000000000000000000000000000000000000000000
χ791212-6-6-6-6-4-43300222200-4-480-4-48000-1-122-4022-400000000000000000000000000000000000000000000000
χ8012-12-612-126-44-660-62-2-44002226-2-2-23002-2-1-1-1-311100000000000000000000000000000000000000000000000
χ8112-12-6-66612-123-300-66-660000000000003-3000000000000000000000000000000000000000000000000000000
χ8212-12-6-666-443-3002-22-2008-4-40-844000-11-42204-2-200000000000000000000000000000000000000000000000
χ8312-12-6-666-443-3002-22-200-48-404-84000-112-420-24-200000000000000000000000000000000000000000000000
χ8412-12-6-666-443-3002-22-200-4-48044-8000-1122-40-2-2400000000000000000000000000000000000000000000000

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