Finite Group Databasebeta

← Group #10596620

Character table — Group #10596620

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1122222444466668888888888121218182424242411222224444666688888888881212181824242424
order123461212336622243366121212121212612446666226461212666622246666121212121212612446666
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111-1-11111111111111-1-1-1-1-1-1111111111111-1-11111111111111-1-1-1-1-1-1
χ31111111−1−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+i321111−1−i32−1−i32−1+i32−1+i321111111−1−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+i321111−1−i32−1−i32−1+i32−1+i32
χ41111111−1−i32−1+i32−1−i32−1+i321-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-11+i321+i321−i321−i321111111−1−i32−1+i32−1−i32−1+i321-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-11+i321+i321−i321−i32
χ51111111−1+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−i321111−1+i32−1+i32−1−i32−1−i321111111−1+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−i321111−1+i32−1+i32−1−i32−1−i32
χ61111111−1+i32−1−i32−1+i32−1−i321-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-11−i321−i321+i321+i321111111−1+i32−1−i32−1+i32−1−i321-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-11−i321−i321+i321+i32
χ7111-11-1-11111-11-111111-1-1-1-1-1-1-111-11-11-1111-11-1-11111-11-111111-1-1-1-1-1-1-111-11-11-1
χ8111-11-1-11111-1-1111111-1-1-1-1-1-1-11-11-11-11111-11-1-11111-1-1111111-1-1-1-1-1-1-11-11-11-11
χ9111-11-1-1−1−i32−1+i32−1−i32−1+i32-11-11−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32-111-1−1−i321+i32−1+i321−i32111-11-1-1−1−i32−1+i32−1−i32−1+i32-11-11−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32-111-1−1−i321+i32−1+i321−i32
χ10111-11-1-1−1−i32−1+i32−1−i32−1+i32-1-111−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32-11-111+i32−1−i321−i32−1+i32111-11-1-1−1−i32−1+i32−1−i32−1+i32-1-111−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32-11-111+i32−1−i321−i32−1+i32
χ11111-11-1-1−1+i32−1−i32−1+i32−1−i32-11-11−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32-111-1−1+i321−i32−1−i321+i32111-11-1-1−1+i32−1−i32−1+i32−1−i32-11-11−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32-111-1−1+i321−i32−1−i321+i32
χ12111-11-1-1−1+i32−1−i32−1+i32−1−i32-1-111−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32-11-111−i32−1+i321+i32−1−i32111-11-1-1−1+i32−1−i32−1+i32−1−i32-1-111−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32-11-111−i32−1+i321+i32−1−i32
χ1322-12-1-1-122222002-1-1-1-122-1-1-1-1-1-100000022-12-1-1-122222002-1-1-1-122-1-1-1-1-1-1000000
χ1422-12-1-1-1−1−i3−1+i3−1−i3−1+i320021+i321−i321+i321−i32−1−i3−1+i31+i321+i321−i321−i32-1-100000022-12-1-1-1−1−i3−1+i3−1−i3−1+i320021+i321−i321+i321−i32−1−i3−1+i31+i321+i321−i321−i32-1-1000000
χ1522-12-1-1-1−1+i3−1−i3−1+i3−1−i320021−i321+i321−i321+i32−1+i3−1−i31−i321−i321+i321+i32-1-100000022-12-1-1-1−1+i3−1−i3−1+i3−1−i320021−i321+i321−i321+i32−1+i3−1−i31−i321−i321+i321+i32-1-1000000
χ1622-1-2-1112222-2002-1-1-1-1-2-211111-100000022-1-2-1112222-2002-1-1-1-1-2-211111-1000000
χ1722-1-2-111−1−i3−1+i3−1−i3−1+i3-20021+i321−i321+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i321-100000022-1-2-111−1−i3−1+i3−1−i3−1+i3-20021+i321−i321+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i321-1000000
χ1822-1-2-111−1+i3−1−i3−1+i3−1−i3-20021−i321+i321−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i321-100000022-1-2-111−1+i3−1−i3−1+i3−1−i3-20021−i321+i321−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i321-1000000
χ1933333330000-133-10000000000-1-1-1-1000033333330000-133-10000000000-1-1-1-10000
χ2033333330000-1-3-3-10000000000-1-111000033333330000-1-3-3-10000000000-1-1110000
χ21333-33-3-3000013-3-100000000001-1-110000333-33-3-3000013-3-100000000001-1-110000
χ22333-33-3-300001-33-100000000001-11-10000333-33-3-300001-33-100000000001-11-10000
χ234-440-400-2-2220000-2-222000000000000004-440-400-2-2220000-2-22200000000000000
χ244-440-4001+i31−i3−1−i3−1+i300001+i31−i3−1−i3−1+i3000000000000004-440-4001+i31−i3−1−i3−1+i300001+i31−i3−1−i3−1+i300000000000000
χ254-440-4001−i31+i3−1+i3−1−i300001−i31+i3−1+i3−1−i3000000000000004-440-4001−i31+i3−1+i3−1−i300001−i31+i3−1+i3−1−i300000000000000
χ264-4-20223−23-2-222000011-1-1003−33−3000000004-4-20223−23-2-222000011-1-1003−33−300000000
χ274-4-20223−231+i31−i3−1−i3−1+i30000−1−i32−1+i321+i321−i32002ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11000000004-4-20223−231+i31−i3−1−i3−1+i30000−1−i32−1+i321+i321−i32002ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ1100000000
χ284-4-20223−231−i31+i3−1+i3−1−i30000−1+i32−1−i321−i321+i3200−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ11000000004-4-20223−231−i31+i3−1+i3−1−i30000−1+i32−1−i321−i321+i3200−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ1100000000
χ294-4-202−2323-2-222000011-1-100−33−33000000004-4-202−2323-2-222000011-1-100−33−3300000000
χ304-4-202−23231+i31−i3−1−i3−1+i30000−1−i32−1+i321+i321−i3200−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ11000000004-4-202−23231+i31−i3−1−i3−1+i30000−1−i32−1+i321+i321−i3200−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ1100000000
χ314-4-202−23231−i31+i3−1+i3−1−i30000−1+i32−1−i321−i321+i3200ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ11000000004-4-202−23231−i31+i3−1+i3−1−i30000−1+i32−1−i321−i321+i3200ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ1100000000
χ3266-36-3-3-30000-200-200000000001100000066-36-3-3-30000-200-2000000000011000000
χ3366-3-6-3330000200-20000000000-1100000066-3-6-3330000200-20000000000-11000000
χ34111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ35111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ361111111−1−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+i321111−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-11+i321−i321+i321−i32-1-1-1-11+i321−i321+i321−i321+i321−i321+i321+i321−i321−i32-1-1-1-11+i321+i321−i321−i32
χ371111111−1−i32−1+i32−1−i32−1+i321-1-11−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-11+i321+i321−i321−i32-1-1-1-1-1-1-11+i321−i321+i321−i32-111-11+i321−i321+i321−i321+i321−i321+i321+i321−i321−i32-1-111−1−i32−1−i32−1+i32−1+i32
χ381111111−1+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−i321111−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-11−i321+i321−i321+i32-1-1-1-11−i321+i321−i321+i321−i321+i321−i321−i321+i321+i32-1-1-1-11−i321−i321+i321+i32
χ391111111−1+i32−1−i32−1+i32−1−i321-1-11−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-11−i321−i321+i321+i32-1-1-1-1-1-1-11−i321+i321−i321+i32-111-11−i321+i321−i321+i321−i321+i321−i321−i321+i321+i32-1-111−1+i32−1+i32−1−i32−1−i32
χ40111-11-1-11111-11-111111-1-1-1-1-1-1-111-11-11-1-1-1-11-111-1-1-1-11-11-1-1-1-1-11111111-1-11-11-11
χ41111-11-1-11111-1-1111111-1-1-1-1-1-1-11-11-11-11-1-1-11-111-1-1-1-111-1-1-1-1-1-11111111-11-11-11-1
χ42111-11-1-1−1−i32−1+i32−1−i32−1+i32-11-11−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32-111-1−1−i321+i32−1+i321−i32-1-1-11-1111+i321−i321+i321−i321-11-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-111+i32−1−i321−i32−1+i32
χ43111-11-1-1−1−i32−1+i32−1−i32−1+i32-1-111−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32-11-111+i32−1−i321−i32−1+i32-1-1-11-1111+i321−i321+i321−i3211-1-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321-11-1−1−i321+i32−1+i321−i32
χ44111-11-1-1−1+i32−1−i32−1+i32−1−i32-11-11−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32-111-1−1+i321−i32−1−i321+i32-1-1-11-1111−i321+i321−i321+i321-11-11−i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-111−i32−1+i321+i32−1−i32
χ45111-11-1-1−1+i32−1−i32−1+i32−1−i32-1-111−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32-11-111−i32−1+i321+i32−1−i32-1-1-11-1111−i321+i321−i321+i3211-1-11−i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321-11-1−1+i321−i32−1−i321+i32
χ4622-12-1-1-122222002-1-1-1-122-1-1-1-1-1-1000000-2-21-2111-2-2-2-2-200-21111-2-2111111000000
χ4722-12-1-1-1−1−i3−1+i3−1−i3−1+i320021+i321−i321+i321−i32−1−i3−1+i31+i321+i321−i321−i32-1-1000000-2-21-21111+i31−i31+i31−i3-200-2−1−i32−1+i32−1−i32−1+i321+i31−i3−1−i32−1−i32−1+i32−1+i3211000000
χ4822-12-1-1-1−1+i3−1−i3−1+i3−1−i320021−i321+i321−i321+i32−1+i3−1−i31−i321−i321+i321+i32-1-1000000-2-21-21111−i31+i31−i31+i3-200-2−1+i32−1−i32−1+i32−1−i321−i31+i3−1+i32−1+i32−1−i32−1−i3211000000
χ4922-1-2-1112222-2002-1-1-1-1-2-211111-1000000-2-2121-1-1-2-2-2-2200-2111122-1-1-1-1-11000000
χ5022-1-2-111−1−i3−1+i3−1−i3−1+i3-20021+i321−i321+i321−i321+i31−i3−1−i32−1−i32−1+i32−1+i321-1000000-2-2121-1-11+i31−i31+i31−i3200-2−1−i32−1+i32−1−i32−1+i32−1−i3−1+i31+i321+i321−i321−i32-11000000
χ5122-1-2-111−1+i3−1−i3−1+i3−1−i3-20021−i321+i321−i321+i321−i31+i3−1+i32−1+i32−1−i32−1−i321-1000000-2-2121-1-11−i31+i31−i31+i3200-2−1+i32−1−i32−1+i32−1−i32−1+i3−1−i31−i321−i321+i321+i32-11000000
χ5233333330000-133-10000000000-1-1-1-10000-3-3-3-3-3-3-300001-3-31000000000011110000
χ5333333330000-1-3-3-10000000000-1-1110000-3-3-3-3-3-3-300001331000000000011-1-10000
χ54333-33-3-3000013-3-100000000001-1-110000-3-3-33-3330000-1-3310000000000-111-10000
χ55333-33-3-300001-33-100000000001-11-10000-3-3-33-3330000-13-310000000000-11-110000
χ564-440-400-2-2220000-2-22200000000000000-44-4040022-2-2000022-2-200000000000000
χ574-440-4001+i31−i3−1−i3−1+i300001+i31−i3−1−i3−1+i300000000000000-44-40400−1−i3−1+i31+i31−i30000−1−i3−1+i31+i31−i300000000000000
χ584-440-4001−i31+i3−1+i3−1−i300001−i31+i3−1+i3−1−i300000000000000-44-40400−1+i3−1−i31−i31+i30000−1+i3−1−i31−i31+i300000000000000
χ594-4-20223−23-2-222000011-1-1003−33−300000000-4420-2−232322-2-20000-1-11100−33−3300000000
χ604-4-20223−231+i31−i3−1−i3−1+i30000−1−i32−1+i321+i321−i32002ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ1100000000-4420-2−2323−1−i3−1+i31+i31−i300001+i321−i32−1−i32−1+i3200−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ1100000000
χ614-4-20223−231−i31+i3−1+i3−1−i30000−1+i32−1−i321−i321+i3200−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ1100000000-4420-2−2323−1+i3−1−i31−i31+i300001−i321+i32−1+i32−1−i3200ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ1100000000
χ624-4-202−2323-2-222000011-1-100−33−3300000000-4420-223−2322-2-20000-1-111003−33−300000000
χ634-4-202−23231+i31−i3−1−i3−1+i30000−1−i32−1+i321+i321−i3200−2ζ7−ζ112ζ7+ζ11ζ7+2ζ11−ζ7−2ζ1100000000-4420-223−23−1−i3−1+i31+i31−i300001+i321−i32−1−i32−1+i32002ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ1100000000
χ644-4-202−23231−i31+i3−1+i3−1−i30000−1+i32−1−i321−i321+i3200ζ7+2ζ11−ζ7−2ζ11−2ζ7−ζ112ζ7+ζ1100000000-4420-223−23−1+i3−1−i31−i31+i300001−i321+i32−1+i32−1−i3200−ζ7−2ζ11ζ7+2ζ112ζ7+ζ11−2ζ7−ζ1100000000
χ6566-36-3-3-30000-200-2000000000011000000-6-63-6333000020020000000000-1-1000000
χ6666-3-6-3330000200-20000000000-11000000-6-6363-3-30000-200200000000001-1000000

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