Finite Group Databasebeta

← Group #13180325

Character table — Group #13180325

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size11224444668888888888121218181824243232323232323232323232323636484848484872727272108108144144
order1236336644333336666612122881212333333666666261212121212242424244866
χ1111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-111111111111111-1111111-1-1-1-1-1-1-1-1
χ31111−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i32111−1−i32−1+i3211111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1+i32
χ41111−1−i32−1+i32−1−i32−1+i3211111−1−i32−1+i32111−1−i32−1+i32111-1-1−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11111−1−i32−1+i321+i321+i321−i321−i32-1-11+i321−i32
χ51111−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i32111−1+i32−1−i3211111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1−i32
χ61111−1+i32−1−i32−1+i32−1−i3211111−1+i32−1−i32111−1+i32−1−i32111-1-1−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11111−1+i32−1−i321−i321−i321+i321+i32-1-11−i321+i32
χ72222222222-1-1-122-1-1-1222220022-1-1-1-1-1-1-1-1-1-1-1-102-1-1-12200000000
χ82222−1−i3−1+i3−1−i3−1+i322-1-1-1−1−i3−1+i3-1-1-1−1−i3−1+i322200−1−i3−1+i31+i321+i321+i321−i321−i321−i321+i321+i321+i321−i321−i321−i3202-1-1-1−1−i3−1+i300000000
χ92222−1+i3−1−i3−1+i3−1−i322-1-1-1−1+i3−1−i3-1-1-1−1+i3−1−i322200−1+i3−1−i31−i321−i321−i321+i321+i321+i321−i321−i321−i321+i321+i321+i3202-1-1-1−1+i3−1−i300000000
χ1022-1-12222222-1-1-1-12-1-1-1-1-1-1200222-1-12-1-12-1-12-1-10-12-1-1-1-100000000
χ1122-1-1222222-12-1-1-1-12-1-1-1-1-120022-12-1-12-1-12-1-12-10-1-12-1-1-100000000
χ1222-1-1222222-1-12-1-1-1-12-1-1-1-120022-1-12-1-12-1-12-1-120-1-1-12-1-100000000
χ1322-1-1−1−i3−1+i3−1−i3−1+i3222-1-11+i321−i322-1-11+i321−i32-1-1200−1−i3−1+i3−1−i31+i321+i32−1+i31−i321−i32−1−i31+i321+i32−1+i31−i321−i320-12-1-11+i321−i3200000000
χ1422-1-1−1−i3−1+i3−1−i3−1+i322-12-11+i321−i32-12-11+i321−i32-1-1200−1−i3−1+i31+i32−1−i31+i321−i32−1+i31−i321+i32−1−i31+i321−i32−1+i31−i320-1-12-11+i321−i3200000000
χ1522-1-1−1−i3−1+i3−1−i3−1+i322-1-121+i321−i32-1-121+i321−i32-1-1200−1−i3−1+i31+i321+i32−1−i31−i321−i32−1+i31+i321+i32−1−i31−i321−i32−1+i30-1-1-121+i321−i3200000000
χ1622-1-1−1+i3−1−i3−1+i3−1−i3222-1-11−i321+i322-1-11−i321+i32-1-1200−1+i3−1−i3−1+i31−i321−i32−1−i31+i321+i32−1+i31−i321−i32−1−i31+i321+i320-12-1-11−i321+i3200000000
χ1722-1-1−1+i3−1−i3−1+i3−1−i322-12-11−i321+i32-12-11−i321+i32-1-1200−1+i3−1−i31−i32−1+i31−i321+i32−1−i31+i321−i32−1+i31−i321+i32−1−i31+i320-1-12-11−i321+i3200000000
χ1822-1-1−1+i3−1−i3−1+i3−1−i322-1-121−i321+i32-1-121−i321+i32-1-1200−1+i3−1−i31−i321−i32−1+i31+i321+i32−1−i31−i321−i32−1+i31+i321+i32−1−i30-1-1-121−i321+i3200000000
χ1933330000-1333300333003-1-133000000000000003-1-1-1-1000000-1-100
χ2033330000-1333300333003-1-1-3-300000000000000-3-1-1-1-10000001100
χ21333333333-10003300033-13-111-1-1000000000000-1-1000-1-11111-11-1-1
χ22333333333-10003300033-13-1-1-1-1-10000000000001-1000-1-1-1-1-1-11-111
χ233333−3−3i32−3+3i32−3−3i32−3+3i323-1000−3−3i32−3+3i32000−3−3i32−3+3i32-13-1111+i321−i32000000000000-1-10001+i321−i32−1−i32−1−i32−1+i32−1+i32-111+i321−i32
χ243333−3−3i32−3+3i32−3−3i32−3+3i323-1000−3−3i32−3+3i32000−3−3i32−3+3i32-13-1-1-11+i321−i320000000000001-10001+i321−i321+i321+i321−i321−i321-1−1−i32−1+i32
χ253333−3+3i32−3−3i32−3+3i32−3−3i323-1000−3+3i32−3−3i32000−3+3i32−3−3i32-13-1111−i321+i32000000000000-1-10001−i321+i32−1+i32−1+i32−1−i32−1−i32-111−i321+i32
χ263333−3+3i32−3−3i32−3+3i32−3−3i323-1000−3+3i32−3−3i32000−3+3i32−3−3i32-13-1-1-11−i321+i320000000000001-10001−i321+i321−i321−i321+i321+i321-1−1+i32−1−i32
χ274-44-4-2-22200-2-2-2-2-222222000−2i22i200111111-1-1-1-1-1-10000000−i2i2−i2i20000
χ284-44-4-2-22200-2-2-2-2-2222220002i2−2i200111111-1-1-1-1-1-10000000i2−i2i2−i20000
χ294-44-41+i31−i3−1−i3−1+i300-2-2-21+i31−i3222−1−i3−1+i3000−2i22i200−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i320000000ζ7+ζ13−ζ7−ζ13ζ5+ζ23−ζ5−ζ230000
χ304-44-41+i31−i3−1−i3−1+i300-2-2-21+i31−i3222−1−i3−1+i30002i2−2i200−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i320000000−ζ7−ζ13ζ7+ζ13−ζ5−ζ23ζ5+ζ230000
χ314-44-41−i31+i3−1+i3−1−i300-2-2-21−i31+i3222−1+i3−1−i3000−2i22i200−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i320000000ζ5+ζ23−ζ5−ζ23ζ7+ζ13−ζ7−ζ130000
χ324-44-41−i31+i3−1+i3−1−i300-2-2-21−i31+i3222−1+i3−1−i30002i2−2i200−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i320000000−ζ5−ζ23ζ5+ζ23−ζ7−ζ13ζ7+ζ130000
χ3366660000-26-3-3-300-3-3-3006-2-200000000000000000-21110000000000
χ3466-3-30000-266-3-3006-3-300-31-2000000000000000001-2110000000000
χ3566-3-30000-26-36-300-36-300-31-20000000000000000011-210000000000
χ3666-3-30000-26-3-3600-3-3600-31-200000000000000000111-20000000000
χ3766-3-366666-2000-3-3000-3-31-3-200-2-2000000000000010001100000000
χ3866-3-3−3−3i3−3+3i3−3−3i3−3+3i36-20003+3i323−3i320003+3i323−3i321-3-2001+i31−i300000000000001000−1−i32−1+i3200000000
χ3966-3-3−3+3i3−3−3i3−3+3i3−3−3i36-20003−3i323+3i320003−3i323+3i321-3-2001−i31+i300000000000001000−1+i32−1−i3200000000
χ408-88-8-4-44400222-4-4-2-2-2440000000-1-1-1-1-1-1111111000000000000000
χ418-88-82+2i32−2i3−2−2i3−2+2i3002222+2i32−2i3-2-2-2−2−2i3−2+2i300000001+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32000000000000000
χ428-88-82−2i32+2i3−2+2i3−2−2i3002222−2i32+2i3-2-2-2−2+2i3−2−2i300000001−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32000000000000000
χ438-8-44-4-4440022-422-2-24-2-20000000-1-12-1-1211-211-2000000000000000
χ448-8-44-4-444002-4222-24-2-2-20000000-12-1-12-11-211-21000000000000000
χ458-8-44-4-44400-422224-2-2-2-200000002-1-12-1-1-211-211000000000000000
χ468-8-442+2i32−2i3−2−2i3−2+2i30022-4−1−i3−1+i3-2-241+i31−i300000001+i321+i32−1−i31−i321−i32−1+i3−1−i32−1−i321+i3−1+i32−1+i321−i3000000000000000
χ478-8-442+2i32−2i3−2−2i3−2+2i3002-42−1−i3−1+i3-24-21+i31−i300000001+i32−1−i31+i321−i32−1+i31−i32−1−i321+i3−1−i32−1+i321−i3−1+i32000000000000000
χ488-8-442+2i32−2i3−2−2i3−2+2i300-422−1−i3−1+i34-2-21+i31−i30000000−1−i31+i321+i32−1+i31−i321−i321+i3−1−i32−1−i321−i3−1+i32−1+i32000000000000000
χ498-8-442−2i32+2i3−2+2i3−2−2i30022-4−1+i3−1−i3-2-241−i31+i300000001−i321−i32−1+i31+i321+i32−1−i3−1+i32−1+i321−i3−1−i32−1−i321+i3000000000000000
χ508-8-442−2i32+2i3−2+2i3−2−2i3002-42−1+i3−1−i3-24-21−i31+i300000001−i32−1+i31−i321+i32−1−i31+i32−1+i321−i3−1+i32−1−i321+i3−1−i32000000000000000
χ518-8-442−2i32+2i3−2+2i3−2−2i300-422−1+i3−1−i34-2-21−i31+i30000000−1+i31−i321−i32−1−i31+i321+i321−i3−1+i32−1+i321+i3−1−i32−1−i32000000000000000
χ5299990000-3-30000000000-3-313300000000000000-310000000001-100
χ5399990000-3-30000000000-3-31-3-30000000000000031000000000-1100
χ541818-9-90000-6-6000000000033200000000000000000-10000000000000

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