Finite Group Databasebeta

← Group #10593589

Character table — Group #10593589

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size112226688888888122424242411222668888888812242424241122266888888881224242424
order124882436121224242424844883612242461236121224242424241212242436122424612361212242424242412122424
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111-1-1-1-11111111111111111-1-1-1-11111111111111111-1-1-1-1
χ3111-1-1111111-1-1-1-1-11-11-1111-1-1111111-1-1-1-1-11-11-1111-1-1111111-1-1-1-1-11-11-1
χ4111-1-1111111-1-1-1-1-1-11-11111-1-1111111-1-1-1-1-1-11-11111-1-1111111-1-1-1-1-1-11-11
χ52222222-1-1-1-1-1-1-1-1200002222222-1-1-1-1-1-1-1-1200002222222-1-1-1-1-1-1-1-120000
χ6222-2-222-1-1-1-11111-20000222-2-222-1-1-1-11111-20000222-2-222-1-1-1-11111-20000
χ722-200-2222-2-200000000022-200-2222-2-200000000022-200-2222-2-2000000000
χ822-200-22-1-11133−3−30000022-200-22-1-11133−3−30000022-200-22-1-11133−3−300000
χ922-200-22-1-111−3−3330000022-200-22-1-111−3−3330000022-200-22-1-111−3−33300000
χ1033333-1-100000000-111-1-133333-1-100000000-111-1-133333-1-100000000-111-1-1
χ1133333-1-100000000-1-1-11133333-1-100000000-1-1-11133333-1-100000000-1-1-111
χ12333-3-3-1-10000000011-1-11333-3-3-1-10000000011-1-11333-3-3-1-10000000011-1-11
χ13333-3-3-1-1000000001-111-1333-3-3-1-1000000001-111-1333-3-3-1-1000000001-111-1
χ144-4022−22001-13−3ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23000004-4022−22001-13−3ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23000004-4022−22001-13−3ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ2300000
χ154-4022−22001-1−33ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7000004-4022−22001-1−33ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7000004-4022−22001-1−33ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ700000
χ164-4022−2200-22002−2−22000004-4022−2200-22002−2−22000004-4022−2200-22002−2−2200000
χ174-40−2222001-13−3−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23000004-40−2222001-13−3−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23000004-40−2222001-13−3−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ2300000
χ184-40−2222001-1−33−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7000004-40−2222001-1−33−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7000004-40−2222001-1−33−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ700000
χ194-40−222200-2200−222−2000004-40−222200-2200−222−2000004-40−222200-2200−222−200000
χ2066-6002-2000000000000066-6002-2000000000000066-6002-20000000000000
χ2111111111111111111111−1+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+i32−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ221111111111111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−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−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ23111-1-1111111-1-1-1-1-11-11-1−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32
χ24111-1-1111111-1-1-1-1-1-11-11−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i321−i32−1+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i32
χ252222222-1-1-1-1-1-1-1-120000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i32−1+i30000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i32−1−i30000
χ26222-2-222-1-1-1-11111-20000−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i30000−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i30000
χ2722-200-2222-2-2000000000−1+i3−1+i31−i3001−i3−1+i3−1+i3−1+i31−i31−i3000000000−1−i3−1−i31+i3001+i3−1−i3−1−i3−1−i31+i31+i3000000000
χ2822-200-22-1-11133−3−300000−1+i3−1+i31−i3001−i3−1+i31−i321−i32−1+i32−1+i32−ζ14−2ζ22−ζ14−2ζ22ζ14+2ζ22ζ14+2ζ2200000−1−i3−1−i31+i3001+i3−1−i31+i321+i32−1−i32−1−i322ζ14+ζ222ζ14+ζ22−2ζ14−ζ22−2ζ14−ζ2200000
χ2922-200-22-1-111−3−33300000−1+i3−1+i31−i3001−i3−1+i31−i321−i32−1+i32−1+i32ζ14+2ζ22ζ14+2ζ22−ζ14−2ζ22−ζ14−2ζ2200000−1−i3−1−i31+i3001+i3−1−i31+i321+i32−1−i32−1−i32−2ζ14−ζ22−2ζ14−ζ222ζ14+ζ222ζ14+ζ2200000
χ3033333-1-100000000-111-1-1−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32000000001−i32−1+i32−1+i321−i321−i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32000000001+i32−1−i32−1−i321+i321+i32
χ3133333-1-100000000-1-1-111−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32000000001−i321−i321−i32−1+i32−1+i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32000000001+i321+i321+i32−1−i32−1−i32
χ32333-3-3-1-10000000011-1-11−3+3i32−3+3i32−3+3i323−3i323−3i321−i321−i3200000000−1+i32−1+i321−i321−i32−1+i32−3−3i32−3−3i32−3−3i323+3i323+3i321+i321+i3200000000−1−i32−1−i321+i321+i32−1−i32
χ33333-3-3-1-1000000001-111-1−3+3i32−3+3i32−3+3i323−3i323−3i321−i321−i3200000000−1+i321−i32−1+i32−1+i321−i32−3−3i32−3−3i32−3−3i323+3i323+3i321+i321+i3200000000−1−i321+i32−1−i32−1−i321+i32
χ344-4022−22001-13−3ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ2300000−2+2i32−2i302ζ5−2ζ23−2ζ5+2ζ2300−1+i321−i32−ζ14−2ζ22ζ14+2ζ22ζ7+ζ13+ζ23−ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ5−ζ7−ζ1300000−2−2i32+2i30−2ζ7+2ζ132ζ7−2ζ1300−1−i321+i322ζ14+ζ22−2ζ14−ζ22−ζ5−ζ13−ζ23ζ5+ζ13+ζ23−ζ5−ζ7−ζ23ζ5+ζ7+ζ2300000
χ354-4022−22001-1−33ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ700000−2+2i32−2i302ζ5−2ζ23−2ζ5+2ζ2300−1+i321−i32ζ14+2ζ22−ζ14−2ζ22−ζ5−ζ7−ζ13ζ5+ζ7+ζ13−ζ7−ζ13−ζ23ζ7+ζ13+ζ2300000−2−2i32+2i30−2ζ7+2ζ132ζ7−2ζ1300−1−i321+i32−2ζ14−ζ222ζ14+ζ22ζ5+ζ7+ζ23−ζ5−ζ7−ζ23ζ5+ζ13+ζ23−ζ5−ζ13−ζ2300000
χ364-4022−2200-22002−2−2200000−2+2i32−2i302ζ5−2ζ23−2ζ5+2ζ23001−i3−1+i300ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ2300000−2−2i32+2i30−2ζ7+2ζ132ζ7−2ζ13001+i3−1−i300−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ1300000
χ374-40−2222001-13−3−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ2300000−2+2i32−2i30−2ζ5+2ζ232ζ5−2ζ2300−1+i321−i32−ζ14−2ζ22ζ14+2ζ22−ζ7−ζ13−ζ23ζ7+ζ13+ζ23−ζ5−ζ7−ζ13ζ5+ζ7+ζ1300000−2−2i32+2i302ζ7−2ζ13−2ζ7+2ζ1300−1−i321+i322ζ14+ζ22−2ζ14−ζ22ζ5+ζ13+ζ23−ζ5−ζ13−ζ23ζ5+ζ7+ζ23−ζ5−ζ7−ζ2300000
χ384-40−2222001-1−33−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ700000−2+2i32−2i30−2ζ5+2ζ232ζ5−2ζ2300−1+i321−i32ζ14+2ζ22−ζ14−2ζ22ζ5+ζ7+ζ13−ζ5−ζ7−ζ13ζ7+ζ13+ζ23−ζ7−ζ13−ζ2300000−2−2i32+2i302ζ7−2ζ13−2ζ7+2ζ1300−1−i321+i32−2ζ14−ζ222ζ14+ζ22−ζ5−ζ7−ζ23ζ5+ζ7+ζ23−ζ5−ζ13−ζ23ζ5+ζ13+ζ2300000
χ394-40−222200-2200−222−200000−2+2i32−2i30−2ζ5+2ζ232ζ5−2ζ23001−i3−1+i300−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ2300000−2−2i32+2i302ζ7−2ζ13−2ζ7+2ζ13001+i3−1−i300ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ1300000
χ4066-6002-20000000000000−3+3i3−3+3i33−3i300−1+i31−i30000000000000−3−3i3−3−3i33+3i300−1−i31+i30000000000000
χ4111111111111111111111−1−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−i32−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ421111111111111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+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+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ43111-1-1111111-1-1-1-1-11-11-1−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i321−i32−1+i321−i32
χ44111-1-1111111-1-1-1-1-1-11-11−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i321−i32−1+i32
χ452222222-1-1-1-1-1-1-1-120000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i32−1−i30000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i32−1+i30000
χ46222-2-222-1-1-1-11111-20000−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i30000−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i30000
χ4722-200-2222-2-2000000000−1−i3−1−i31+i3001+i3−1−i3−1−i3−1−i31+i31+i3000000000−1+i3−1+i31−i3001−i3−1+i3−1+i3−1+i31−i31−i3000000000
χ4822-200-22-1-11133−3−300000−1−i3−1−i31+i3001+i3−1−i31+i321+i32−1−i32−1−i322ζ14+ζ222ζ14+ζ22−2ζ14−ζ22−2ζ14−ζ2200000−1+i3−1+i31−i3001−i3−1+i31−i321−i32−1+i32−1+i32−ζ14−2ζ22−ζ14−2ζ22ζ14+2ζ22ζ14+2ζ2200000
χ4922-200-22-1-111−3−33300000−1−i3−1−i31+i3001+i3−1−i31+i321+i32−1−i32−1−i32−2ζ14−ζ22−2ζ14−ζ222ζ14+ζ222ζ14+ζ2200000−1+i3−1+i31−i3001−i3−1+i31−i321−i32−1+i32−1+i32ζ14+2ζ22ζ14+2ζ22−ζ14−2ζ22−ζ14−2ζ2200000
χ5033333-1-100000000-111-1-1−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32000000001+i32−1−i32−1−i321+i321+i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32000000001−i32−1+i32−1+i321−i321−i32
χ5133333-1-100000000-1-1-111−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i32000000001+i321+i321+i32−1−i32−1−i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i32000000001−i321−i321−i32−1+i32−1+i32
χ52333-3-3-1-10000000011-1-11−3−3i32−3−3i32−3−3i323+3i323+3i321+i321+i3200000000−1−i32−1−i321+i321+i32−1−i32−3+3i32−3+3i32−3+3i323−3i323−3i321−i321−i3200000000−1+i32−1+i321−i321−i32−1+i32
χ53333-3-3-1-1000000001-111-1−3−3i32−3−3i32−3−3i323+3i323+3i321+i321+i3200000000−1−i321+i32−1−i32−1−i321+i32−3+3i32−3+3i32−3+3i323−3i323−3i321−i321−i3200000000−1+i321−i32−1+i32−1+i321−i32
χ544-4022−22001-13−3ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ2300000−2−2i32+2i30−2ζ7+2ζ132ζ7−2ζ1300−1−i321+i322ζ14+ζ22−2ζ14−ζ22−ζ5−ζ13−ζ23ζ5+ζ13+ζ23−ζ5−ζ7−ζ23ζ5+ζ7+ζ2300000−2+2i32−2i302ζ5−2ζ23−2ζ5+2ζ2300−1+i321−i32−ζ14−2ζ22ζ14+2ζ22ζ7+ζ13+ζ23−ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ5−ζ7−ζ1300000
χ554-4022−22001-1−33ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ700000−2−2i32+2i30−2ζ7+2ζ132ζ7−2ζ1300−1−i321+i32−2ζ14−ζ222ζ14+ζ22ζ5+ζ7+ζ23−ζ5−ζ7−ζ23ζ5+ζ13+ζ23−ζ5−ζ13−ζ2300000−2+2i32−2i302ζ5−2ζ23−2ζ5+2ζ2300−1+i321−i32ζ14+2ζ22−ζ14−2ζ22−ζ5−ζ7−ζ13ζ5+ζ7+ζ13−ζ7−ζ13−ζ23ζ7+ζ13+ζ2300000
χ564-4022−2200-22002−2−2200000−2−2i32+2i30−2ζ7+2ζ132ζ7−2ζ13001+i3−1−i300−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ1300000−2+2i32−2i302ζ5−2ζ23−2ζ5+2ζ23001−i3−1+i300ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ2300000
χ574-40−2222001-13−3−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ2300000−2−2i32+2i302ζ7−2ζ13−2ζ7+2ζ1300−1−i321+i322ζ14+ζ22−2ζ14−ζ22ζ5+ζ13+ζ23−ζ5−ζ13−ζ23ζ5+ζ7+ζ23−ζ5−ζ7−ζ2300000−2+2i32−2i30−2ζ5+2ζ232ζ5−2ζ2300−1+i321−i32−ζ14−2ζ22ζ14+2ζ22−ζ7−ζ13−ζ23ζ7+ζ13+ζ23−ζ5−ζ7−ζ13ζ5+ζ7+ζ1300000
χ584-40−2222001-1−33−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ700000−2−2i32+2i302ζ7−2ζ13−2ζ7+2ζ1300−1−i321+i32−2ζ14−ζ222ζ14+ζ22−ζ5−ζ7−ζ23ζ5+ζ7+ζ23−ζ5−ζ13−ζ23ζ5+ζ13+ζ2300000−2+2i32−2i30−2ζ5+2ζ232ζ5−2ζ2300−1+i321−i32ζ14+2ζ22−ζ14−2ζ22ζ5+ζ7+ζ13−ζ5−ζ7−ζ13ζ7+ζ13+ζ23−ζ7−ζ13−ζ2300000
χ594-40−222200-2200−222−200000−2−2i32+2i302ζ7−2ζ13−2ζ7+2ζ13001+i3−1−i300ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ1300000−2+2i32−2i30−2ζ5+2ζ232ζ5−2ζ23001−i3−1+i300−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ2300000
χ6066-6002-20000000000000−3−3i3−3−3i33+3i300−1−i31+i30000000000000−3+3i3−3+3i33−3i300−1+i31−i30000000000000

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