Finite Group Databasebeta

← Group #72321

Character table — Group #72321

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122444488888888888881111224444888888888888811112244448888888888888
order122222444422444444488883666661212121266121212121212122424242436666612121212661212121212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1
χ311111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-111111111111-1-1-1-11111-1-1-1-1
χ411111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11111
χ5111111-1-111-111-1-111-1-111-1-1111111-1-111-111-1-111-1-111-1-1111111-1-111-111-1-111-1-111-1-1
χ6111111-1-111-111-1-1-1-111-1-111111111-1-111-111-1-1-1-111-1-111111111-1-111-111-1-1-1-111-1-111
χ7111111-1-111-1-1-11111-1-1-1-111111111-1-111-1-1-11111-1-1-1-111111111-1-111-1-1-11111-1-1-1-111
χ8111111-1-111-1-1-111-1-11111-1-1111111-1-111-1-1-111-1-11111-1-1111111-1-111-1-1-111-1-11111-1-1
χ922222222-2-2-200000000000022222222-2-2-200000000000022222222-2-2-2000000000000
χ10222222-2-2-2-22000000000000222222-2-2-2-22000000000000222222-2-2-2-22000000000000
χ112222-2-2002-20002-2000000002222-2-2002-20002-2000000002222-2-2002-20002-200000000
χ122222-2-2002-2000-22000000002222-2-2002-2000-22000000002222-2-2002-2000-2200000000
χ132222-2-200-2202-200000000002222-2-200-2202-200000000002222-2-200-2202-20000000000
χ142222-2-200-220-2200000000002222-2-200-220-2200000000002222-2-200-220-220000000000
χ1522-2-2-222i−2i00000000000i2−i22−222-2-2-222i−2i00000000000i2−i22−222-2-2-222i−2i00000000000i2−i22−2
χ1622-2-2-222i−2i00000000000−i2i2−2222-2-2-222i−2i00000000000−i2i2−2222-2-2-222i−2i00000000000−i2i2−22
χ1722-2-2-22−2i2i00000000000i2−i2−2222-2-2-22−2i2i00000000000i2−i2−2222-2-2-22−2i2i00000000000i2−i2−22
χ1822-2-2-22−2i2i00000000000−i2i22−222-2-2-22−2i2i00000000000−i2i22−222-2-2-22−2i2i00000000000−i2i22−2
χ1944-4-44-40000000000000000044-4-44-40000000000000000044-4-44-400000000000000000
χ204-44-400000000000002i−2i00004-44-400000000000002i−2i00004-44-400000000000002i−2i0000
χ214-44-40000000000000−2i2i00004-44-40000000000000−2i2i00004-44-40000000000000−2i2i0000
χ224-4-44000000000002-20000004-4-44000000000002-20000004-4-44000000000002-2000000
χ234-4-4400000000000-220000004-4-4400000000000-220000004-4-4400000000000-22000000
χ2411111111111111111111111−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ25111111111111111-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−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−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ2611111111111-1-1-1-11111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ2711111111111-1-1-1-1-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−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−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ28111111-1-111-111-1-111-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ29111111-1-111-111-1-1-1-111-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ30111111-1-111-1-1-11111-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−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−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ31111111-1-111-1-1-111-1-11111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−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+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ3222222222-2-2-2000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i3000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i3000000000000
χ33222222-2-2-2-22000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i3000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i3000000000000
χ342222-2-2002-20002-200000000−1+i3−1+i3−1+i3−1+i31−i31−i300−1+i31−i3000−1+i31−i300000000−1−i3−1−i3−1−i3−1−i31+i31+i300−1−i31+i3000−1−i31+i300000000
χ352222-2-2002-2000-2200000000−1+i3−1+i3−1+i3−1+i31−i31−i300−1+i31−i30001−i3−1+i300000000−1−i3−1−i3−1−i3−1−i31+i31+i300−1−i31+i30001+i3−1−i300000000
χ362222-2-200-2202-20000000000−1+i3−1+i3−1+i3−1+i31−i31−i3001−i3−1+i30−1+i31−i30000000000−1−i3−1−i3−1−i3−1−i31+i31+i3001+i3−1−i30−1−i31+i30000000000
χ372222-2-200-220-220000000000−1+i3−1+i3−1+i3−1+i31−i31−i3001−i3−1+i301−i3−1+i30000000000−1−i3−1−i3−1−i3−1−i31+i31+i3001+i3−1−i301+i3−1−i30000000000
χ3822-2-2-222i−2i00000000000i2−i22−2−1+i3−1+i31−i31−i31−i3−1+i32ζ14−2ζ1400000000000−ζ5−ζ23ζ5+ζ23ζ5−ζ23−ζ5+ζ23−1−i3−1−i31+i31+i31+i3−1−i32ζ22−2ζ2200000000000−ζ7−ζ13ζ7+ζ13−ζ7+ζ13ζ7−ζ13
χ3922-2-2-222i−2i00000000000−i2i2−22−1+i3−1+i31−i31−i31−i3−1+i32ζ14−2ζ1400000000000ζ5+ζ23−ζ5−ζ23−ζ5+ζ23ζ5−ζ23−1−i3−1−i31+i31+i31+i3−1−i32ζ22−2ζ2200000000000ζ7+ζ13−ζ7−ζ13ζ7−ζ13−ζ7+ζ13
χ4022-2-2-22−2i2i00000000000i2−i2−22−1+i3−1+i31−i31−i31−i3−1+i3−2ζ142ζ1400000000000−ζ5−ζ23ζ5+ζ23−ζ5+ζ23ζ5−ζ23−1−i3−1−i31+i31+i31+i3−1−i3−2ζ222ζ2200000000000−ζ7−ζ13ζ7+ζ13ζ7−ζ13−ζ7+ζ13
χ4122-2-2-22−2i2i00000000000−i2i22−2−1+i3−1+i31−i31−i31−i3−1+i3−2ζ142ζ1400000000000ζ5+ζ23−ζ5−ζ23ζ5−ζ23−ζ5+ζ23−1−i3−1−i31+i31+i31+i3−1−i3−2ζ222ζ2200000000000ζ7+ζ13−ζ7−ζ13−ζ7+ζ13ζ7−ζ13
χ4244-4-44-400000000000000000−2+2i3−2+2i32−2i32−2i3−2+2i32−2i300000000000000000−2−2i3−2−2i32+2i32+2i3−2−2i32+2i300000000000000000
χ434-44-400000000000002i−2i0000−2+2i32−2i3−2+2i32−2i300000000000002ζ14−2ζ140000−2−2i32+2i3−2−2i32+2i300000000000002ζ22−2ζ220000
χ444-44-40000000000000−2i2i0000−2+2i32−2i3−2+2i32−2i30000000000000−2ζ142ζ140000−2−2i32+2i3−2−2i32+2i30000000000000−2ζ222ζ220000
χ454-4-44000000000002-2000000−2+2i32−2i32−2i3−2+2i300000000000−1+i31−i3000000−2−2i32+2i32+2i3−2−2i300000000000−1−i31+i3000000
χ464-4-4400000000000-22000000−2+2i32−2i32−2i3−2+2i3000000000001−i3−1+i3000000−2−2i32+2i32+2i3−2−2i3000000000001+i3−1−i3000000
χ4711111111111111111111111−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ48111111111111111-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+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+i321−i321−i321−i321−i321−i321−i321−i321−i32
χ4911111111111-1-1-1-11111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+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+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ5011111111111-1-1-1-1-1-1-1-11111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+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+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ51111111-1-111-111-1-111-1-111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ52111111-1-111-111-1-1-1-111-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32
χ53111111-1-111-1-1-11111-1-1-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+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+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32
χ54111111-1-111-1-1-111-1-11111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+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−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ5522222222-2-2-2000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i3000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i3000000000000
χ56222222-2-2-2-22000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i3000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i3000000000000
χ572222-2-2002-20002-200000000−1−i3−1−i3−1−i3−1−i31+i31+i300−1−i31+i3000−1−i31+i300000000−1+i3−1+i3−1+i3−1+i31−i31−i300−1+i31−i3000−1+i31−i300000000
χ582222-2-2002-2000-2200000000−1−i3−1−i3−1−i3−1−i31+i31+i300−1−i31+i30001+i3−1−i300000000−1+i3−1+i3−1+i3−1+i31−i31−i300−1+i31−i30001−i3−1+i300000000
χ592222-2-200-2202-20000000000−1−i3−1−i3−1−i3−1−i31+i31+i3001+i3−1−i30−1−i31+i30000000000−1+i3−1+i3−1+i3−1+i31−i31−i3001−i3−1+i30−1+i31−i30000000000
χ602222-2-200-220-220000000000−1−i3−1−i3−1−i3−1−i31+i31+i3001+i3−1−i301+i3−1−i30000000000−1+i3−1+i3−1+i3−1+i31−i31−i3001−i3−1+i301−i3−1+i30000000000
χ6122-2-2-222i−2i00000000000i2−i22−2−1−i3−1−i31+i31+i31+i3−1−i32ζ22−2ζ2200000000000−ζ7−ζ13ζ7+ζ13−ζ7+ζ13ζ7−ζ13−1+i3−1+i31−i31−i31−i3−1+i32ζ14−2ζ1400000000000−ζ5−ζ23ζ5+ζ23ζ5−ζ23−ζ5+ζ23
χ6222-2-2-222i−2i00000000000−i2i2−22−1−i3−1−i31+i31+i31+i3−1−i32ζ22−2ζ2200000000000ζ7+ζ13−ζ7−ζ13ζ7−ζ13−ζ7+ζ13−1+i3−1+i31−i31−i31−i3−1+i32ζ14−2ζ1400000000000ζ5+ζ23−ζ5−ζ23−ζ5+ζ23ζ5−ζ23
χ6322-2-2-22−2i2i00000000000i2−i2−22−1−i3−1−i31+i31+i31+i3−1−i3−2ζ222ζ2200000000000−ζ7−ζ13ζ7+ζ13ζ7−ζ13−ζ7+ζ13−1+i3−1+i31−i31−i31−i3−1+i3−2ζ142ζ1400000000000−ζ5−ζ23ζ5+ζ23−ζ5+ζ23ζ5−ζ23
χ6422-2-2-22−2i2i00000000000−i2i22−2−1−i3−1−i31+i31+i31+i3−1−i3−2ζ222ζ2200000000000ζ7+ζ13−ζ7−ζ13−ζ7+ζ13ζ7−ζ13−1+i3−1+i31−i31−i31−i3−1+i3−2ζ142ζ1400000000000ζ5+ζ23−ζ5−ζ23ζ5−ζ23−ζ5+ζ23
χ6544-4-44-400000000000000000−2−2i3−2−2i32+2i32+2i3−2−2i32+2i300000000000000000−2+2i3−2+2i32−2i32−2i3−2+2i32−2i300000000000000000
χ664-44-400000000000002i−2i0000−2−2i32+2i3−2−2i32+2i300000000000002ζ22−2ζ220000−2+2i32−2i3−2+2i32−2i300000000000002ζ14−2ζ140000
χ674-44-40000000000000−2i2i0000−2−2i32+2i3−2−2i32+2i30000000000000−2ζ222ζ220000−2+2i32−2i3−2+2i32−2i30000000000000−2ζ142ζ140000
χ684-4-44000000000002-2000000−2−2i32+2i32+2i3−2−2i300000000000−1−i31+i3000000−2+2i32−2i32−2i3−2+2i300000000000−1+i31−i3000000
χ694-4-4400000000000-22000000−2−2i32+2i32+2i3−2−2i3000000000001+i3−1−i3000000−2+2i32−2i32−2i3−2+2i3000000000001−i3−1+i3000000

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