Finite Group Databasebeta

← Group #72413

Character table — Group #72413

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122224444488888888161611112222444448888888816161111222244444888888881616
order122244444888844888888243666121212121224242424121224242424242461236661212121212242424241212242424242424612
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1
χ31111111111111-1-1-1-11111-1-11111111111111-1-1-1-11111-1-11111111111111-1-1-1-11111-1-1
χ41111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-111
χ5111111111-1-1-1-111-1-111-1-11-1111111111-1-1-1-111-1-111-1-11-1111111111-1-1-1-111-1-111-1-11-1
χ6111111111-1-1-1-111-1-1-1-111-11111111111-1-1-1-111-1-1-1-111-11111111111-1-1-1-111-1-1-1-111-11
χ7111111111-1-1-1-1-1-11111-1-1-11111111111-1-1-1-1-1-11111-1-1-11111111111-1-1-1-1-1-11111-1-1-11
χ8111111111-1-1-1-1-1-111-1-1111-1111111111-1-1-1-1-1-111-1-1111-1111111111-1-1-1-1-1-111-1-1111-1
χ922222-2-22-200002-20000000022222-2-22-200002-20000000022222-2-22-200002-200000000
χ1022222-2-22-20000-220000000022222-2-22-20000-220000000022222-2-22-20000-2200000000
χ112222-222-2-222-2-200000000002222-222-2-222-2-200000000002222-222-2-222-2-20000000000
χ122222-222-2-2-2-22200000000002222-222-2-2-2-22200000000002222-222-2-2-2-2220000000000
χ132222-2-2-2-220000002i−2i0000002222-2-2-2-220000002i−2i0000002222-2-2-2-220000002i−2i000000
χ142222-2-2-2-22000000−2i2i0000002222-2-2-2-22000000−2i2i0000002222-2-2-2-22000000−2i2i000000
χ1522-2-20-22002i−2i000000i2−i22−20022-2-20-22002i−2i000000i2−i22−20022-2-20-22002i−2i000000i2−i22−200
χ1622-2-20-22002i−2i000000−i2i2−220022-2-20-22002i−2i000000−i2i2−220022-2-20-22002i−2i000000−i2i2−2200
χ1722-2-20-2200−2i2i000000i2−i2−220022-2-20-2200−2i2i000000i2−i2−220022-2-20-2200−2i2i000000i2−i2−2200
χ1822-2-20-2200−2i2i000000−i2i22−20022-2-20-2200−2i2i000000−i2i22−20022-2-20-2200−2i2i000000−i2i22−200
χ1944-4-404-4000000000000000044-4-404-4000000000000000044-4-404-40000000000000000
χ204-44-4400-40000000000000004-44-4400-40000000000000004-44-4400-4000000000000000
χ214-44-4-40040000000000000004-44-4-40040000000000000004-44-4-4004000000000000000
χ224-4-44000000022−2200000000004-4-44000000022−2200000000004-4-44000000022−220000000000
χ234-4-440000000−222200000000004-4-440000000−222200000000004-4-440000000−22220000000000
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
χ2511111111111111111-1-1-1-1-1-1−1+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+i32−1+i32−1+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−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32
χ261111111111111-1-1-1-11111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ271111111111111-1-1-1-1-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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
χ28111111111-1-1-1-111-1-111-1-11-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−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−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32
χ29111111111-1-1-1-111-1-1-1-111-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−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−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32
χ30111111111-1-1-1-1-1-11111-1-1-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−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+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32
χ31111111111-1-1-1-1-1-111-1-1111-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32
χ3222222-2-22-200002-200000000−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i30000−1+i31−i300000000−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i30000−1−i31+i300000000
χ3322222-2-22-20000-2200000000−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i300001−i3−1+i300000000−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i300001+i3−1−i300000000
χ342222-222-2-222-2-20000000000−1+i3−1+i3−1+i3−1+i31−i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i30000000000−1−i3−1−i3−1−i3−1−i31+i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i30000000000
χ352222-222-2-2-2-2220000000000−1+i3−1+i3−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i30000000000−1−i3−1−i3−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i30000000000
χ362222-2-2-2-220000002i−2i000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i30000002ζ14−2ζ14000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i30000002ζ22−2ζ22000000
χ372222-2-2-2-22000000−2i2i000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i3000000−2ζ142ζ14000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i3000000−2ζ222ζ22000000
χ3822-2-20-22002i−2i000000i2−i22−200−1+i3−1+i31−i31−i301−i3−1+i3002ζ14−2ζ14000000−ζ5−ζ23ζ5+ζ23ζ5−ζ23−ζ5+ζ2300−1−i3−1−i31+i31+i301+i3−1−i3002ζ22−2ζ22000000−ζ7−ζ13ζ7+ζ13−ζ7+ζ13ζ7−ζ1300
χ3922-2-20-22002i−2i000000−i2i2−2200−1+i3−1+i31−i31−i301−i3−1+i3002ζ14−2ζ14000000ζ5+ζ23−ζ5−ζ23−ζ5+ζ23ζ5−ζ2300−1−i3−1−i31+i31+i301+i3−1−i3002ζ22−2ζ22000000ζ7+ζ13−ζ7−ζ13ζ7−ζ13−ζ7+ζ1300
χ4022-2-20-2200−2i2i000000i2−i2−2200−1+i3−1+i31−i31−i301−i3−1+i300−2ζ142ζ14000000−ζ5−ζ23ζ5+ζ23−ζ5+ζ23ζ5−ζ2300−1−i3−1−i31+i31+i301+i3−1−i300−2ζ222ζ22000000−ζ7−ζ13ζ7+ζ13ζ7−ζ13−ζ7+ζ1300
χ4122-2-20-2200−2i2i000000−i2i22−200−1+i3−1+i31−i31−i301−i3−1+i300−2ζ142ζ14000000ζ5+ζ23−ζ5−ζ23ζ5−ζ23−ζ5+ζ2300−1−i3−1−i31+i31+i301+i3−1−i300−2ζ222ζ22000000ζ7+ζ13−ζ7−ζ13−ζ7+ζ13ζ7−ζ1300
χ4244-4-404-40000000000000000−2+2i3−2+2i32−2i32−2i30−2+2i32−2i30000000000000000−2−2i3−2−2i32+2i32+2i30−2−2i32+2i30000000000000000
χ434-44-4400-4000000000000000−2+2i32−2i3−2+2i32−2i3−2+2i3002−2i3000000000000000−2−2i32+2i3−2−2i32+2i3−2−2i3002+2i3000000000000000
χ444-44-4-4004000000000000000−2+2i32−2i3−2+2i32−2i32−2i300−2+2i3000000000000000−2−2i32+2i3−2−2i32+2i32+2i300−2−2i3000000000000000
χ454-4-44000000022−220000000000−2+2i32−2i32−2i3−2+2i300000002ζ5−2ζ23−2ζ5+2ζ230000000000−2−2i32+2i32+2i3−2−2i30000000−2ζ7+2ζ132ζ7−2ζ130000000000
χ464-4-440000000−22220000000000−2+2i32−2i32−2i3−2+2i30000000−2ζ5+2ζ232ζ5−2ζ230000000000−2−2i32+2i32+2i3−2−2i300000002ζ7−2ζ13−2ζ7+2ζ130000000000
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
χ4811111111111111111-1-1-1-1-1-1−1−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−i32−1−i32−1−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+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32
χ491111111111111-1-1-1-11111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−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+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ501111111111111-1-1-1-1-1-1-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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
χ51111111111-1-1-1-111-1-111-1-11-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+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+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32
χ52111111111-1-1-1-111-1-1-1-111-11−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+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+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32
χ53111111111-1-1-1-1-1-11111-1-1-11−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+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−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32
χ54111111111-1-1-1-1-1-111-1-1111-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32
χ5522222-2-22-200002-200000000−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i30000−1−i31+i300000000−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i30000−1+i31−i300000000
χ5622222-2-22-20000-2200000000−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i31+i300001+i3−1−i300000000−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i31−i300001−i3−1+i300000000
χ572222-222-2-222-2-20000000000−1−i3−1−i3−1−i3−1−i31+i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i30000000000−1+i3−1+i3−1+i3−1+i31−i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i30000000000
χ582222-222-2-2-2-2220000000000−1−i3−1−i3−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i30000000000−1+i3−1+i3−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i30000000000
χ592222-2-2-2-220000002i−2i000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i30000002ζ22−2ζ22000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i30000002ζ14−2ζ14000000
χ602222-2-2-2-22000000−2i2i000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i3000000−2ζ222ζ22000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i3000000−2ζ142ζ14000000
χ6122-2-20-22002i−2i000000i2−i22−200−1−i3−1−i31+i31+i301+i3−1−i3002ζ22−2ζ22000000−ζ7−ζ13ζ7+ζ13−ζ7+ζ13ζ7−ζ1300−1+i3−1+i31−i31−i301−i3−1+i3002ζ14−2ζ14000000−ζ5−ζ23ζ5+ζ23ζ5−ζ23−ζ5+ζ2300
χ6222-2-20-22002i−2i000000−i2i2−2200−1−i3−1−i31+i31+i301+i3−1−i3002ζ22−2ζ22000000ζ7+ζ13−ζ7−ζ13ζ7−ζ13−ζ7+ζ1300−1+i3−1+i31−i31−i301−i3−1+i3002ζ14−2ζ14000000ζ5+ζ23−ζ5−ζ23−ζ5+ζ23ζ5−ζ2300
χ6322-2-20-2200−2i2i000000i2−i2−2200−1−i3−1−i31+i31+i301+i3−1−i300−2ζ222ζ22000000−ζ7−ζ13ζ7+ζ13ζ7−ζ13−ζ7+ζ1300−1+i3−1+i31−i31−i301−i3−1+i300−2ζ142ζ14000000−ζ5−ζ23ζ5+ζ23−ζ5+ζ23ζ5−ζ2300
χ6422-2-20-2200−2i2i000000−i2i22−200−1−i3−1−i31+i31+i301+i3−1−i300−2ζ222ζ22000000ζ7+ζ13−ζ7−ζ13−ζ7+ζ13ζ7−ζ1300−1+i3−1+i31−i31−i301−i3−1+i300−2ζ142ζ14000000ζ5+ζ23−ζ5−ζ23ζ5−ζ23−ζ5+ζ2300
χ6544-4-404-40000000000000000−2−2i3−2−2i32+2i32+2i30−2−2i32+2i30000000000000000−2+2i3−2+2i32−2i32−2i30−2+2i32−2i30000000000000000
χ664-44-4400-4000000000000000−2−2i32+2i3−2−2i32+2i3−2−2i3002+2i3000000000000000−2+2i32−2i3−2+2i32−2i3−2+2i3002−2i3000000000000000
χ674-44-4-4004000000000000000−2−2i32+2i3−2−2i32+2i32+2i300−2−2i3000000000000000−2+2i32−2i3−2+2i32−2i32−2i300−2+2i3000000000000000
χ684-4-44000000022−220000000000−2−2i32+2i32+2i3−2−2i30000000−2ζ7+2ζ132ζ7−2ζ130000000000−2+2i32−2i32−2i3−2+2i300000002ζ5−2ζ23−2ζ5+2ζ230000000000
χ694-4-440000000−22220000000000−2−2i32+2i32+2i3−2−2i300000002ζ7−2ζ13−2ζ7+2ζ130000000000−2+2i32−2i32−2i3−2+2i30000000−2ζ5+2ζ232ζ5−2ζ230000000000

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