Finite Group Databasebeta

← Group #64039

Character table — Group #64039

Order 288.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size112222233444446668812121122222334444466688121211222223344444666881212
order123468844241224242886122436312624241212612122424624246126123631262424121261212242462424612612
χ1111111111111111111111111111111111111111111111111111111111111111
χ2111111111-1-1111111-1-1-1-1111111111-1-1111111-1-1-1-1111111111-1-1111111-1-1-1-1
χ31111111-1-111111-1-1-111-1-11111111-1-111111-1-1-111-1-11111111-1-111111-1-1-111-1-1
χ41111111-1-1-1-1111-1-1-1-1-1111111111-1-1-1-1111-1-1-1-1-1111111111-1-1-1-1111-1-1-1-1-111
χ511111-1-1111-11-1-11-1-11-1-1111111-1-1111-11-1-11-1-11-1-1111111-1-1111-11-1-11-1-11-1-11
χ611111-1-111-111-1-11-1-1-111-111111-1-111-111-1-11-1-1-111-111111-1-111-111-1-11-1-1-111-1
χ711111-1-1-1-11-11-1-1-1111-11-111111-1-1-1-11-11-1-1-1111-11-111111-1-1-1-11-11-1-1-1111-11-1
χ811111-1-1-1-1-111-1-1-111-11-1111111-1-1-1-1-111-1-1-111-11-1111111-1-1-1-1-111-1-1-111-11-11
χ9222-22002200-200-2000000222-22002200-200-2000000222-22002200-200-2000000
χ10222-2200-2-200-2002000000222-2200-2-200-2002000000222-2200-2-200-2002000000
χ1122-12-1220022-1-1-1000-1-10022-12-1220022-1-1-1000-1-10022-12-1220022-1-1-1000-1-100
χ1222-12-12200-2-2-1-1-1000110022-12-12200-2-2-1-1-1000110022-12-12200-2-2-1-1-10001100
χ1322-12-1-2-2002-2-111000-110022-12-1-2-2002-2-111000-110022-12-1-2-2002-2-111000-1100
χ1422-12-1-2-200-22-1110001-10022-12-1-2-200-22-1110001-10022-12-1-2-200-22-1110001-100
χ152-220-2i2−i22i−2i000i2−i202−200002-220-2i2−i22i−2i000i2−i202−200002-220-2i2−i22i−2i000i2−i202−20000
χ162-220-2i2−i2−2i2i000i2−i20−2200002-220-2i2−i2−2i2i000i2−i20−2200002-220-2i2−i2−2i2i000i2−i20−220000
χ172-220-2−i2i22i−2i000−i2i20−2200002-220-2−i2i22i−2i000−i2i20−2200002-220-2−i2i22i−2i000−i2i20−220000
χ182-220-2−i2i2−2i2i000−i2i202−200002-220-2−i2i2−2i2i000−i2i202−200002-220-2−i2i2−2i2i000−i2i202−20000
χ1944-2-4-2000000200000000044-2-4-2000000200000000044-2-4-20000002000000000
χ204-4-2022i2−2i200000−i2i200000004-4-2022i2−2i200000−i2i200000004-4-2022i2−2i200000−i2i20000000
χ214-4-202−2i22i200000i2−i200000004-4-202−2i22i200000i2−i200000004-4-202−2i22i200000i2−i20000000
χ22111111111111111111111−1+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
χ23111111111-1-1111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−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+i32
χ241111111-1-111111-1-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32
χ251111111-1-1-1-1111-1-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−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−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ2611111-1-1111-11-1-11-1-11-1-11−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32
χ2711111-1-111-111-1-11-1-1-111-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i321−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−i321+i321+i321+i32−1−i32−1−i321+i32
χ2811111-1-1-1-11-11-1-1-1111-11-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i32
χ2911111-1-1-1-1-111-1-1-111-11-11−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i32
χ30222-22002200-200-2000000−1+i3−1+i3−1+i31−i3−1+i300−1+i3−1+i3001−i3001−i3000000−1−i3−1−i3−1−i31+i3−1−i300−1−i3−1−i3001+i3001+i3000000
χ31222-2200-2-200-2002000000−1+i3−1+i3−1+i31−i3−1+i3001−i31−i3001−i300−1+i3000000−1−i3−1−i3−1−i31+i3−1−i3001+i31+i3001+i300−1−i3000000
χ3222-12-1220022-1-1-1000-1-100−1+i3−1+i31−i32−1+i31−i32−1+i3−1+i300−1+i3−1+i31−i321−i321−i320001−i321−i3200−1−i3−1−i31+i32−1−i31+i32−1−i3−1−i300−1−i3−1−i31+i321+i321+i320001+i321+i3200
χ3322-12-12200-2-2-1-1-10001100−1+i3−1+i31−i32−1+i31−i32−1+i3−1+i3001−i31−i31−i321−i321−i32000−1+i32−1+i3200−1−i3−1−i31+i32−1−i31+i32−1−i3−1−i3001+i31+i31+i321+i321+i32000−1−i32−1−i3200
χ3422-12-1-2-2002-2-111000-1100−1+i3−1+i31−i32−1+i31−i321−i31−i300−1+i31−i31−i32−1+i32−1+i320001−i32−1+i3200−1−i3−1−i31+i32−1−i31+i321+i31+i300−1−i31+i31+i32−1−i32−1−i320001+i32−1−i3200
χ3522-12-1-2-200-22-1110001-100−1+i3−1+i31−i32−1+i31−i321−i31−i3001−i3−1+i31−i32−1+i32−1+i32000−1+i321−i3200−1−i3−1−i31+i32−1−i31+i321+i31+i3001+i3−1−i31+i32−1−i32−1−i32000−1−i321+i3200
χ362-220-2i2−i22i−2i000i2−i202−20000−1+i31−i3−1+i301−i3−ζ5−ζ23ζ5+ζ232ζ14−2ζ14000−ζ5−ζ23ζ5+ζ230ζ5−ζ23−ζ5+ζ230000−1−i31+i3−1−i301+i3−ζ7−ζ13ζ7+ζ132ζ22−2ζ22000−ζ7−ζ13ζ7+ζ130−ζ7+ζ13ζ7−ζ130000
χ372-220-2i2−i2−2i2i000i2−i20−220000−1+i31−i3−1+i301−i3−ζ5−ζ23ζ5+ζ23−2ζ142ζ14000−ζ5−ζ23ζ5+ζ230−ζ5+ζ23ζ5−ζ230000−1−i31+i3−1−i301+i3−ζ7−ζ13ζ7+ζ13−2ζ222ζ22000−ζ7−ζ13ζ7+ζ130ζ7−ζ13−ζ7+ζ130000
χ382-220-2−i2i22i−2i000−i2i20−220000−1+i31−i3−1+i301−i3ζ5+ζ23−ζ5−ζ232ζ14−2ζ14000ζ5+ζ23−ζ5−ζ230−ζ5+ζ23ζ5−ζ230000−1−i31+i3−1−i301+i3ζ7+ζ13−ζ7−ζ132ζ22−2ζ22000ζ7+ζ13−ζ7−ζ130ζ7−ζ13−ζ7+ζ130000
χ392-220-2−i2i2−2i2i000−i2i202−20000−1+i31−i3−1+i301−i3ζ5+ζ23−ζ5−ζ23−2ζ142ζ14000ζ5+ζ23−ζ5−ζ230ζ5−ζ23−ζ5+ζ230000−1−i31+i3−1−i301+i3ζ7+ζ13−ζ7−ζ13−2ζ222ζ22000ζ7+ζ13−ζ7−ζ130−ζ7+ζ13ζ7−ζ130000
χ4044-2-4-20000002000000000−2+2i3−2+2i31−i32−2i31−i3000000−1+i3000000000−2−2i3−2−2i31+i32+2i31+i3000000−1−i3000000000
χ414-4-2022i2−2i200000−i2i20000000−2+2i32−2i31−i30−1+i3−2ζ5−2ζ232ζ5+2ζ2300000ζ5+ζ23−ζ5−ζ230000000−2−2i32+2i31+i30−1−i3−2ζ7−2ζ132ζ7+2ζ1300000ζ7+ζ13−ζ7−ζ130000000
χ424-4-202−2i22i200000i2−i20000000−2+2i32−2i31−i30−1+i32ζ5+2ζ23−2ζ5−2ζ2300000−ζ5−ζ23ζ5+ζ230000000−2−2i32+2i31+i30−1−i32ζ7+2ζ13−2ζ7−2ζ1300000−ζ7−ζ13ζ7+ζ130000000
χ43111111111111111111111−1−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
χ44111111111-1-1111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+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−i32
χ451111111-1-111111-1-1-111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32
χ461111111-1-1-1-1111-1-1-1-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+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+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32
χ4711111-1-1111-11-1-11-1-11-1-11−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32
χ4811111-1-111-111-1-11-1-1-111-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i321+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+i321−i321−i321−i32−1+i32−1+i321−i32
χ4911111-1-1-1-11-11-1-1-1111-11-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i32
χ5011111-1-1-1-1-111-1-1-111-11-11−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i32
χ51222-22002200-200-2000000−1−i3−1−i3−1−i31+i3−1−i300−1−i3−1−i3001+i3001+i3000000−1+i3−1+i3−1+i31−i3−1+i300−1+i3−1+i3001−i3001−i3000000
χ52222-2200-2-200-2002000000−1−i3−1−i3−1−i31+i3−1−i3001+i31+i3001+i300−1−i3000000−1+i3−1+i3−1+i31−i3−1+i3001−i31−i3001−i300−1+i3000000
χ5322-12-1220022-1-1-1000-1-100−1−i3−1−i31+i32−1−i31+i32−1−i3−1−i300−1−i3−1−i31+i321+i321+i320001+i321+i3200−1+i3−1+i31−i32−1+i31−i32−1+i3−1+i300−1+i3−1+i31−i321−i321−i320001−i321−i3200
χ5422-12-12200-2-2-1-1-10001100−1−i3−1−i31+i32−1−i31+i32−1−i3−1−i3001+i31+i31+i321+i321+i32000−1−i32−1−i3200−1+i3−1+i31−i32−1+i31−i32−1+i3−1+i3001−i31−i31−i321−i321−i32000−1+i32−1+i3200
χ5522-12-1-2-2002-2-111000-1100−1−i3−1−i31+i32−1−i31+i321+i31+i300−1−i31+i31+i32−1−i32−1−i320001+i32−1−i3200−1+i3−1+i31−i32−1+i31−i321−i31−i300−1+i31−i31−i32−1+i32−1+i320001−i32−1+i3200
χ5622-12-1-2-200-22-1110001-100−1−i3−1−i31+i32−1−i31+i321+i31+i3001+i3−1−i31+i32−1−i32−1−i32000−1−i321+i3200−1+i3−1+i31−i32−1+i31−i321−i31−i3001−i3−1+i31−i32−1+i32−1+i32000−1+i321−i3200
χ572-220-2i2−i22i−2i000i2−i202−20000−1−i31+i3−1−i301+i3−ζ7−ζ13ζ7+ζ132ζ22−2ζ22000−ζ7−ζ13ζ7+ζ130−ζ7+ζ13ζ7−ζ130000−1+i31−i3−1+i301−i3−ζ5−ζ23ζ5+ζ232ζ14−2ζ14000−ζ5−ζ23ζ5+ζ230ζ5−ζ23−ζ5+ζ230000
χ582-220-2i2−i2−2i2i000i2−i20−220000−1−i31+i3−1−i301+i3−ζ7−ζ13ζ7+ζ13−2ζ222ζ22000−ζ7−ζ13ζ7+ζ130ζ7−ζ13−ζ7+ζ130000−1+i31−i3−1+i301−i3−ζ5−ζ23ζ5+ζ23−2ζ142ζ14000−ζ5−ζ23ζ5+ζ230−ζ5+ζ23ζ5−ζ230000
χ592-220-2−i2i22i−2i000−i2i20−220000−1−i31+i3−1−i301+i3ζ7+ζ13−ζ7−ζ132ζ22−2ζ22000ζ7+ζ13−ζ7−ζ130ζ7−ζ13−ζ7+ζ130000−1+i31−i3−1+i301−i3ζ5+ζ23−ζ5−ζ232ζ14−2ζ14000ζ5+ζ23−ζ5−ζ230−ζ5+ζ23ζ5−ζ230000
χ602-220-2−i2i2−2i2i000−i2i202−20000−1−i31+i3−1−i301+i3ζ7+ζ13−ζ7−ζ13−2ζ222ζ22000ζ7+ζ13−ζ7−ζ130−ζ7+ζ13ζ7−ζ130000−1+i31−i3−1+i301−i3ζ5+ζ23−ζ5−ζ23−2ζ142ζ14000ζ5+ζ23−ζ5−ζ230ζ5−ζ23−ζ5+ζ230000
χ6144-2-4-20000002000000000−2−2i3−2−2i31+i32+2i31+i3000000−1−i3000000000−2+2i3−2+2i31−i32−2i31−i3000000−1+i3000000000
χ624-4-2022i2−2i200000−i2i20000000−2−2i32+2i31+i30−1−i3−2ζ7−2ζ132ζ7+2ζ1300000ζ7+ζ13−ζ7−ζ130000000−2+2i32−2i31−i30−1+i3−2ζ5−2ζ232ζ5+2ζ2300000ζ5+ζ23−ζ5−ζ230000000
χ634-4-202−2i22i200000i2−i20000000−2−2i32+2i31+i30−1−i32ζ7+2ζ13−2ζ7−2ζ1300000−ζ7−ζ13ζ7+ζ130000000−2+2i32−2i31−i30−1+i32ζ5+2ζ23−2ζ5−2ζ2300000−ζ5−ζ23ζ5+ζ230000000

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