Finite Group Databasebeta

← Group #67926

Character table — Group #67926

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size112222222444488888888161611222222244448888888816161122222224444888888881616
order122448888448816161616161616164436612122424242412122424484848484848484812123661212242424241212242448484848484848481212
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
χ511111-1-1-1-111-1-1ii−i−iii−i−i1-111111-1-1-1-111-1-1ii−i−iii−i−i1-111111-1-1-1-111-1-1ii−i−iii−i−i1-1
χ611111-1-1-1-111-1-1ii−i−i−i−iii-1111111-1-1-1-111-1-1ii−i−i−i−iii-1111111-1-1-1-111-1-1ii−i−i−i−iii-11
χ711111-1-1-1-111-1-1−i−iiiii−i−i-1111111-1-1-1-111-1-1−i−iiiii−i−i-1111111-1-1-1-111-1-1−i−iiiii−i−i-11
χ811111-1-1-1-111-1-1−i−iii−i−iii1-111111-1-1-1-111-1-1−i−iii−i−iii1-111111-1-1-1-111-1-1−i−iii−i−iii1-1
χ92222222-2-2-2-22-200000000002222222-2-2-2-22-200000000002222222-2-2-2-22-20000000000
χ1022222-2-222-2-2-22000000000022222-2-222-2-2-22000000000022222-2-222-2-2-220000000000
χ1122-22-20022000-2i2−i2i2−i200000022-22-20022000-2i2−i2i2−i200000022-22-20022000-2i2−i2i2−i2000000
χ1222-22-20022000-2−i2i2−i2i200000022-22-20022000-2−i2i2−i2i200000022-22-20022000-2−i2i2−i2i2000000
χ1322-22-200-2-200022−2−2200000022-22-200-2-200022−2−2200000022-22-200-2-200022−2−22000000
χ1422-22-200-2-20002−222−200000022-22-200-2-20002−222−200000022-22-200-2-20002−222−2000000
χ1522-2-22220000-200000i2−i2i2−i20022-2-22220000-200000i2−i2i2−i20022-2-22220000-200000i2−i2i2−i200
χ1622-2-22220000-200000−i2i2−i2i20022-2-22220000-200000−i2i2−i2i20022-2-22220000-200000−i2i2−i2i200
χ1722-2-22-2-200002000002−2−220022-2-22-2-200002000002−2−220022-2-22-2-200002000002−2−2200
χ1822-2-22-2-20000200000−222−20022-2-22-2-20000200000−222−20022-2-22-2-20000200000−222−200
χ19444-4-4000000000000000000444-4-4000000000000000000444-4-4000000000000000000
χ204-40002i2−2i222−222i−2i0000000000004-40002i2−2i222−222i−2i0000000000004-40002i2−2i222−222i−2i000000000000
χ214-40002i2−2i2−2222−2i2i0000000000004-40002i2−2i2−2222−2i2i0000000000004-40002i2−2i2−2222−2i2i000000000000
χ224-4000−2i22i222−22−2i2i0000000000004-4000−2i22i222−22−2i2i0000000000004-4000−2i22i222−22−2i2i000000000000
χ234-4000−2i22i2−22222i−2i0000000000004-4000−2i22i2−22222i−2i0000000000004-4000−2i22i2−22222i−2i000000000000
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
χ2811111-1-1-1-111-1-1ii−i−iii−i−i1-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32ζ14ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ14−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32ζ22ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ22−1−i321+i32
χ2911111-1-1-1-111-1-1ii−i−i−i−iii-11−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32ζ14ζ14−ζ14−ζ14−ζ14−ζ14ζ14ζ141−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32ζ22ζ22−ζ22−ζ22−ζ22−ζ22ζ22ζ221+i32−1−i32
χ3011111-1-1-1-111-1-1−i−iiiii−i−i-11−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−ζ14−ζ14ζ14ζ14ζ14ζ14−ζ14−ζ141−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−ζ22−ζ22ζ22ζ22ζ22ζ22−ζ22−ζ221+i32−1−i32
χ3111111-1-1-1-111-1-1−i−iii−i−iii1-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−ζ14−ζ14ζ14ζ14−ζ14−ζ14ζ14ζ14−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−ζ22−ζ22ζ22ζ22−ζ22−ζ22ζ22ζ22−1−i321+i32
χ322222222-2-2-2-22-20000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i31−i30000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i31+i30000000000
χ3322222-2-222-2-2-220000000000−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i31−i3−1+i30000000000−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i31+i3−1−i30000000000
χ3422-22-20022000-2i2−i2i2−i2000000−1+i3−1+i31−i3−1+i31−i300−1+i3−1+i30001−i3−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ23000000−1−i3−1−i31+i3−1−i31+i300−1−i3−1−i30001+i3−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ13000000
χ3522-22-20022000-2−i2i2−i2i2000000−1+i3−1+i31−i3−1+i31−i300−1+i3−1+i30001−i3ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ23000000−1−i3−1−i31+i3−1−i31+i300−1−i3−1−i30001+i3ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13000000
χ3622-22-200-2-200022−2−22000000−1+i3−1+i31−i3−1+i31−i3001−i31−i3000−1+i3ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ23000000−1−i3−1−i31+i3−1−i31+i3001+i31+i3000−1−i3−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ13000000
χ3722-22-200-2-20002−222−2000000−1+i3−1+i31−i3−1+i31−i3001−i31−i3000−1+i3−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ23000000−1−i3−1−i31+i3−1−i31+i3001+i31+i3000−1−i3ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ13000000
χ3822-2-22220000-200000i2−i2i2−i200−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i300001−i300000−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ2300−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i300001+i300000−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ1300
χ3922-2-22220000-200000−i2i2−i2i200−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i300001−i300000ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ2300−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i300001+i300000ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ1300
χ4022-2-22-2-200002000002−2−2200−1+i3−1+i31−i31−i3−1+i31−i31−i30000−1+i300000ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ2300−1−i3−1−i31+i31+i3−1−i31+i31+i30000−1−i300000−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ1300
χ4122-2-22-2-20000200000−222−200−1+i3−1+i31−i31−i3−1+i31−i31−i30000−1+i300000−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ2300−1−i3−1−i31+i31+i3−1−i31+i31+i30000−1−i300000ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ1300
χ42444-4-4000000000000000000−2+2i3−2+2i3−2+2i32−2i32−2i3000000000000000000−2−2i3−2−2i3−2−2i32+2i32+2i3000000000000000000
χ434-40002i2−2i222−222i−2i000000000000−2+2i32−2i3000−2ζ5−2ζ232ζ5+2ζ232ζ5−2ζ23−2ζ5+2ζ232ζ14−2ζ14000000000000−2−2i32+2i3000−2ζ7−2ζ132ζ7+2ζ13−2ζ7+2ζ132ζ7−2ζ132ζ22−2ζ22000000000000
χ444-40002i2−2i2−2222−2i2i000000000000−2+2i32−2i3000−2ζ5−2ζ232ζ5+2ζ23−2ζ5+2ζ232ζ5−2ζ23−2ζ142ζ14000000000000−2−2i32+2i3000−2ζ7−2ζ132ζ7+2ζ132ζ7−2ζ13−2ζ7+2ζ13−2ζ222ζ22000000000000
χ454-4000−2i22i222−22−2i2i000000000000−2+2i32−2i30002ζ5+2ζ23−2ζ5−2ζ232ζ5−2ζ23−2ζ5+2ζ23−2ζ142ζ14000000000000−2−2i32+2i30002ζ7+2ζ13−2ζ7−2ζ13−2ζ7+2ζ132ζ7−2ζ13−2ζ222ζ22000000000000
χ464-4000−2i22i2−22222i−2i000000000000−2+2i32−2i30002ζ5+2ζ23−2ζ5−2ζ23−2ζ5+2ζ232ζ5−2ζ232ζ14−2ζ14000000000000−2−2i32+2i30002ζ7+2ζ13−2ζ7−2ζ132ζ7−2ζ13−2ζ7+2ζ132ζ22−2ζ22000000000000
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
χ5111111-1-1-1-111-1-1ii−i−iii−i−i1-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32ζ22ζ22−ζ22−ζ22ζ22ζ22−ζ22−ζ22−1−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32ζ14ζ14−ζ14−ζ14ζ14ζ14−ζ14−ζ14−1+i321−i32
χ5211111-1-1-1-111-1-1ii−i−i−i−iii-11−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32ζ22ζ22−ζ22−ζ22−ζ22−ζ22ζ22ζ221+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32ζ14ζ14−ζ14−ζ14−ζ14−ζ14ζ14ζ141−i32−1+i32
χ5311111-1-1-1-111-1-1−i−iiiii−i−i-11−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−ζ22−ζ22ζ22ζ22ζ22ζ22−ζ22−ζ221+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−ζ14−ζ14ζ14ζ14ζ14ζ14−ζ14−ζ141−i32−1+i32
χ5411111-1-1-1-111-1-1−i−iii−i−iii1-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−ζ22−ζ22ζ22ζ22−ζ22−ζ22ζ22ζ22−1−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−ζ14−ζ14ζ14ζ14−ζ14−ζ14ζ14ζ14−1+i321−i32
χ552222222-2-2-2-22-20000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i31+i30000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i31−i30000000000
χ5622222-2-222-2-2-220000000000−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i31+i3−1−i30000000000−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i31−i3−1+i30000000000
χ5722-22-20022000-2i2−i2i2−i2000000−1−i3−1−i31+i3−1−i31+i300−1−i3−1−i30001+i3−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ13000000−1+i3−1+i31−i3−1+i31−i300−1+i3−1+i30001−i3−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ23000000
χ5822-22-20022000-2−i2i2−i2i2000000−1−i3−1−i31+i3−1−i31+i300−1−i3−1−i30001+i3ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13000000−1+i3−1+i31−i3−1+i31−i300−1+i3−1+i30001−i3ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ23000000
χ5922-22-200-2-200022−2−22000000−1−i3−1−i31+i3−1−i31+i3001+i31+i3000−1−i3−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ13000000−1+i3−1+i31−i3−1+i31−i3001−i31−i3000−1+i3ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ23000000
χ6022-22-200-2-20002−222−2000000−1−i3−1−i31+i3−1−i31+i3001+i31+i3000−1−i3ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ13000000−1+i3−1+i31−i3−1+i31−i3001−i31−i3000−1+i3−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ23000000
χ6122-2-22220000-200000i2−i2i2−i200−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i300001+i300000−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ1300−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i300001−i300000−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ2300
χ6222-2-22220000-200000−i2i2−i2i200−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i300001+i300000ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ1300−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i300001−i300000ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ2300
χ6322-2-22-2-200002000002−2−2200−1−i3−1−i31+i31+i3−1−i31+i31+i30000−1−i300000−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ1300−1+i3−1+i31−i31−i3−1+i31−i31−i30000−1+i300000ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ2300
χ6422-2-22-2-20000200000−222−200−1−i3−1−i31+i31+i3−1−i31+i31+i30000−1−i300000ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ1300−1+i3−1+i31−i31−i3−1+i31−i31−i30000−1+i300000−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ2300
χ65444-4-4000000000000000000−2−2i3−2−2i3−2−2i32+2i32+2i3000000000000000000−2+2i3−2+2i3−2+2i32−2i32−2i3000000000000000000
χ664-40002i2−2i222−222i−2i000000000000−2−2i32+2i3000−2ζ7−2ζ132ζ7+2ζ13−2ζ7+2ζ132ζ7−2ζ132ζ22−2ζ22000000000000−2+2i32−2i3000−2ζ5−2ζ232ζ5+2ζ232ζ5−2ζ23−2ζ5+2ζ232ζ14−2ζ14000000000000
χ674-40002i2−2i2−2222−2i2i000000000000−2−2i32+2i3000−2ζ7−2ζ132ζ7+2ζ132ζ7−2ζ13−2ζ7+2ζ13−2ζ222ζ22000000000000−2+2i32−2i3000−2ζ5−2ζ232ζ5+2ζ23−2ζ5+2ζ232ζ5−2ζ23−2ζ142ζ14000000000000
χ684-4000−2i22i222−22−2i2i000000000000−2−2i32+2i30002ζ7+2ζ13−2ζ7−2ζ13−2ζ7+2ζ132ζ7−2ζ13−2ζ222ζ22000000000000−2+2i32−2i30002ζ5+2ζ23−2ζ5−2ζ232ζ5−2ζ23−2ζ5+2ζ23−2ζ142ζ14000000000000
χ694-4000−2i22i2−22222i−2i000000000000−2−2i32+2i30002ζ7+2ζ13−2ζ7−2ζ132ζ7−2ζ13−2ζ7+2ζ132ζ22−2ζ22000000000000−2+2i32−2i30002ζ5+2ζ23−2ζ5−2ζ23−2ζ5+2ζ232ζ5−2ζ232ζ14−2ζ14000000000000

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