Finite Group Databasebeta

← Group #5341

Character table — Group #5341

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222222222888811112222222222222288881111222222222222228888
order12222244448888888844443666661212121224242424242424241212121236666612121212242424242424242412121212
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111-1-1-1-1111111111111111111-1-1-1-1111111111111111111-1-1-1-1
χ31111111111-1-1-1-1-1-1-1-11-11-11111111111-1-1-1-1-1-1-1-11-11-11111111111-1-1-1-1-1-1-1-11-11-1
χ41111111111-1-1-1-1-1-1-1-1-11-111111111111-1-1-1-1-1-1-1-1-11-111111111111-1-1-1-1-1-1-1-1-11-11
χ51111-1-11-1-111111-1-1-1-111-1-11111-1-11-1-111111-1-1-1-111-1-11111-1-11-1-111111-1-1-1-111-1-1
χ61111-1-11-1-111111-1-1-1-1-1-1111111-1-11-1-111111-1-1-1-1-1-1111111-1-11-1-111111-1-1-1-1-1-111
χ71111-1-11-1-11-1-1-1-111111-1-111111-1-11-1-11-1-1-1-111111-1-111111-1-11-1-11-1-1-1-111111-1-11
χ81111-1-11-1-11-1-1-1-11111-111-11111-1-11-1-11-1-1-1-11111-111-11111-1-11-1-11-1-1-1-11111-111-1
χ9222222-2-2-2-2000000000000222222-2-2-2-2000000000000222222-2-2-2-2000000000000
χ102222-2-2-222-20000000000002222-2-2-222-20000000000002222-2-2-222-2000000000000
χ1122-2-22-2000022−2−222−2−2000022-2-22-2000022−2−222−2−2000022-2-22-2000022−2−222−2−20000
χ1222-2-22-20000−2−222−2−222000022-2-22-20000−2−222−2−222000022-2-22-20000−2−222−2−2220000
χ1322-2-2-22000022−2−2−2−222000022-2-2-22000022−2−2−2−222000022-2-2-22000022−2−2−2−2220000
χ1422-2-2-220000−2−22222−2−2000022-2-2-220000−2−22222−2−2000022-2-2-220000−2−22222−2−20000
χ152-22-20002i−2i02−22−2i2−i2i2−i200002-22-20002i−2i02−22−2i2−i2i2−i200002-22-20002i−2i02−22−2i2−i2i2−i20000
χ162-22-20002i−2i0−22−22−i2i2−i2i200002-22-20002i−2i0−22−22−i2i2−i2i200002-22-20002i−2i0−22−22−i2i2−i2i20000
χ172-22-2000−2i2i02−22−2−i2i2−i2i200002-22-2000−2i2i02−22−2−i2i2−i2i200002-22-2000−2i2i02−22−2−i2i2−i2i20000
χ182-22-2000−2i2i0−22−22i2−i2i2−i200002-22-2000−2i2i0−22−22i2−i2i2−i200002-22-2000−2i2i0−22−22i2−i2i2−i20000
χ192-2-2200200-200002i−2i−2i2i00002-2-2200200-200002i−2i−2i2i00002-2-2200200-200002i−2i−2i2i0000
χ202-2-2200200-20000−2i2i2i−2i00002-2-2200200-20000−2i2i2i−2i00002-2-2200200-20000−2i2i2i−2i0000
χ212-2-2200-20022-2-22000000002-2-2200-20022-2-22000000002-2-2200-20022-2-2200000000
χ222-2-2200-2002-222-2000000002-2-2200-2002-222-2000000002-2-2200-2002-222-200000000
χ231111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ24111111111111111111-1-1-1-1−1+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+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−i32−1−i32−1−i321+i321+i321+i321+i32
χ251111111111-1-1-1-1-1-1-1-11-11-1−1+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+i321−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+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32
χ261111111111-1-1-1-1-1-1-1-1-11-11−1+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−i321−i32−1+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+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i32
χ271111-1-11-1-111111-1-1-1-111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32
χ281111-1-11-1-111111-1-1-1-1-1-111−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−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−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ291111-1-11-1-11-1-1-1-111111-1-11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32
χ301111-1-11-1-11-1-1-1-11111-111-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32
χ31222222-2-2-2-2000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3000000000000
χ322222-2-2-222-2000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i3−1+i3−1+i31−i3000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i3−1−i3−1−i31+i3000000000000
χ3322-2-22-2000022−2−222−2−20000−1+i3−1+i31−i31−i3−1+i31−i30000ζ5−ζ23ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ23−ζ5+ζ230000−1−i3−1−i31+i31+i3−1−i31+i30000−ζ7+ζ13−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ13ζ7−ζ130000
χ3422-2-22-20000−2−222−2−2220000−1+i3−1+i31−i31−i3−1+i31−i30000−ζ5+ζ23−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ23ζ5−ζ230000−1−i3−1−i31+i31+i3−1−i31+i30000ζ7−ζ13ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ13−ζ7+ζ130000
χ3522-2-2-22000022−2−2−2−2220000−1+i3−1+i31−i31−i31−i3−1+i30000ζ5−ζ23ζ5−ζ23−ζ5+ζ23−ζ5+ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ23ζ5−ζ230000−1−i3−1−i31+i31+i31+i3−1−i30000−ζ7+ζ13−ζ7+ζ13ζ7−ζ13ζ7−ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ13−ζ7+ζ130000
χ3622-2-2-220000−2−22222−2−20000−1+i3−1+i31−i31−i31−i3−1+i30000−ζ5+ζ23−ζ5+ζ23ζ5−ζ23ζ5−ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ23−ζ5+ζ230000−1−i3−1−i31+i31+i31+i3−1−i30000ζ7−ζ13ζ7−ζ13−ζ7+ζ13−ζ7+ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ13ζ7−ζ130000
χ372-22-20002i−2i02−22−2i2−i2i2−i20000−1+i31−i3−1+i31−i30002ζ14−2ζ140ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ230000−1−i31+i3−1−i31+i30002ζ22−2ζ220−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ130000
χ382-22-20002i−2i0−22−22−i2i2−i2i20000−1+i31−i3−1+i31−i30002ζ14−2ζ140−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ230000−1−i31+i3−1−i31+i30002ζ22−2ζ220ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ130000
χ392-22-2000−2i2i02−22−2−i2i2−i2i20000−1+i31−i3−1+i31−i3000−2ζ142ζ140ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ230000−1−i31+i3−1−i31+i3000−2ζ222ζ220−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ130000
χ402-22-2000−2i2i0−22−22i2−i2i2−i20000−1+i31−i3−1+i31−i3000−2ζ142ζ140−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ230000−1−i31+i3−1−i31+i3000−2ζ222ζ220ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ130000
χ412-2-2200200-200002i−2i−2i2i0000−1+i31−i31−i3−1+i300−1+i3001−i300002ζ14−2ζ14−2ζ142ζ140000−1−i31+i31+i3−1−i300−1−i3001+i300002ζ22−2ζ22−2ζ222ζ220000
χ422-2-2200200-20000−2i2i2i−2i0000−1+i31−i31−i3−1+i300−1+i3001−i30000−2ζ142ζ142ζ14−2ζ140000−1−i31+i31+i3−1−i300−1−i3001+i30000−2ζ222ζ222ζ22−2ζ220000
χ432-2-2200-20022-2-2200000000−1+i31−i31−i3−1+i3001−i300−1+i3−1+i31−i31−i3−1+i300000000−1−i31+i31+i3−1−i3001+i300−1−i3−1−i31+i31+i3−1−i300000000
χ442-2-2200-2002-222-200000000−1+i31−i31−i3−1+i3001−i300−1+i31−i3−1+i3−1+i31−i300000000−1−i31+i31+i3−1−i3001+i300−1−i31+i3−1−i3−1−i31+i300000000
χ451111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ46111111111111111111-1-1-1-1−1−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−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+i32−1+i32−1+i321−i321−i321−i321−i32
χ471111111111-1-1-1-1-1-1-1-11-11-1−1−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−i321+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−i321−i321−i321−i321−i32−1+i321−i32−1+i321−i32
χ481111111111-1-1-1-1-1-1-1-1-11-11−1−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+i321+i32−1−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−i321−i321−i321−i321−i321−i32−1+i321−i32−1+i32
χ491111-1-11-1-111111-1-1-1-111-1-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32
χ501111-1-11-1-111111-1-1-1-1-1-111−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+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+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32
χ511111-1-11-1-11-1-1-1-111111-1-11−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32
χ521111-1-11-1-11-1-1-1-11111-111-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i32
χ53222222-2-2-2-2000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3000000000000
χ542222-2-2-222-2000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i3−1−i3−1−i31+i3000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i3−1+i3−1+i31−i3000000000000
χ5522-2-22-2000022−2−222−2−20000−1−i3−1−i31+i31+i3−1−i31+i30000−ζ7+ζ13−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ13ζ7−ζ130000−1+i3−1+i31−i31−i3−1+i31−i30000ζ5−ζ23ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ23−ζ5+ζ230000
χ5622-2-22-20000−2−222−2−2220000−1−i3−1−i31+i31+i3−1−i31+i30000ζ7−ζ13ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ13−ζ7+ζ130000−1+i3−1+i31−i31−i3−1+i31−i30000−ζ5+ζ23−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ23ζ5−ζ230000
χ5722-2-2-22000022−2−2−2−2220000−1−i3−1−i31+i31+i31+i3−1−i30000−ζ7+ζ13−ζ7+ζ13ζ7−ζ13ζ7−ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ13−ζ7+ζ130000−1+i3−1+i31−i31−i31−i3−1+i30000ζ5−ζ23ζ5−ζ23−ζ5+ζ23−ζ5+ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ23ζ5−ζ230000
χ5822-2-2-220000−2−22222−2−20000−1−i3−1−i31+i31+i31+i3−1−i30000ζ7−ζ13ζ7−ζ13−ζ7+ζ13−ζ7+ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ13ζ7−ζ130000−1+i3−1+i31−i31−i31−i3−1+i30000−ζ5+ζ23−ζ5+ζ23ζ5−ζ23ζ5−ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ23−ζ5+ζ230000
χ592-22-20002i−2i02−22−2i2−i2i2−i20000−1−i31+i3−1−i31+i30002ζ22−2ζ220−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ130000−1+i31−i3−1+i31−i30002ζ14−2ζ140ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ230000
χ602-22-20002i−2i0−22−22−i2i2−i2i20000−1−i31+i3−1−i31+i30002ζ22−2ζ220ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ130000−1+i31−i3−1+i31−i30002ζ14−2ζ140−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ230000
χ612-22-2000−2i2i02−22−2−i2i2−i2i20000−1−i31+i3−1−i31+i3000−2ζ222ζ220−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ130000−1+i31−i3−1+i31−i3000−2ζ142ζ140ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ230000
χ622-22-2000−2i2i0−22−22i2−i2i2−i20000−1−i31+i3−1−i31+i3000−2ζ222ζ220ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ13−ζ7−ζ13ζ7+ζ13−ζ7−ζ13ζ7+ζ130000−1+i31−i3−1+i31−i3000−2ζ142ζ140−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5−ζ23ζ5+ζ23−ζ5−ζ23ζ5+ζ230000
χ632-2-2200200-200002i−2i−2i2i0000−1−i31+i31+i3−1−i300−1−i3001+i300002ζ22−2ζ22−2ζ222ζ220000−1+i31−i31−i3−1+i300−1+i3001−i300002ζ14−2ζ14−2ζ142ζ140000
χ642-2-2200200-20000−2i2i2i−2i0000−1−i31+i31+i3−1−i300−1−i3001+i30000−2ζ222ζ222ζ22−2ζ220000−1+i31−i31−i3−1+i300−1+i3001−i30000−2ζ142ζ142ζ14−2ζ140000
χ652-2-2200-20022-2-2200000000−1−i31+i31+i3−1−i3001+i300−1−i3−1−i31+i31+i3−1−i300000000−1+i31−i31−i3−1+i3001−i300−1+i3−1+i31−i31−i3−1+i300000000
χ662-2-2200-2002-222-200000000−1−i31+i31+i3−1−i3001+i300−1−i31+i3−1−i3−1−i31+i300000000−1+i31−i31−i3−1+i3001−i300−1+i31−i3−1+i3−1+i31−i300000000

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