Finite Group Databasebeta

← Group #5321

Character table — Group #5321

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size111122224444444448811112222444444444881111222244444444488
order1222224422224888824366666121266661224242424612366666121266661224242424612
χ1111111111111111111111111111111111111111111111111111111111
χ21111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1
χ311111111-1-1-1-111111-1-111111111-1-1-1-111111-1-111111111-1-1-1-111111-1-1
χ411111111-1-1-1-11-1-1-1-11111111111-1-1-1-11-1-1-1-11111111111-1-1-1-11-1-1-1-111
χ51111-1-11111-1-1-111-1-11-11111-1-11111-1-1-111-1-11-11111-1-11111-1-1-111-1-11-1
χ61111-1-11111-1-1-1-1-111-111111-1-11111-1-1-1-1-111-111111-1-11111-1-1-1-1-111-11
χ71111-1-111-1-111-111-1-1-111111-1-111-1-111-111-1-1-111111-1-111-1-111-111-1-1-11
χ81111-1-111-1-111-1-1-1111-11111-1-111-1-111-1-1-1111-11111-1-111-1-111-1-1-1111-1
χ9222222-2-20000-2000000222222-2-20000-2000000222222-2-20000-2000000
χ102222-2-2-2-2000020000002222-2-2-2-2000020000002222-2-2-2-200002000000
χ112-22-2002-2002-200000002-22-2002-2002-200000002-22-2002-2002-20000000
χ122-22-2002-200-2200000002-22-2002-200-2200000002-22-2002-200-220000000
χ132-22-200-222-20000000002-22-200-222-20000000002-22-200-222-2000000000
χ142-22-200-22-220000000002-22-200-22-220000000002-22-200-22-22000000000
χ152-2-222-200000002−22−2002-2-222-200000002−22−2002-2-222-200000002−22−200
χ162-2-222-20000000−22−22002-2-222-20000000−22−22002-2-222-20000000−22−2200
χ172-2-22-2200000002−2−22002-2-22-2200000002−2−22002-2-22-2200000002−2−2200
χ182-2-22-220000000−222−2002-2-22-220000000−222−2002-2-22-220000000−222−200
χ1944-4-400000000000000044-4-400000000000000044-4-4000000000000000
χ201111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ211111111111111-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i321+i321+i321+i321+i321+i321+i32
χ2211111111-1-1-1-111111-1-1−1+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+i321−i321−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−i321+i321+i32
χ2311111111-1-1-1-11-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−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−i321+i321+i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ241111-1-11111-1-1-111-1-11-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32
χ251111-1-11111-1-1-1-1-111-11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32
χ261111-1-111-1-111-111-1-1-11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i32
χ271111-1-111-1-111-1-1-1111-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i32
χ28222222-2-20000-2000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i300001−i3000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i300001+i3000000
χ292222-2-2-2-200002000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i30000−1+i3000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i30000−1−i3000000
χ302-22-2002-2002-20000000−1+i31−i3−1+i31−i300−1+i31−i300−1+i31−i30000000−1−i31+i3−1−i31+i300−1−i31+i300−1−i31+i30000000
χ312-22-2002-200-220000000−1+i31−i3−1+i31−i300−1+i31−i3001−i3−1+i30000000−1−i31+i3−1−i31+i300−1−i31+i3001+i3−1−i30000000
χ322-22-200-222-2000000000−1+i31−i3−1+i31−i3001−i3−1+i3−1+i31−i3000000000−1−i31+i3−1−i31+i3001+i3−1−i3−1−i31+i3000000000
χ332-22-200-22-22000000000−1+i31−i3−1+i31−i3001−i3−1+i31−i3−1+i3000000000−1−i31+i3−1−i31+i3001+i3−1−i31+i3−1−i3000000000
χ342-2-222-200000002−22−200−1+i31−i31−i3−1+i3−1+i31−i30000000ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ2300−1−i31+i31+i3−1−i3−1−i31+i30000000−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ1300
χ352-2-222-20000000−22−2200−1+i31−i31−i3−1+i3−1+i31−i30000000−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ2300−1−i31+i31+i3−1−i3−1−i31+i30000000ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ1300
χ362-2-22-2200000002−2−2200−1+i31−i31−i3−1+i31−i3−1+i30000000ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ2300−1−i31+i31+i3−1−i31+i3−1−i30000000−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ1300
χ372-2-22-220000000−222−200−1+i31−i31−i3−1+i31−i3−1+i30000000−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ2300−1−i31+i31+i3−1−i31+i3−1−i30000000ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ1300
χ3844-4-4000000000000000−2+2i3−2+2i32−2i32−2i3000000000000000−2−2i3−2−2i32+2i32+2i3000000000000000
χ391111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ401111111111111-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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+i321−i321−i321−i321−i321−i321−i32
χ4111111111-1-1-1-111111-1-1−1−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−i321+i321+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+i321−i321−i32
χ4211111111-1-1-1-11-1-1-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+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+i321−i321−i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32
χ431111-1-11111-1-1-111-1-11-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32
χ441111-1-11111-1-1-1-1-111-11−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32
χ451111-1-111-1-111-111-1-1-11−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i32
χ461111-1-111-1-111-1-1-1111-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−i32
χ47222222-2-20000-2000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i300001+i3000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i300001−i3000000
χ482222-2-2-2-200002000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i30000−1−i3000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i30000−1+i3000000
χ492-22-2002-2002-20000000−1−i31+i3−1−i31+i300−1−i31+i300−1−i31+i30000000−1+i31−i3−1+i31−i300−1+i31−i300−1+i31−i30000000
χ502-22-2002-200-220000000−1−i31+i3−1−i31+i300−1−i31+i3001+i3−1−i30000000−1+i31−i3−1+i31−i300−1+i31−i3001−i3−1+i30000000
χ512-22-200-222-2000000000−1−i31+i3−1−i31+i3001+i3−1−i3−1−i31+i3000000000−1+i31−i3−1+i31−i3001−i3−1+i3−1+i31−i3000000000
χ522-22-200-22-22000000000−1−i31+i3−1−i31+i3001+i3−1−i31+i3−1−i3000000000−1+i31−i3−1+i31−i3001−i3−1+i31−i3−1+i3000000000
χ532-2-222-200000002−22−200−1−i31+i31+i3−1−i3−1−i31+i30000000−ζ7+ζ13ζ7−ζ13−ζ7+ζ13ζ7−ζ1300−1+i31−i31−i3−1+i3−1+i31−i30000000ζ5−ζ23−ζ5+ζ23ζ5−ζ23−ζ5+ζ2300
χ542-2-222-20000000−22−2200−1−i31+i31+i3−1−i3−1−i31+i30000000ζ7−ζ13−ζ7+ζ13ζ7−ζ13−ζ7+ζ1300−1+i31−i31−i3−1+i3−1+i31−i30000000−ζ5+ζ23ζ5−ζ23−ζ5+ζ23ζ5−ζ2300
χ552-2-22-2200000002−2−2200−1−i31+i31+i3−1−i31+i3−1−i30000000−ζ7+ζ13ζ7−ζ13ζ7−ζ13−ζ7+ζ1300−1+i31−i31−i3−1+i31−i3−1+i30000000ζ5−ζ23−ζ5+ζ23−ζ5+ζ23ζ5−ζ2300
χ562-2-22-220000000−222−200−1−i31+i31+i3−1−i31+i3−1−i30000000ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ1300−1+i31−i31−i3−1+i31−i3−1+i30000000−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ2300
χ5744-4-4000000000000000−2−2i3−2−2i32+2i32+2i3000000000000000−2+2i3−2+2i32−2i32−2i3000000000000000

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