Finite Group Databasebeta

← Group #5359

Character table — Group #5359

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size111122224444444448811112222444444444881111222244444444488
order1222444424444888844366612121212612121212242424241212366612121212612121212242424241212
χ1111111111111111111111111111111111111111111111111111111111
χ21111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1
χ3111111111-1-1-1-11111-1-1111111111-1-1-1-11111-1-1111111111-1-1-1-11111-1-1
χ4111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-111
χ51111-1-111-111-1-111-1-11-11111-1-111-111-1-111-1-11-11111-1-111-111-1-111-1-11-1
χ61111-1-111-111-1-1-1-111-111111-1-111-111-1-1-1-111-111111-1-111-111-1-1-1-111-11
χ71111-1-111-1-1-11111-1-1-111111-1-111-1-1-11111-1-1-111111-1-111-1-1-11111-1-1-11
χ81111-1-111-1-1-111-1-1111-11111-1-111-1-1-111-1-1111-11111-1-111-1-1-111-1-1111-1
χ9222222-2-2-20000000000222222-2-2-20000000000222222-2-2-20000000000
χ102222-2-2-2-2200000000002222-2-2-2-2200000000002222-2-2-2-220000000000
χ112-22-2002-20002i−2i0000002-22-2002-20002i−2i0000002-22-2002-20002i−2i000000
χ122-22-2002-2000−2i2i0000002-22-2002-2000−2i2i0000002-22-2002-2000−2i2i000000
χ132-22-200-2202i−2i000000002-22-200-2202i−2i000000002-22-200-2202i−2i00000000
χ142-22-200-220−2i2i000000002-22-200-220−2i2i000000002-22-200-220−2i2i00000000
χ152-2-222i−2i00000002−2i2−i2002-2-222i−2i00000002−2i2−i2002-2-222i−2i00000002−2i2−i200
χ162-2-222i−2i0000000−22−i2i2002-2-222i−2i0000000−22−i2i2002-2-222i−2i0000000−22−i2i200
χ172-2-22−2i2i00000002−2−i2i2002-2-22−2i2i00000002−2−i2i2002-2-22−2i2i00000002−2−i2i200
χ182-2-22−2i2i0000000−22i2−i2002-2-22−2i2i0000000−22i2−i2002-2-22−2i2i0000000−22i2−i200
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
χ22111111111-1-1-1-11111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+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−i32−1−i321+i321+i32
χ23111111111-1-1-1-1-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ241111-1-111-111-1-111-1-11-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+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−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32
χ251111-1-111-111-1-1-1-111-11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+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−i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32
χ261111-1-111-1-1-11111-1-1-11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+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+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32
χ271111-1-111-1-1-111-1-1111-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+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+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32
χ28222222-2-2-20000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i30000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i30000000000
χ292222-2-2-2-220000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i30000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i30000000000
χ302-22-2002-20002i−2i000000−1+i31−i3−1+i31−i300−1+i31−i30002ζ14−2ζ14000000−1−i31+i3−1−i31+i300−1−i31+i30002ζ22−2ζ22000000
χ312-22-2002-2000−2i2i000000−1+i31−i3−1+i31−i300−1+i31−i3000−2ζ142ζ14000000−1−i31+i3−1−i31+i300−1−i31+i3000−2ζ222ζ22000000
χ322-22-200-2202i−2i00000000−1+i31−i3−1+i31−i3001−i3−1+i302ζ14−2ζ1400000000−1−i31+i3−1−i31+i3001+i3−1−i302ζ22−2ζ2200000000
χ332-22-200-220−2i2i00000000−1+i31−i3−1+i31−i3001−i3−1+i30−2ζ142ζ1400000000−1−i31+i3−1−i31+i3001+i3−1−i30−2ζ222ζ2200000000
χ342-2-222i−2i00000002−2i2−i200−1+i31−i31−i3−1+i32ζ14−2ζ140000000ζ5−ζ23−ζ5+ζ23−ζ5−ζ23ζ5+ζ2300−1−i31+i31+i3−1−i32ζ22−2ζ220000000−ζ7+ζ13ζ7−ζ13−ζ7−ζ13ζ7+ζ1300
χ352-2-222i−2i0000000−22−i2i200−1+i31−i31−i3−1+i32ζ14−2ζ140000000−ζ5+ζ23ζ5−ζ23ζ5+ζ23−ζ5−ζ2300−1−i31+i31+i3−1−i32ζ22−2ζ220000000ζ7−ζ13−ζ7+ζ13ζ7+ζ13−ζ7−ζ1300
χ362-2-22−2i2i00000002−2−i2i200−1+i31−i31−i3−1+i3−2ζ142ζ140000000ζ5−ζ23−ζ5+ζ23ζ5+ζ23−ζ5−ζ2300−1−i31+i31+i3−1−i3−2ζ222ζ220000000−ζ7+ζ13ζ7−ζ13ζ7+ζ13−ζ7−ζ1300
χ372-2-22−2i2i0000000−22i2−i200−1+i31−i31−i3−1+i3−2ζ142ζ140000000−ζ5+ζ23ζ5−ζ23−ζ5−ζ23ζ5+ζ2300−1−i31+i31+i3−1−i3−2ζ222ζ220000000ζ7−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
χ41111111111-1-1-1-11111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−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+i32−1+i321−i321−i32
χ42111111111-1-1-1-1-1-1-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32
χ431111-1-111-111-1-111-1-11-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−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+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32
χ441111-1-111-111-1-1-1-111-11−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−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+i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32
χ451111-1-111-1-1-11111-1-1-11−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−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−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32
χ461111-1-111-1-1-111-1-1111-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−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−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32
χ47222222-2-2-20000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i30000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i30000000000
χ482222-2-2-2-220000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i30000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i30000000000
χ492-22-2002-20002i−2i000000−1−i31+i3−1−i31+i300−1−i31+i30002ζ22−2ζ22000000−1+i31−i3−1+i31−i300−1+i31−i30002ζ14−2ζ14000000
χ502-22-2002-2000−2i2i000000−1−i31+i3−1−i31+i300−1−i31+i3000−2ζ222ζ22000000−1+i31−i3−1+i31−i300−1+i31−i3000−2ζ142ζ14000000
χ512-22-200-2202i−2i00000000−1−i31+i3−1−i31+i3001+i3−1−i302ζ22−2ζ2200000000−1+i31−i3−1+i31−i3001−i3−1+i302ζ14−2ζ1400000000
χ522-22-200-220−2i2i00000000−1−i31+i3−1−i31+i3001+i3−1−i30−2ζ222ζ2200000000−1+i31−i3−1+i31−i3001−i3−1+i30−2ζ142ζ1400000000
χ532-2-222i−2i00000002−2i2−i200−1−i31+i31+i3−1−i32ζ22−2ζ220000000−ζ7+ζ13ζ7−ζ13−ζ7−ζ13ζ7+ζ1300−1+i31−i31−i3−1+i32ζ14−2ζ140000000ζ5−ζ23−ζ5+ζ23−ζ5−ζ23ζ5+ζ2300
χ542-2-222i−2i0000000−22−i2i200−1−i31+i31+i3−1−i32ζ22−2ζ220000000ζ7−ζ13−ζ7+ζ13ζ7+ζ13−ζ7−ζ1300−1+i31−i31−i3−1+i32ζ14−2ζ140000000−ζ5+ζ23ζ5−ζ23ζ5+ζ23−ζ5−ζ2300
χ552-2-22−2i2i00000002−2−i2i200−1−i31+i31+i3−1−i3−2ζ222ζ220000000−ζ7+ζ13ζ7−ζ13ζ7+ζ13−ζ7−ζ1300−1+i31−i31−i3−1+i3−2ζ142ζ140000000ζ5−ζ23−ζ5+ζ23ζ5+ζ23−ζ5−ζ2300
χ562-2-22−2i2i0000000−22i2−i200−1−i31+i31+i3−1−i3−2ζ222ζ220000000ζ7−ζ13−ζ7+ζ13−ζ7−ζ13ζ7+ζ1300−1+i31−i31−i3−1+i3−2ζ142ζ140000000−ζ5+ζ23ζ5−ζ23−ζ5−ζ23ζ5+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.