Finite Group Databasebeta

← Group #5337

Character table — Group #5337

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57
size111122224444444448811112222444444444881111222244444444488
order122244442244488882436661212121266121212242424246123666121212126612121224242424612
χ1111111111111111111111111111111111111111111111111111111111
χ21111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-11111111111111-1-1-1-1-1-1
χ311111111-1-11-1-11111-1-111111111-1-11-1-11111-1-111111111-1-11-1-11111-1-1
χ411111111-1-11-1-1-1-1-1-11111111111-1-11-1-1-1-1-1-11111111111-1-11-1-1-1-1-1-111
χ511111-1-1111-1-1-111-1-11-111111-1-1111-1-1-111-1-11-111111-1-1111-1-1-111-1-11-1
χ611111-1-1111-1-1-1-1-111-1111111-1-1111-1-1-1-1-111-1111111-1-1111-1-1-1-1-111-11
χ711111-1-11-1-1-11111-1-1-1111111-1-11-1-1-11111-1-1-1111111-1-11-1-1-11111-1-1-11
χ811111-1-11-1-1-111-1-1111-111111-1-11-1-1-111-1-1111-111111-1-11-1-1-111-1-1111-1
χ92222-222-200-2000000002222-222-200-2000000002222-222-200-200000000
χ102222-2-2-2-2002000000002222-2-2-2-2002000000002222-2-2-2-200200000000
χ1122-2-202i−2i0000002−2i2−i20022-2-202i−2i0000002−2i2−i20022-2-202i−2i0000002−2i2−i200
χ1222-2-202i−2i000000−22−i2i20022-2-202i−2i000000−22−i2i20022-2-202i−2i000000−22−i2i200
χ1322-2-20−2i2i0000002−2−i2i20022-2-20−2i2i0000002−2−i2i20022-2-20−2i2i0000002−2−i2i200
χ1422-2-20−2i2i000000−22i2−i20022-2-20−2i2i000000−22i2−i20022-2-20−2i2i000000−22i2−i200
χ152-22-2200-20002i−2i0000002-22-2200-20002i−2i0000002-22-2200-20002i−2i000000
χ162-22-2200-2000−2i2i0000002-22-2200-2000−2i2i0000002-22-2200-2000−2i2i000000
χ172-22-2-20022-20000000002-22-2-20022-20000000002-22-2-20022-2000000000
χ182-22-2-2002-220000000002-22-2-2002-220000000002-22-2-2002-22000000000
χ194-4-440000000000000004-4-440000000000000004-4-44000000000000000
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
χ2211111111-1-11-1-11111-1-1−1+i32−1+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+i321−i321−i32−1−i32−1−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−i321+i321+i32
χ2311111111-1-11-1-1-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−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−i321+i321+i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ2411111-1-1111-1-1-111-1-11-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−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−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32
χ2511111-1-1111-1-1-1-1-111-11−1+i32−1+i32−1+i32−1+i32−1+i321−i321−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−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32
χ2611111-1-11-1-1-11111-1-1-11−1+i32−1+i32−1+i32−1+i32−1+i321−i321−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−i32−1−i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32
χ2711111-1-11-1-1-111-1-1111-1−1+i32−1+i32−1+i32−1+i32−1+i321−i321−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−i32−1−i321+i321+i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32
χ282222-222-200-200000000−1+i3−1+i3−1+i3−1+i31−i3−1+i3−1+i31−i3001−i300000000−1−i3−1−i3−1−i3−1−i31+i3−1−i3−1−i31+i3001+i300000000
χ292222-2-2-2-200200000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i300−1+i300000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i300−1−i300000000
χ3022-2-202i−2i0000002−2i2−i200−1+i3−1+i31−i31−i302ζ14−2ζ14000000ζ5−ζ23−ζ5+ζ23−ζ5−ζ23ζ5+ζ2300−1−i3−1−i31+i31+i302ζ22−2ζ22000000−ζ7+ζ13ζ7−ζ13−ζ7−ζ13ζ7+ζ1300
χ3122-2-202i−2i000000−22−i2i200−1+i3−1+i31−i31−i302ζ14−2ζ14000000−ζ5+ζ23ζ5−ζ23ζ5+ζ23−ζ5−ζ2300−1−i3−1−i31+i31+i302ζ22−2ζ22000000ζ7−ζ13−ζ7+ζ13ζ7+ζ13−ζ7−ζ1300
χ3222-2-20−2i2i0000002−2−i2i200−1+i3−1+i31−i31−i30−2ζ142ζ14000000ζ5−ζ23−ζ5+ζ23ζ5+ζ23−ζ5−ζ2300−1−i3−1−i31+i31+i30−2ζ222ζ22000000−ζ7+ζ13ζ7−ζ13ζ7+ζ13−ζ7−ζ1300
χ3322-2-20−2i2i000000−22i2−i200−1+i3−1+i31−i31−i30−2ζ142ζ14000000−ζ5+ζ23ζ5−ζ23−ζ5−ζ23ζ5+ζ2300−1−i3−1−i31+i31+i30−2ζ222ζ22000000ζ7−ζ13−ζ7+ζ13−ζ7−ζ13ζ7+ζ1300
χ342-22-2200-20002i−2i000000−1+i31−i3−1+i31−i3−1+i3001−i30002ζ14−2ζ14000000−1−i31+i3−1−i31+i3−1−i3001+i30002ζ22−2ζ22000000
χ352-22-2200-2000−2i2i000000−1+i31−i3−1+i31−i3−1+i3001−i3000−2ζ142ζ14000000−1−i31+i3−1−i31+i3−1−i3001+i3000−2ζ222ζ22000000
χ362-22-2-20022-2000000000−1+i31−i3−1+i31−i31−i300−1+i3−1+i31−i3000000000−1−i31+i3−1−i31+i31+i300−1−i3−1−i31+i3000000000
χ372-22-2-2002-22000000000−1+i31−i3−1+i31−i31−i300−1+i31−i3−1+i3000000000−1−i31+i3−1−i31+i31+i300−1−i31+i3−1−i3000000000
χ384-4-44000000000000000−2+2i32−2i32−2i3−2+2i3000000000000000−2−2i32+2i32+2i3−2−2i3000000000000000
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
χ4111111111-1-11-1-11111-1-1−1−i32−1−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−i321+i321+i32−1+i32−1+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+i321−i321−i32
χ4211111111-1-11-1-1-1-1-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+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+i321−i321−i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32
χ4311111-1-1111-1-1-111-1-11-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+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+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32
χ4411111-1-1111-1-1-1-1-111-11−1−i32−1−i32−1−i32−1−i32−1−i321+i321+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+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32
χ4511111-1-11-1-1-11111-1-1-11−1−i32−1−i32−1−i32−1−i32−1−i321+i321+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+i32−1+i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32
χ4611111-1-11-1-1-111-1-1111-1−1−i32−1−i32−1−i32−1−i32−1−i321+i321+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+i32−1+i321−i321−i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32
χ472222-222-200-200000000−1−i3−1−i3−1−i3−1−i31+i3−1−i3−1−i31+i3001+i300000000−1+i3−1+i3−1+i3−1+i31−i3−1+i3−1+i31−i3001−i300000000
χ482222-2-2-2-200200000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i300−1−i300000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i300−1+i300000000
χ4922-2-202i−2i0000002−2i2−i200−1−i3−1−i31+i31+i302ζ22−2ζ22000000−ζ7+ζ13ζ7−ζ13−ζ7−ζ13ζ7+ζ1300−1+i3−1+i31−i31−i302ζ14−2ζ14000000ζ5−ζ23−ζ5+ζ23−ζ5−ζ23ζ5+ζ2300
χ5022-2-202i−2i000000−22−i2i200−1−i3−1−i31+i31+i302ζ22−2ζ22000000ζ7−ζ13−ζ7+ζ13ζ7+ζ13−ζ7−ζ1300−1+i3−1+i31−i31−i302ζ14−2ζ14000000−ζ5+ζ23ζ5−ζ23ζ5+ζ23−ζ5−ζ2300
χ5122-2-20−2i2i0000002−2−i2i200−1−i3−1−i31+i31+i30−2ζ222ζ22000000−ζ7+ζ13ζ7−ζ13ζ7+ζ13−ζ7−ζ1300−1+i3−1+i31−i31−i30−2ζ142ζ14000000ζ5−ζ23−ζ5+ζ23ζ5+ζ23−ζ5−ζ2300
χ5222-2-20−2i2i000000−22i2−i200−1−i3−1−i31+i31+i30−2ζ222ζ22000000ζ7−ζ13−ζ7+ζ13−ζ7−ζ13ζ7+ζ1300−1+i3−1+i31−i31−i30−2ζ142ζ14000000−ζ5+ζ23ζ5−ζ23−ζ5−ζ23ζ5+ζ2300
χ532-22-2200-20002i−2i000000−1−i31+i3−1−i31+i3−1−i3001+i30002ζ22−2ζ22000000−1+i31−i3−1+i31−i3−1+i3001−i30002ζ14−2ζ14000000
χ542-22-2200-2000−2i2i000000−1−i31+i3−1−i31+i3−1−i3001+i3000−2ζ222ζ22000000−1+i31−i3−1+i31−i3−1+i3001−i3000−2ζ142ζ14000000
χ552-22-2-20022-2000000000−1−i31+i3−1−i31+i31+i300−1−i3−1−i31+i3000000000−1+i31−i3−1+i31−i31−i300−1+i3−1+i31−i3000000000
χ562-22-2-2002-22000000000−1−i31+i3−1−i31+i31+i300−1−i31+i3−1−i3000000000−1+i31−i3−1+i31−i31−i300−1+i31−i3−1+i3000000000
χ574-4-44000000000000000−2−2i32+2i32+2i3−2−2i3000000000000000−2+2i32−2i32−2i3−2+2i3000000000000000

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