Finite Group Databasebeta

← Group #5271

Character table — Group #5271

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111111114444444444444411111111444444444444441111111144444444444444
order122222222244444444444436666666661212121212121212121212123666666666121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ31111111111-1-1-1-111-1-111-1-11111111111-1-1-1-111-1-111-1-11111111111-1-1-1-111-1-111-1-1
χ41111111111-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-111-1-111
χ511111111-1-111-1-11111-1-1-1-111111111-1-111-1-11111-1-1-1-111111111-1-111-1-11111-1-1-1-1
χ611111111-1-111-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11111
χ711111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-111
χ811111111-1-1-1-111-1-11111-1-111111111-1-1-1-111-1-11111-1-111111111-1-1-1-111-1-11111-1-1
χ9222-2-2-2-2200002i−2i00000000222-2-2-2-2200002i−2i00000000222-2-2-2-2200002i−2i00000000
χ10222-2-2-2-220000−2i2i00000000222-2-2-2-220000−2i2i00000000222-2-2-2-220000−2i2i00000000
χ1122-222-2-2-20000000000002i−2i22-222-2-2-20000000000002i−2i22-222-2-2-20000000000002i−2i
χ1222-222-2-2-2000000000000−2i2i22-222-2-2-2000000000000−2i2i22-222-2-2-2000000000000−2i2i
χ1322-2-2-222-20000002i−2i00000022-2-2-222-20000002i−2i00000022-2-2-222-20000002i−2i000000
χ1422-2-2-222-2000000−2i2i00000022-2-2-222-2000000−2i2i00000022-2-2-222-2000000−2i2i000000
χ152-222-22-2-200000000002i−2i002-222-22-2-200000000002i−2i002-222-22-2-200000000002i−2i00
χ162-222-22-2-20000000000−2i2i002-222-22-2-20000000000−2i2i002-222-22-2-20000000000−2i2i00
χ172-22-22-22-2000000002i−2i00002-22-22-22-2000000002i−2i00002-22-22-22-2000000002i−2i0000
χ182-22-22-22-200000000−2i2i00002-22-22-22-200000000−2i2i00002-22-22-22-200000000−2i2i0000
χ192-2-22-2-222002-200000000002-2-22-2-222002-200000000002-2-22-2-222002-20000000000
χ202-2-22-2-22200-2200000000002-2-22-2-22200-2200000000002-2-22-2-22200-220000000000
χ212-2-2-222-222-20000000000002-2-2-222-222-20000000000002-2-2-222-222-2000000000000
χ222-2-2-222-22-220000000000002-2-2-222-22-220000000000002-2-2-222-22-22000000000000
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
χ2411111111111111-1-1-1-1-1-1-1-1−1+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+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−i321+i321+i321+i321+i321+i321+i321+i321+i32
χ251111111111-1-1-1-111-1-111-1-1−1+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+i321−i321−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−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ261111111111-1-1-1-1-1-111-1-111−1+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+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−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ2711111111-1-111-1-11111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−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−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ2811111111-1-111-1-1-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−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−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ2911111111-1-1-1-11111-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ3011111111-1-1-1-111-1-11111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+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+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ31222-2-2-2-2200002i−2i00000000−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i300002ζ7−2ζ700000000−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i300002ζ11−2ζ1100000000
χ32222-2-2-2-220000−2i2i00000000−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i30000−2ζ72ζ700000000−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i30000−2ζ112ζ1100000000
χ3322-222-2-2-20000000000002i−2i−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i30000000000002ζ7−2ζ7−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i30000000000002ζ11−2ζ11
χ3422-222-2-2-2000000000000−2i2i−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i3000000000000−2ζ72ζ7−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i3000000000000−2ζ112ζ11
χ3522-2-2-222-20000002i−2i000000−1+i3−1+i31−i31−i31−i3−1+i3−1+i31−i30000002ζ7−2ζ7000000−1−i3−1−i31+i31+i31+i3−1−i3−1−i31+i30000002ζ11−2ζ11000000
χ3622-2-2-222-2000000−2i2i000000−1+i3−1+i31−i31−i31−i3−1+i3−1+i31−i3000000−2ζ72ζ7000000−1−i3−1−i31+i31+i31+i3−1−i3−1−i31+i3000000−2ζ112ζ11000000
χ372-222-22-2-200000000002i−2i00−1+i31−i3−1+i3−1+i31−i3−1+i31−i31−i300000000002ζ7−2ζ700−1−i31+i3−1−i3−1−i31+i3−1−i31+i31+i300000000002ζ11−2ζ1100
χ382-222-22-2-20000000000−2i2i00−1+i31−i3−1+i3−1+i31−i3−1+i31−i31−i30000000000−2ζ72ζ700−1−i31+i3−1−i3−1−i31+i3−1−i31+i31+i30000000000−2ζ112ζ1100
χ392-22-22-22-2000000002i−2i0000−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i3000000002ζ7−2ζ70000−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i3000000002ζ11−2ζ110000
χ402-22-22-22-200000000−2i2i0000−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i300000000−2ζ72ζ70000−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i300000000−2ζ112ζ110000
χ412-2-22-2-222002-20000000000−1+i31−i31−i3−1+i31−i31−i3−1+i3−1+i300−1+i31−i30000000000−1−i31+i31+i3−1−i31+i31+i3−1−i3−1−i300−1−i31+i30000000000
χ422-2-22-2-22200-220000000000−1+i31−i31−i3−1+i31−i31−i3−1+i3−1+i3001−i3−1+i30000000000−1−i31+i31+i3−1−i31+i31+i3−1−i3−1−i3001+i3−1−i30000000000
χ432-2-2-222-222-2000000000000−1+i31−i31−i31−i3−1+i3−1+i31−i3−1+i3−1+i31−i3000000000000−1−i31+i31+i31+i3−1−i3−1−i31+i3−1−i3−1−i31+i3000000000000
χ442-2-2-222-22-22000000000000−1+i31−i31−i31−i3−1+i3−1+i31−i3−1+i31−i3−1+i3000000000000−1−i31+i31+i31+i3−1−i3−1−i31+i3−1−i31+i3−1−i3000000000000
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
χ4611111111111111-1-1-1-1-1-1-1-1−1−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−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+i321−i321−i321−i321−i321−i321−i321−i321−i32
χ471111111111-1-1-1-111-1-111-1-1−1−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−i321+i321+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+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ481111111111-1-1-1-1-1-111-1-111−1−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−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+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32
χ4911111111-1-111-1-11111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+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+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ5011111111-1-111-1-1-1-1-1-11111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+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+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ5111111111-1-1-1-11111-1-1-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−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+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32
χ5211111111-1-1-1-111-1-11111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−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−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ53222-2-2-2-2200002i−2i00000000−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i300002ζ11−2ζ1100000000−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i300002ζ7−2ζ700000000
χ54222-2-2-2-220000−2i2i00000000−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i30000−2ζ112ζ1100000000−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i30000−2ζ72ζ700000000
χ5522-222-2-2-20000000000002i−2i−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i30000000000002ζ11−2ζ11−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i30000000000002ζ7−2ζ7
χ5622-222-2-2-2000000000000−2i2i−1−i3−1−i31+i3−1−i3−1−i31+i31+i31+i3000000000000−2ζ112ζ11−1+i3−1+i31−i3−1+i3−1+i31−i31−i31−i3000000000000−2ζ72ζ7
χ5722-2-2-222-20000002i−2i000000−1−i3−1−i31+i31+i31+i3−1−i3−1−i31+i30000002ζ11−2ζ11000000−1+i3−1+i31−i31−i31−i3−1+i3−1+i31−i30000002ζ7−2ζ7000000
χ5822-2-2-222-2000000−2i2i000000−1−i3−1−i31+i31+i31+i3−1−i3−1−i31+i3000000−2ζ112ζ11000000−1+i3−1+i31−i31−i31−i3−1+i3−1+i31−i3000000−2ζ72ζ7000000
χ592-222-22-2-200000000002i−2i00−1−i31+i3−1−i3−1−i31+i3−1−i31+i31+i300000000002ζ11−2ζ1100−1+i31−i3−1+i3−1+i31−i3−1+i31−i31−i300000000002ζ7−2ζ700
χ602-222-22-2-20000000000−2i2i00−1−i31+i3−1−i3−1−i31+i3−1−i31+i31+i30000000000−2ζ112ζ1100−1+i31−i3−1+i3−1+i31−i3−1+i31−i31−i30000000000−2ζ72ζ700
χ612-22-22-22-2000000002i−2i0000−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i3000000002ζ11−2ζ110000−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i3000000002ζ7−2ζ70000
χ622-22-22-22-200000000−2i2i0000−1−i31+i3−1−i31+i3−1−i31+i3−1−i31+i300000000−2ζ112ζ110000−1+i31−i3−1+i31−i3−1+i31−i3−1+i31−i300000000−2ζ72ζ70000
χ632-2-22-2-222002-20000000000−1−i31+i31+i3−1−i31+i31+i3−1−i3−1−i300−1−i31+i30000000000−1+i31−i31−i3−1+i31−i31−i3−1+i3−1+i300−1+i31−i30000000000
χ642-2-22-2-22200-220000000000−1−i31+i31+i3−1−i31+i31+i3−1−i3−1−i3001+i3−1−i30000000000−1+i31−i31−i3−1+i31−i31−i3−1+i3−1+i3001−i3−1+i30000000000
χ652-2-2-222-222-2000000000000−1−i31+i31+i31+i3−1−i3−1−i31+i3−1−i3−1−i31+i3000000000000−1+i31−i31−i31−i3−1+i3−1+i31−i3−1+i3−1+i31−i3000000000000
χ662-2-2-222-22-22000000000000−1−i31+i31+i31+i3−1−i3−1−i31+i3−1−i31+i3−1−i3000000000000−1+i31−i31−i31−i3−1+i3−1+i31−i3−1+i31−i3−1+i3000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.