Finite Group Databasebeta

← Group #5274

Character table — Group #5274

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111111114444444444444411111111444444444444441111111144444444444444
order1222222244444444444444366666661212121212121212121212121212366666661212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111-1-111-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1
χ31111111111-1-111-1-111-1-1-1-11111111111-1-111-1-111-1-1-1-11111111111-1-111-1-111-1-1-1-1
χ41111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111
χ511111111-1-11111-1-1-1-111-1-111111111-1-11111-1-1-1-111-1-111111111-1-11111-1-1-1-111-1-1
χ611111111-1-111-1-1-1-111-1-11111111111-1-111-1-1-1-111-1-11111111111-1-111-1-1-1-111-1-111
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
χ811111111-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1111111-1-1
χ92222-2-2-2-200002-2000000002222-2-2-2-200002-2000000002222-2-2-2-200002-200000000
χ102222-2-2-2-20000-22000000002222-2-2-2-20000-22000000002222-2-2-2-20000-2200000000
χ1122-2-22-22-2000000002i−2i000022-2-22-22-2000000002i−2i000022-2-22-22-2000000002i−2i0000
χ1222-2-22-22-200000000−2i2i000022-2-22-22-200000000−2i2i000022-2-22-22-200000000−2i2i0000
χ1322-2-2-22-222i−2i00000000000022-2-2-22-222i−2i00000000000022-2-2-22-222i−2i000000000000
χ1422-2-2-22-22−2i2i00000000000022-2-2-22-22−2i2i00000000000022-2-2-22-22−2i2i000000000000
χ152-22-22-2-22002i−2i00000000002-22-22-2-22002i−2i00000000002-22-22-2-22002i−2i0000000000
χ162-22-22-2-2200−2i2i00000000002-22-22-2-2200−2i2i00000000002-22-22-2-2200−2i2i0000000000
χ172-22-2-222-200000000002i−2i002-22-2-222-200000000002i−2i002-22-2-222-200000000002i−2i00
χ182-22-2-222-20000000000−2i2i002-22-2-222-20000000000−2i2i002-22-2-222-20000000000−2i2i00
χ192-2-2222-2-20000000000002i−2i2-2-2222-2-20000000000002i−2i2-2-2222-2-20000000000002i−2i
χ202-2-2222-2-2000000000000−2i2i2-2-2222-2-2000000000000−2i2i2-2-2222-2-2000000000000−2i2i
χ212-2-22-2-2220000002-20000002-2-22-2-2220000002-20000002-2-22-2-2220000002-2000000
χ222-2-22-2-222000000-220000002-2-22-2-222000000-220000002-2-22-2-222000000-22000000
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
χ24111111111111-1-111-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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
χ251111111111-1-111-1-111-1-1-1-1−1+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−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+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32
χ261111111111-1-1-1-1-1-1-1-11111−1+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+i32−1−i32−1−i32−1−i32−1−i32
χ2711111111-1-11111-1-1-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−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−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32
χ2811111111-1-111-1-1-1-111-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−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+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+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
χ3011111111-1-1-1-1-1-1111111-1-1−1+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+i321−i321−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−i321+i321+i32
χ312222-2-2-2-200002-200000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i30000−1+i31−i300000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i30000−1−i31+i300000000
χ322222-2-2-2-20000-2200000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i300001−i3−1+i300000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i300001+i3−1−i300000000
χ3322-2-22-22-2000000002i−2i0000−1+i3−1+i31−i31−i3−1+i31−i3−1+i31−i3000000002ζ7−2ζ70000−1−i3−1−i31+i31+i3−1−i31+i3−1−i31+i3000000002ζ11−2ζ110000
χ3422-2-22-22-200000000−2i2i0000−1+i3−1+i31−i31−i3−1+i31−i3−1+i31−i300000000−2ζ72ζ70000−1−i3−1−i31+i31+i3−1−i31+i3−1−i31+i300000000−2ζ112ζ110000
χ3522-2-2-22-222i−2i000000000000−1+i3−1+i31−i31−i31−i3−1+i31−i3−1+i32ζ7−2ζ7000000000000−1−i3−1−i31+i31+i31+i3−1−i31+i3−1−i32ζ11−2ζ11000000000000
χ3622-2-2-22-22−2i2i000000000000−1+i3−1+i31−i31−i31−i3−1+i31−i3−1+i3−2ζ72ζ7000000000000−1−i3−1−i31+i31+i31+i3−1−i31+i3−1−i3−2ζ112ζ11000000000000
χ372-22-22-2-22002i−2i0000000000−1+i31−i3−1+i31−i3−1+i31−i31−i3−1+i3002ζ7−2ζ70000000000−1−i31+i3−1−i31+i3−1−i31+i31+i3−1−i3002ζ11−2ζ110000000000
χ382-22-22-2-2200−2i2i0000000000−1+i31−i3−1+i31−i3−1+i31−i31−i3−1+i300−2ζ72ζ70000000000−1−i31+i3−1−i31+i3−1−i31+i31+i3−1−i300−2ζ112ζ110000000000
χ392-22-2-222-200000000002i−2i00−1+i31−i3−1+i31−i31−i3−1+i3−1+i31−i300000000002ζ7−2ζ700−1−i31+i3−1−i31+i31+i3−1−i3−1−i31+i300000000002ζ11−2ζ1100
χ402-22-2-222-20000000000−2i2i00−1+i31−i3−1+i31−i31−i3−1+i3−1+i31−i30000000000−2ζ72ζ700−1−i31+i3−1−i31+i31+i3−1−i3−1−i31+i30000000000−2ζ112ζ1100
χ412-2-2222-2-20000000000002i−2i−1+i31−i31−i3−1+i3−1+i3−1+i31−i31−i30000000000002ζ7−2ζ7−1−i31+i31+i3−1−i3−1−i3−1−i31+i31+i30000000000002ζ11−2ζ11
χ422-2-2222-2-2000000000000−2i2i−1+i31−i31−i3−1+i3−1+i3−1+i31−i31−i3000000000000−2ζ72ζ7−1−i31+i31+i3−1−i3−1−i3−1−i31+i31+i3000000000000−2ζ112ζ11
χ432-2-22-2-2220000002-2000000−1+i31−i31−i3−1+i31−i31−i3−1+i3−1+i3000000−1+i31−i3000000−1−i31+i31+i3−1−i31+i31+i3−1−i3−1−i3000000−1−i31+i3000000
χ442-2-22-2-222000000-22000000−1+i31−i31−i3−1+i31−i31−i3−1+i3−1+i30000001−i3−1+i3000000−1−i31+i31+i3−1−i31+i31+i3−1−i3−1−i30000001+i3−1−i3000000
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
χ46111111111111-1-111-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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
χ471111111111-1-111-1-111-1-1-1-1−1−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+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−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32
χ481111111111-1-1-1-1-1-1-1-11111−1−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−i32−1+i32−1+i32−1+i32−1+i32
χ4911111111-1-11111-1-1-1-111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+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+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32
χ5011111111-1-111-1-1-1-111-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+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−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−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
χ5211111111-1-1-1-1-1-1111111-1-1−1−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−i321+i321+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+i321−i321−i32
χ532222-2-2-2-200002-200000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i30000−1−i31+i300000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i30000−1+i31−i300000000
χ542222-2-2-2-20000-2200000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i300001+i3−1−i300000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i300001−i3−1+i300000000
χ5522-2-22-22-2000000002i−2i0000−1−i3−1−i31+i31+i3−1−i31+i3−1−i31+i3000000002ζ11−2ζ110000−1+i3−1+i31−i31−i3−1+i31−i3−1+i31−i3000000002ζ7−2ζ70000
χ5622-2-22-22-200000000−2i2i0000−1−i3−1−i31+i31+i3−1−i31+i3−1−i31+i300000000−2ζ112ζ110000−1+i3−1+i31−i31−i3−1+i31−i3−1+i31−i300000000−2ζ72ζ70000
χ5722-2-2-22-222i−2i000000000000−1−i3−1−i31+i31+i31+i3−1−i31+i3−1−i32ζ11−2ζ11000000000000−1+i3−1+i31−i31−i31−i3−1+i31−i3−1+i32ζ7−2ζ7000000000000
χ5822-2-2-22-22−2i2i000000000000−1−i3−1−i31+i31+i31+i3−1−i31+i3−1−i3−2ζ112ζ11000000000000−1+i3−1+i31−i31−i31−i3−1+i31−i3−1+i3−2ζ72ζ7000000000000
χ592-22-22-2-22002i−2i0000000000−1−i31+i3−1−i31+i3−1−i31+i31+i3−1−i3002ζ11−2ζ110000000000−1+i31−i3−1+i31−i3−1+i31−i31−i3−1+i3002ζ7−2ζ70000000000
χ602-22-22-2-2200−2i2i0000000000−1−i31+i3−1−i31+i3−1−i31+i31+i3−1−i300−2ζ112ζ110000000000−1+i31−i3−1+i31−i3−1+i31−i31−i3−1+i300−2ζ72ζ70000000000
χ612-22-2-222-200000000002i−2i00−1−i31+i3−1−i31+i31+i3−1−i3−1−i31+i300000000002ζ11−2ζ1100−1+i31−i3−1+i31−i31−i3−1+i3−1+i31−i300000000002ζ7−2ζ700
χ622-22-2-222-20000000000−2i2i00−1−i31+i3−1−i31+i31+i3−1−i3−1−i31+i30000000000−2ζ112ζ1100−1+i31−i3−1+i31−i31−i3−1+i3−1+i31−i30000000000−2ζ72ζ700
χ632-2-2222-2-20000000000002i−2i−1−i31+i31+i3−1−i3−1−i3−1−i31+i31+i30000000000002ζ11−2ζ11−1+i31−i31−i3−1+i3−1+i3−1+i31−i31−i30000000000002ζ7−2ζ7
χ642-2-2222-2-2000000000000−2i2i−1−i31+i31+i3−1−i3−1−i3−1−i31+i31+i3000000000000−2ζ112ζ11−1+i31−i31−i3−1+i3−1+i3−1+i31−i31−i3000000000000−2ζ72ζ7
χ652-2-22-2-2220000002-2000000−1−i31+i31+i3−1−i31+i31+i3−1−i3−1−i3000000−1−i31+i3000000−1+i31−i31−i3−1+i31−i31−i3−1+i3−1+i3000000−1+i31−i3000000
χ662-2-22-2-222000000-22000000−1−i31+i31+i3−1−i31+i31+i3−1−i3−1−i30000001+i3−1−i3000000−1+i31−i31−i3−1+i31−i31−i3−1+i3−1+i30000001−i3−1+i3000000

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