Finite Group Databasebeta

← Group #13052090

Character table — Group #13052090

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122446666777777778812121212121214141414242424242828282828282828282828282828282856565656565656565656
order1222448871414143366666644282856565656121212122828282824668812122424242424242424441212121212121212
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ311111111111111111111-1-11111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ5111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ6111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211111111−1−i32−1+i32−1−i32−1+i321111-1-11+i321−i32-1-11+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ7111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1111111−1−i32−1+i32−1−i32−1+i32-1-1-1-111−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11+i321+i321−i321−i321+i321+i321−i321−i32
χ8111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-11+i321−i32-1-11+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ9111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ10111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211111111−1+i32−1−i32−1+i32−1−i321111-1-11−i321+i32-1-11−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ11111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1111111−1+i32−1−i32−1+i32−1−i32-1-1-1-111−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11−i321−i321+i321+i321−i321−i321+i321+i32
χ12111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-11−i321+i32-1-11−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ13111111-1-11111111111111-111-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-1-1-11-11-11-11-11-1
χ14111111-1-11111111111111-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111-11-11-111-11-1
χ15111111-1-1111111111111-1111-1-1-1-11111-1-1111111-1-111-1-1-1-1-1-1-1-1-11-11-11-11-11
χ16111111-1-1111111111111-1111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-111111-11-11-1-11-11
χ17111111-1-11111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-111-1-1-1-1−1−i32−1+i32−1−i32−1+i3211-1-111−1−i32−1+i32-1-1−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32
χ18111111-1-11111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-111-1-1-1-1−1−i32−1+i32−1−i32−1+i3211-1-1-1-11+i321−i32111+i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-111+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32
χ19111111-1-11111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1111-1-1-1-1−1−i32−1+i32−1−i32−1+i32-1-11111−1−i32−1+i32-1-1−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-111+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32
χ20111111-1-11111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1111-1-1-1-1−1−i32−1+i32−1−i32−1+i32-1-111-1-11+i321−i32111+i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-1−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32
χ21111111-1-11111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-111-1-1-1-1−1+i32−1−i32−1+i32−1−i3211-1-111−1+i32−1−i32-1-1−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32
χ22111111-1-11111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-111-1-1-1-1−1+i32−1−i32−1+i32−1−i3211-1-1-1-11−i321+i32111−i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-111−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32
χ23111111-1-11111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1111-1-1-1-1−1+i32−1−i32−1+i32−1−i32-1-11111−1+i32−1−i32-1-1−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-111−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32
χ24111111-1-11111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1111-1-1-1-1−1+i32−1−i32−1+i32−1−i32-1-111-1-11−i321+i32111−i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-1−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32
χ252222-2-20022222222222200-2-20000-2-2-2-200002-22200-2-2000000000000000000
χ262222-2-20022222222222200-2-20000-2-2-2-20000-22-2-20022000000000000000000
χ272222-2-2002222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i300-2-200001+i31−i31+i31−i300002-2−1−i3−1+i3001+i31−i3000000000000000000
χ282222-2-2002222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i300-2-200001+i31−i31+i31−i30000-221+i31−i300−1−i3−1+i3000000000000000000
χ292222-2-2002222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i300-2-200001−i31+i31−i31+i300002-2−1+i3−1−i3001−i31+i3000000000000000000
χ302222-2-2002222−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i300-2-200001−i31+i31−i31+i30000-221−i31+i300−1+i3−1−i3000000000000000000
χ3122-2-22-2002-2-2222-2-2-2-222002-2000022-2-2000000002i−2i0000002i−2i2i−2i0000000000
χ3222-2-22-2002-2-2222-2-2-2-222002-2000022-2-200000000−2i2i000000−2i2i−2i2i0000000000
χ3322-2-22-2002-2-22−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i3002-20000−1−i3−1+i31+i31−i3000000002i−2i0000002ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1662ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1580000000000
χ3422-2-22-2002-2-22−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i3002-20000−1−i3−1+i31+i31−i300000000−2i2i000000−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1662ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1582ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ1580000000000
χ3522-2-22-2002-2-22−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i3002-20000−1+i3−1−i31−i31+i3000000002i−2i0000002ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1582ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1660000000000
χ3622-2-22-2002-2-22−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i3002-20000−1+i3−1−i31−i31+i300000000−2i2i000000−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1582ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1662ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ1660000000000
χ3722-2-2-222-22-2-2222-2-2-2-22200-2222-2-2-2-2220000000000002-22-200000000000000
χ3822-2-2-222-22-2-22−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i300-2222-2-21+i31−i3−1−i3−1+i3000000000000−1−i31+i3−1+i31−i300000000000000
χ3922-2-2-222-22-2-22−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i300-2222-2-21−i31+i3−1+i3−1−i3000000000000−1+i31−i3−1−i31+i300000000000000
χ4022-2-2-22-222-2-2222-2-2-2-22200-22-2-222-2-222000000000000-22-2200000000000000
χ4122-2-2-22-222-2-22−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i300-22-2-2221+i31−i3−1−i3−1+i30000000000001+i3−1−i31−i3−1+i300000000000000
χ4222-2-2-22-222-2-22−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i300-22-2-2221−i31+i3−1+i3−1−i30000000000001−i3−1+i31+i3−1−i300000000000000
χ434-44-4000044-4-4444-44-4-4-4000000000000000000000000000000000000000000
χ444-44-4000044-4-4−2−2i3−2+2i3−2−2i32+2i3−2+2i32−2i32+2i32−2i3000000000000000000000000000000000000000000
χ454-44-4000044-4-4−2+2i3−2−2i3−2+2i32−2i3−2−2i32+2i32−2i32+2i3000000000000000000000000000000000000000000
χ464-4-4400004-44-444-44-44-4-4000000000000000000000000000000000000000000
χ474-4-4400004-44-4−2−2i3−2+2i32+2i3−2−2i32−2i3−2+2i32+2i32−2i3000000000000000000000000000000000000000000
χ484-4-4400004-44-4−2+2i3−2−2i32−2i3−2+2i32+2i3−2−2i32−2i32+2i3000000000000000000000000000000000000000000
χ4966666666-1-1-1-10000000066-1-1-1-1-1-10000-1-1-1-100000000000000000000000000
χ5066666666-1-1-1-100000000-6-6-1-1-1-1-1-10000111100000000000000000000000000
χ51666666-6-6-1-1-1-1000000006-6-1-111110000-1-11100000000000000000000000000
χ52666666-6-6-1-1-1-100000000-66-1-11111000011-1-100000000000000000000000000
χ5366-6-6-666-6-111-100000000001-1-1-1110000−i7i7−i7i700000000000000000000000000
χ5466-6-6-666-6-111-100000000001-1-1-1110000i7−i7i7−i700000000000000000000000000
χ5566-6-6-66-66-111-100000000001-111-1-10000−i7i7i7−i700000000000000000000000000
χ5666-6-6-66-66-111-100000000001-111-1-10000i7−i7−i7i700000000000000000000000000
χ5712121212-12-1200-2-2-2-200000000002200000000000000000000000000000000000000
χ581212-12-1212-1200-222-20000000000-2200000000000000000000000000000000000000
χ5912-1212-120000-2-222000000000000i14−i14i14−i140000000000000000000000000000000000
χ6012-1212-120000-2-222000000000000−i14i14−i14i140000000000000000000000000000000000
χ6112-12-12120000-22-22000000000000i14−i14−i14i140000000000000000000000000000000000
χ6212-12-12120000-22-22000000000000−i14i14i14−i140000000000000000000000000000000000

Here ζ is a primitive root of unity of order 168 (ζ168 = 1); i = ζ42.