Finite Group Databasebeta

← Group #13055004

Character table — Group #13055004

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size112222233334444466666666667777888812121212121212121212141414141414141414142424242424242424282828282828282828285656565656565656
order12244887714142488814142828282856565656336644881414282856565656565666121212122424242428282828565656566612122424242424241212121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111−1−i32−1+i32−1−i32−1+i3211111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i3211111111−1−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
χ411111111111111111111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-11111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ511111111111111111111111111−1+i32−1−i32−1+i32−1−i3211111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i3211111111−1+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
χ611111111111111111111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-11111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ711111111111-1-11-1-11111111111111111-1-1-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-1
χ811111111111-1-11-1-111111111111111-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-11111
χ911111111111-1-11-1-11111111111−1−i32−1+i32−1−i32−1+i3211-1-1-1-1-1-111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111-1-1-1-11+i321−i321+i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ1011111111111-1-11-1-11111111111−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-111111+i321−i321+i321−i32−1−i321+i321+i32−1+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ1111111111111-1-11-1-11111111111−1+i32−1−i32−1+i32−1−i3211-1-1-1-1-1-111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111-1-1-1-11−i321+i321−i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ1211111111111-1-11-1-11111111111−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-111111−i321+i321−i321+i32−1+i321−i321−i32−1−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ1311111-1-1111111-1-1-1111111-1-1-1-111111-11-11111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11-11-11-11-1
χ1411111-1-1111111-1-1-1111111-1-1-1-11111-11-111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-11-11-11-11
χ1511111-1-1111111-1-1-1111111-1-1-1-1−1−i32−1+i32−1−i32−1+i321-11-11111-1-1-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211-1-111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321+i321−i321−i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32
χ1611111-1-1111111-1-1-1111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32-11-111111-1-1-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-111-1-111−1−i32−1+i32−1−i32−1+i321+i321+i321+i321−i321−i321−i321+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32
χ1711111-1-1111111-1-1-1111111-1-1-1-1−1+i32−1−i32−1+i32−1−i321-11-11111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321−i321+i321+i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32
χ1811111-1-1111111-1-1-1111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32-11-111111-1-1-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-111-1-111−1+i32−1−i32−1+i32−1−i321−i321−i321−i321+i321+i321+i321−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32
χ1911111-1-11111-1-1-111111111-1-1-1-111111-1-11-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-111-1-1-1-1-111-1111-11-1-11-11
χ2011111-1-11111-1-1-111111111-1-1-1-11111-111-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-111-111-11-111-11-1
χ2111111-1-11111-1-1-111111111-1-1-1-1−1−i32−1+i32−1−i32−1+i321-1-11-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211-1-1-1-1111+i321−i321+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32
χ2211111-1-11111-1-1-111111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32-111-1-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-11111-1-11+i321−i321+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i321+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32
χ2311111-1-11111-1-1-111111111-1-1-1-1−1+i32−1−i32−1+i32−1−i321-1-11-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211-1-1-1-1111−i321+i321−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32
χ2411111-1-11111-1-1-111111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32-111-1-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-11111-1-11−i321+i321−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i321−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32
χ25222-2-20022220002i−2i22-2-2-2-20000222200000000002i2i−2i−2i22-2-2-2-2000000000000000002i−2i02i−2i00000000
χ26222-2-20022220002i−2i22-2-2-2-20000−1−i3−1+i3−1−i3−1+i300000000002i2i−2i−2i−1−i3−1+i31+i31+i31−i31−i3000000000000000002ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ16602ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ15800000000
χ27222-2-20022220002i−2i22-2-2-2-20000−1+i3−1−i3−1+i3−1−i300000000002i2i−2i−2i−1+i3−1−i31−i31−i31+i31+i3000000000000000002ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ15802ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ16600000000
χ28222-2-2002222000−2i2i22-2-2-2-2000022220000000000−2i−2i2i2i22-2-2-2-200000000000000000−2i2i0−2i2i00000000
χ29222-2-2002222000−2i2i22-2-2-2-20000−1−i3−1+i3−1−i3−1+i30000000000−2i−2i2i2i−1−i3−1+i31+i31+i31−i31−i300000000000000000−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1662ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ1660−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1582ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ15800000000
χ30222-2-2002222000−2i2i22-2-2-2-20000−1+i3−1−i3−1+i3−1−i30000000000−2i−2i2i2i−1+i3−1−i31−i31−i31+i31+i300000000000000000−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1582ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ1580−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1662ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ16600000000
χ3122-22-20022222-2000-2-222-2-200002222000022-2-2000000-2-22-22-200000000000022-2-200000000000000
χ3222-22-20022222-2000-2-222-2-20000−1−i3−1+i3−1−i3−1+i3000022-2-20000001+i31−i3−1−i31+i3−1+i31−i3000000000000−1−i3−1+i31+i31−i300000000000000
χ3322-22-20022222-2000-2-222-2-20000−1+i3−1−i3−1+i3−1−i3000022-2-20000001−i31+i3−1+i31−i3−1−i31+i3000000000000−1+i3−1−i31−i31+i300000000000000
χ3422-22-2002222-22000-2-222-2-2000022220000-2-222000000-2-22-22-2000000000000-2-22200000000000000
χ3522-22-2002222-22000-2-222-2-20000−1−i3−1+i3−1−i3−1+i30000-2-2220000001+i31−i3−1−i31+i3−1+i31−i30000000000001+i31−i3−1−i3−1+i300000000000000
χ3622-22-2002222-22000-2-222-2-20000−1+i3−1−i3−1+i3−1−i30000-2-2220000001−i31+i3−1+i31−i3−1−i31+i30000000000001−i31+i3−1+i3−1−i300000000000000
χ3722-2-2222222200-200-2-2-2-2222222222200000000-2-20000-2-2-22-222222000000000000-200-20000000000
χ3822-2-2222222200-200-2-2-2-2222222−1−i3−1+i3−1−i3−1+i300000000-2-200001+i31−i31+i3−1−i31−i3−1+i3−1−i3−1−i3−1+i3−1+i30000000000001+i3001−i30000000000
χ3922-2-2222222200-200-2-2-2-2222222−1+i3−1−i3−1+i3−1−i300000000-2-200001−i31+i31−i3−1+i31+i3−1−i3−1+i3−1+i3−1−i3−1−i30000000000001−i3001+i30000000000
χ4022-2-22-2-2222200200-2-2-2-222-2-2-2-2222200000000220000-2-2-22-22-2-2-2-200000000000020020000000000
χ4122-2-22-2-2222200200-2-2-2-222-2-2-2-2−1−i3−1+i3−1−i3−1+i3000000002200001+i31−i31+i3−1−i31−i3−1+i31+i31+i31−i31−i3000000000000−1−i300−1+i30000000000
χ4222-2-22-2-2222200200-2-2-2-222-2-2-2-2−1+i3−1−i3−1+i3−1−i3000000002200001−i31+i31−i3−1+i31+i3−1−i31−i31−i31+i31+i3000000000000−1+i300−1−i30000000000
χ433333333−1−i72−1+i72−1−i72−1+i7233333−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i7200003333−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i720000000000−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72000000000000000000
χ443333333−1−i72−1+i72−1−i72−1+i7233333−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i720000-3-3-3-3−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i7200000000001+i721−i721+i721−i721+i721−i721+i721−i72000000000000000000
χ453333333−1−i72−1+i72−1−i72−1+i72-3-33-3-3−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i72000033-3-31+i721−i721+i721−i72−1−i72−1+i721+i721−i721+i721−i720000000000−1−i72−1+i72−1−i72−1+i721+i721−i721+i721−i72000000000000000000
χ463333333−1−i72−1+i72−1−i72−1+i72-3-33-3-3−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i720000-3-3331+i721−i721+i721−i72−1−i72−1+i721+i721−i721+i721−i7200000000001+i721−i721+i721−i72−1−i72−1+i72−1−i72−1+i72000000000000000000
χ473333333−1+i72−1−i72−1+i72−1−i7233333−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1+i72−1−i72−1−i7200003333−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i720000000000−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72000000000000000000
χ483333333−1+i72−1−i72−1+i72−1−i7233333−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1+i72−1−i72−1−i720000-3-3-3-3−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i7200000000001−i721+i721−i721+i721−i721+i721−i721+i72000000000000000000
χ493333333−1+i72−1−i72−1+i72−1−i72-3-33-3-3−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1+i72−1−i72−1−i72000033-3-31−i721+i721−i721+i72−1+i72−1−i721−i721+i721−i721+i720000000000−1+i72−1−i72−1+i72−1−i721−i721+i721−i721+i72000000000000000000
χ503333333−1+i72−1−i72−1+i72−1−i72-3-33-3-3−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1+i72−1−i72−1−i720000-3-3331−i721+i721−i721+i72−1+i72−1−i721−i721+i721−i721+i7200000000001−i721+i721−i721+i72−1+i72−1−i72−1+i72−1−i72000000000000000000
χ5133333-3-3−1−i72−1+i72−1−i72−1+i7233-3-3-3−1−i72−1+i72−1−i72−1+i72−1−i72−1+i721+i721+i721−i721−i7200003-33-3−1−i72−1+i72−1−i72−1+i721+i721−i721+i721−i721+i721−i720000000000−1−i72−1+i721+i721−i72−1−i72−1+i721+i721−i72000000000000000000
χ5233333-3-3−1−i72−1+i72−1−i72−1+i7233-3-3-3−1−i72−1+i72−1−i72−1+i72−1−i72−1+i721+i721+i721−i721−i720000-33-33−1−i72−1+i72−1−i72−1+i721+i721−i721+i721−i721+i721−i7200000000001+i721−i72−1−i72−1+i721+i721−i72−1−i72−1+i72000000000000000000
χ5333333-3-3−1−i72−1+i72−1−i72−1+i72-3-3-333−1−i72−1+i72−1−i72−1+i72−1−i72−1+i721+i721+i721−i721−i7200003-3-331+i721−i721+i721−i721+i721−i72−1−i72−1+i72−1−i72−1+i720000000000−1−i72−1+i721+i721−i721+i721−i72−1−i72−1+i72000000000000000000
χ5433333-3-3−1−i72−1+i72−1−i72−1+i72-3-3-333−1−i72−1+i72−1−i72−1+i72−1−i72−1+i721+i721+i721−i721−i720000-333-31+i721−i721+i721−i721+i721−i72−1−i72−1+i72−1−i72−1+i7200000000001+i721−i72−1−i72−1+i72−1−i72−1+i721+i721−i72000000000000000000
χ5533333-3-3−1+i72−1−i72−1+i72−1−i7233-3-3-3−1+i72−1−i72−1+i72−1−i72−1+i72−1−i721−i721−i721+i721+i7200003-33-3−1+i72−1−i72−1+i72−1−i721−i721+i721−i721+i721−i721+i720000000000−1+i72−1−i721−i721+i72−1+i72−1−i721−i721+i72000000000000000000
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χ7712-1200062−62−2−2i7−2+2i72+2i72−2i7000000000002ζ23−2ζ29−2ζ37−2ζ53+2ζ71+2ζ79−2ζ85+2ζ95−2ζ109+2ζ127−2ζ149+2ζ151−2ζ23+2ζ29+2ζ37+2ζ53−2ζ71−2ζ79+2ζ85−2ζ95+2ζ109−2ζ127+2ζ149−2ζ151−2ζ5−2ζ13+2ζ31+2ζ47+2ζ55−2ζ61−2ζ101+2ζ103−2ζ125+2ζ143−2ζ157+2ζ1672ζ5+2ζ13−2ζ31−2ζ47−2ζ55+2ζ61+2ζ101−2ζ103+2ζ125−2ζ143+2ζ157−2ζ167000000000000000000000000000000000000000000000000000000
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χ8012-12000−6262−2+2i7−2−2i72−2i72+2i7000000000002ζ5+2ζ13−2ζ31−2ζ47−2ζ55+2ζ61+2ζ101−2ζ103+2ζ125−2ζ143+2ζ157−2ζ167−2ζ5−2ζ13+2ζ31+2ζ47+2ζ55−2ζ61−2ζ101+2ζ103−2ζ125+2ζ143−2ζ157+2ζ167−2ζ23+2ζ29+2ζ37+2ζ53−2ζ71−2ζ79+2ζ85−2ζ95+2ζ109−2ζ127+2ζ149−2ζ1512ζ23−2ζ29−2ζ37−2ζ53+2ζ71+2ζ79−2ζ85+2ζ95−2ζ109+2ζ127−2ζ149+2ζ151000000000000000000000000000000000000000000000000000000

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