Finite Group Databasebeta

← Group #13055000

Character table — Group #13055000

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111223333333344444466667777777788881212121212121212121212121414141424242424242424242828282828282828282828285656565656565656
order12224477141414141414248888282828283366666622441414282856565656565656561212121214141414282828286612122424242424242424666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111111111111−1−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−i32−1+i32−1+i32
χ4111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1111111111111−1−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+i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ5111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111111111111−1+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+i32−1−i32−1−i32
χ6111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1111111111111−1+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−i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ71111111111111111-1-1-1-11111111111111-11-11111-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11-11-11-11-1
χ81111111111111111-1-1-1-1111111111111-11-111111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-1-11-11-11-11
χ91111111111111111-1-1-1-11111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321-11-11111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i3211-1-111-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32
χ101111111111111111-1-1-1-11111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-11-111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1+i32-1-111-1-111−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32
χ111111111111111111-1-1-1-11111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321-11-11111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i3211-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32
χ121111111111111111-1-1-1-11111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-11-111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1−i32-1-111-1-111−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32
χ1311111111111111-1-111-1-111111111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ1411111111111111-1-111-1-1111111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111
χ1511111111111111-1-111-1-11111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211-1-1-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i321111-1-1-1-11+i321−i321+i321−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
χ1611111111111111-1-111-1-11111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-111-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1+i32-1-1-1-111111+i321−i321+i321−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
χ1711111111111111-1-111-1-11111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211-1-1-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i321111-1-1-1-11−i321+i321−i321+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
χ1811111111111111-1-111-1-11111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-111-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1−i32-1-1-1-111111−i321+i321−i321+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
χ1911111111111111-1-1-1-1111111111111111-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-1111-11-1-11-11
χ2011111111111111-1-1-1-111111111111111-111-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111-1-111-11-111-11-1
χ2111111111111111-1-1-1-1111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321-1-11-1-1-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1+i3211-1-1-1-1111+i321−i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32
χ2211111111111111-1-1-1-1111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-111-1-1-1-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1+i32-1-11111-1-11+i321−i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32
χ2311111111111111-1-1-1-1111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321-1-11-1-1-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1−i3211-1-1-1-1111−i321+i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32
χ2411111111111111-1-1-1-1111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-111-1-1-1-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1−i32-1-11111-1-11−i321+i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32
χ252222-2-2222222222-20000-2-2-2-222222222000022-2-200000000-2-2-2-20000000022-2-20000000000000000
χ262222-2-2222222222-20000-2-2-2-2−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3000022-2-2000000001+i31−i31+i31−i300000000−1−i3−1+i31+i31−i30000000000000000
χ272222-2-2222222222-20000-2-2-2-2−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3000022-2-2000000001−i31+i31−i31+i300000000−1+i3−1−i31−i31+i30000000000000000
χ282222-2-222222222-220000-2-2-2-2222222220000-2-22200000000-2-2-2-200000000-2-2220000000000000000
χ292222-2-222222222-220000-2-2-2-2−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i30000-2-222000000001+i31−i31+i31−i3000000001+i31−i3−1−i3−1+i30000000000000000
χ302222-2-222222222-220000-2-2-2-2−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i30000-2-222000000001−i31+i31−i31+i3000000001−i31+i3−1+i3−1−i30000000000000000
χ3122-2-22-22222-2-2-2-200002i−2i22-2-2222-2-22-2-20000000000002i2i−2i−2i22-2-2000000000000002i−2i002i−2i00000000
χ3222-2-22-22222-2-2-2-200002i−2i22-2-2−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i30000000000002i2i−2i−2i−1−i3−1+i31+i31−i3000000000000002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ83002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ7900000000
χ3322-2-22-22222-2-2-2-200002i−2i22-2-2−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i30000000000002i2i−2i−2i−1+i3−1−i31−i31+i3000000000000002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ79002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ8300000000
χ3422-2-22-22222-2-2-2-20000−2i2i22-2-2222-2-22-2-2000000000000−2i−2i2i2i22-2-200000000000000−2i2i00−2i2i00000000
χ3522-2-22-22222-2-2-2-20000−2i2i22-2-2−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i3000000000000−2i−2i2i2i−1−i3−1+i31+i31−i300000000000000−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ8300−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ7900000000
χ3622-2-22-22222-2-2-2-20000−2i2i22-2-2−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i3000000000000−2i−2i2i2i−1+i3−1−i31−i31+i300000000000000−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ7900−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ8300000000
χ3722-2-2-222222-2-2-2-2002-200-2-222222-2-22-2-20000000022-2-20000-2-2220000000000002-2002-20000000000
χ3822-2-2-222222-2-2-2-2002-200-2-222−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i30000000022-2-200001+i31−i3−1−i3−1+i3000000000000−1−i31+i300−1+i31−i30000000000
χ3922-2-2-222222-2-2-2-2002-200-2-222−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i30000000022-2-200001−i31+i3−1+i3−1−i3000000000000−1+i31−i300−1−i31+i30000000000
χ4022-2-2-222222-2-2-2-200-2200-2-222222-2-22-2-200000000-2-2220000-2-222000000000000-2200-220000000000
χ4122-2-2-222222-2-2-2-200-2200-2-222−1−i3−1+i3−1−i31+i31+i3−1+i31−i31−i300000000-2-22200001+i31−i3−1−i3−1+i30000000000001+i3−1−i3001−i3−1+i30000000000
χ4222-2-2-222222-2-2-2-200-2200-2-222−1+i3−1−i3−1+i31−i31−i3−1−i31+i31+i300000000-2-22200001−i31+i3−1+i3−1−i30000000000001−i3−1+i3001+i3−1−i30000000000
χ43333333−1−i72−1+i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i72333333−1−i72−1+i72−1−i72−1+i72000000003333−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i720000−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i7200000000000000000000
χ44333333−1−i72−1+i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i72333333−1−i72−1+i72−1−i72−1+i7200000000-3-3-3-3−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i7200001+i721−i721+i721−i721+i721−i721+i721−i7200000000000000000000
χ45333333−1−i72−1+i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i7233-3-3-3-3−1−i72−1+i72−1−i72−1+i72000000003-33-3−1−i72−1+i72−1−i72−1+i721+i721−i721+i721−i721+i721−i721+i721−i720000−1−i72−1+i721+i721−i72−1−i72−1+i721+i721−i7200000000000000000000
χ46333333−1−i72−1+i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i7233-3-3-3-3−1−i72−1+i72−1−i72−1+i7200000000-33-33−1−i72−1+i72−1−i72−1+i721+i721−i721+i721−i721+i721−i721+i721−i7200001+i721−i72−1−i72−1+i721+i721−i72−1−i72−1+i7200000000000000000000
χ47333333−1−i72−1+i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i72-3-333-3-3−1−i72−1+i72−1−i72−1+i720000000033-3-31+i721−i721+i721−i72−1−i72−1+i72−1−i72−1+i721+i721−i721+i721−i720000−1−i72−1+i72−1−i72−1+i721+i721−i721+i721−i7200000000000000000000
χ48333333−1−i72−1+i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i72-3-333-3-3−1−i72−1+i72−1−i72−1+i7200000000-3-3331+i721−i721+i721−i72−1−i72−1+i72−1−i72−1+i721+i721−i721+i721−i7200001+i721−i721+i721−i72−1−i72−1+i72−1−i72−1+i7200000000000000000000
χ49333333−1−i72−1+i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i72-3-3-3-333−1−i72−1+i72−1−i72−1+i72000000003-3-331+i721−i721+i721−i721+i721−i721+i721−i72−1−i72−1+i72−1−i72−1+i720000−1−i72−1+i721+i721−i721+i721−i72−1−i72−1+i7200000000000000000000
χ50333333−1−i72−1+i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i72-3-3-3-333−1−i72−1+i72−1−i72−1+i7200000000-333-31+i721−i721+i721−i721+i721−i721+i721−i72−1−i72−1+i72−1−i72−1+i7200001+i721−i72−1−i72−1+i72−1−i72−1+i721+i721−i7200000000000000000000
χ51333333−1+i72−1−i72−1+i72−1−i72−1+i72−1+i72−1−i72−1−i72333333−1+i72−1−i72−1+i72−1−i72000000003333−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i720000−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i7200000000000000000000
χ52333333−1+i72−1−i72−1+i72−1−i72−1+i72−1+i72−1−i72−1−i72333333−1+i72−1−i72−1+i72−1−i7200000000-3-3-3-3−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i7200001−i721+i721−i721+i721−i721+i721−i721+i7200000000000000000000
χ53333333−1+i72−1−i72−1+i72−1−i72−1+i72−1+i72−1−i72−1−i7233-3-3-3-3−1+i72−1−i72−1+i72−1−i72000000003-33-3−1+i72−1−i72−1+i72−1−i721−i721+i721−i721+i721−i721+i721−i721+i720000−1+i72−1−i721−i721+i72−1+i72−1−i721−i721+i7200000000000000000000
χ54333333−1+i72−1−i72−1+i72−1−i72−1+i72−1+i72−1−i72−1−i7233-3-3-3-3−1+i72−1−i72−1+i72−1−i7200000000-33-33−1+i72−1−i72−1+i72−1−i721−i721+i721−i721+i721−i721+i721−i721+i7200001−i721+i72−1+i72−1−i721−i721+i72−1+i72−1−i7200000000000000000000
χ55333333−1+i72−1−i72−1+i72−1−i72−1+i72−1+i72−1−i72−1−i72-3-333-3-3−1+i72−1−i72−1+i72−1−i720000000033-3-31−i721+i721−i721+i72−1+i72−1−i72−1+i72−1−i721−i721+i721−i721+i720000−1+i72−1−i72−1+i72−1−i721−i721+i721−i721+i7200000000000000000000
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χ7812-1212-1200−2+2i7−2−2i72−2i72+2i7−2+2i72−2i7−2−2i72+2i7000000000000000000000000000000000000000000000000000000000000000000
χ7912-12-121200−2−2i7−2+2i72+2i72−2i72+2i7−2−2i72−2i7−2+2i7000000000000000000000000000000000000000000000000000000000000000000
χ8012-12-121200−2+2i7−2−2i72−2i72+2i72−2i7−2+2i72+2i7−2−2i7000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.