Finite Group Databasebeta

← Group #13051079

Character table — Group #13051079

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11233334444466777788888121212121212121212121414242424242424242424242828282828282828282856565656565656565656
order12277141422224141433664448814141414141414142828662828282828285656565666666666121212121212121224242424
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ311111111111111−1−i32−1+i32−1−i32−1+i32111111111111111−1−i32−1+i321111111111−1−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
χ411111111111111−1−i32−1+i32−1−i32−1+i321-1-1-1-11111111111−1−i32−1+i3211-1-1-1-1-1-1-1-1−1−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
χ511111111111111−1+i32−1−i32−1+i32−1−i32111111111111111−1+i32−1−i321111111111−1+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
χ611111111111111−1+i32−1−i32−1+i32−1−i321-1-1-1-11111111111−1+i32−1−i3211-1-1-1-1-1-1-1-1−1+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
χ71111111111-1-1111111-1i−ii−i111111-1-1-1-111-1-1ii−i−iii−i−i111111-1-1-1-1-1-1i−ii−ii−ii−i
χ81111111111-1-1111111-1−ii−ii111111-1-1-1-111-1-1−i−iii−i−iii111111-1-1-1-1-1-1−ii−ii−ii−ii
χ91111111111-1-111−1−i32−1+i32−1−i32−1+i32-1i−ii−i111111-1-1-1-1−1−i32−1+i32-1-1ii−i−iii−i−i−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i321+i321−i321+i321−i32ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ101111111111-1-111−1−i32−1+i32−1−i32−1+i32-1−ii−ii111111-1-1-1-1−1−i32−1+i32-1-1−i−iii−i−iii−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321−i321+i321−i321+i321−i32−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ111111111111-1-111−1+i32−1−i32−1+i32−1−i32-1i−ii−i111111-1-1-1-1−1+i32−1−i32-1-1ii−i−iii−i−i−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i321−i321+i321−i321+i32ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ121111111111-1-111−1+i32−1−i32−1+i32−1−i32-1−ii−ii111111-1-1-1-1−1+i32−1−i32-1-1−i−iii−i−iii−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321+i321−i321+i321−i321+i32−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ1311111111-1-111111111-111-1-111-1-1-1-1111111-1-11111-1-1-1-11-1-11-1-11111-1-11111-1-1-1-1
χ1411111111-1-111111111-1-1-11111-1-1-1-1111111-1-1-1-1-1-111111-1-11-1-11111-1-1-1-1-1-11111
χ1511111111-1-11111−1−i32−1+i32−1−i32−1+i32-111-1-111-1-1-1-11111−1−i32−1+i32-1-11111-1-1-1-1−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ1611111111-1-11111−1−i32−1+i32−1−i32−1+i32-1-1-11111-1-1-1-11111−1−i32−1+i32-1-1-1-1-1-11111−1−i321+i321+i32−1+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ1711111111-1-11111−1+i32−1−i32−1+i32−1−i32-111-1-111-1-1-1-11111−1+i32−1−i32-1-11111-1-1-1-1−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ1811111111-1-11111−1+i32−1−i32−1+i32−1−i32-1-1-11111-1-1-1-11111−1+i32−1−i32-1-1-1-1-1-11111−1+i321−i321−i32−1−i321+i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ1911111111-1-1-1-11111111i−i−ii11-1-1-1-1-1-1-1-11111ii−i−i−i−iii1-1-11-1-1-1-1-1-111i−ii−i−ii−ii
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χ2111111111-1-1-1-111−1−i32−1+i32−1−i32−1+i321i−i−ii11-1-1-1-1-1-1-1-1−1−i32−1+i3211ii−i−i−i−iii−1−i321+i321+i32−1+i321−i321−i321+i321−i321+i321−i32−1−i32−1+i32ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ2211111111-1-1-1-111−1−i32−1+i32−1−i32−1+i321−iii−i11-1-1-1-1-1-1-1-1−1−i32−1+i3211−i−iiiii−i−i−1−i321+i321+i32−1+i321−i321−i321+i321−i321+i321−i32−1−i32−1+i32−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ2311111111-1-1-1-111−1+i32−1−i32−1+i32−1−i321i−i−ii11-1-1-1-1-1-1-1-1−1+i32−1−i3211ii−i−i−i−iii−1+i321−i321−i32−1−i321+i321+i321−i321+i321−i321+i32−1+i32−1−i32ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ2411111111-1-1-1-111−1+i32−1−i32−1+i32−1−i321−iii−i11-1-1-1-1-1-1-1-1−1+i32−1−i3211−i−iiiii−i−i−1+i321−i321−i32−1−i321+i321+i321−i321+i321−i321+i32−1+i32−1−i32−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ252222222-2002-222222200000-2-2000022-2-2220000000000-200-20022-2-20000000000
χ262222222-2002-222−1−i3−1+i3−1−i3−1+i300000-2-2000022-2-2−1−i3−1+i300000000001+i3001−i300−1−i3−1+i31+i31−i30000000000
χ272222222-2002-222−1+i3−1−i3−1+i3−1−i300000-2-2000022-2-2−1+i3−1−i300000000001−i3001+i300−1+i3−1−i31−i31+i30000000000
χ282222222-200-2222222200000-2-20000-2-222220000000000-200-200-2-2220000000000
χ292222222-200-2222−1−i3−1+i3−1−i3−1+i300000-2-20000-2-222−1−i3−1+i300000000001+i3001−i3001+i31−i3−1−i3−1+i30000000000
χ302222222-200-2222−1+i3−1−i3−1+i3−1−i300000-2-20000-2-222−1+i3−1−i300000000001−i3001+i3001−i31+i3−1+i3−1−i30000000000
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χ32333−1−i72−1+i72−1−i72−1+i7233333−1−i72−1+i7200003-3-3-3-3−1−i72−1+i72−1−i72−1−i72−1+i72−1+i72−1−i72−1+i72−1−i72−1+i7200−1−i72−1+i721+i721−i721+i721−i721+i721−i721+i721−i7200000000000000000000
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χ4744-4444400000-4-44444000000000000000-4-4000000000000000000000000000000
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χ58666−1+i7−1−i7−1+i7−1−i7-6006-6−1+i7−1−i70000000001−i71+i70000−1+i7−1−i71−i71+i700000000000000000000000000000000
χ59666−1+i7−1−i7−1+i7−1−i7-600-66−1+i7−1−i70000000001−i71+i700001−i71+i7−1+i7−1−i700000000000000000000000000000000
χ601212-12−2−2i7−2+2i7−2−2i7−2+2i7000002+2i72−2i7000000000000000000000000000000000000000000000000000
χ611212-12−2+2i7−2−2i7−2+2i7−2−2i7000002−2i72+2i7000000000000000000000000000000000000000000000000000
χ6212-120−2−2i7−2+2i72+2i72−2i706-6000000000000000−1−i71+i7−1+i71−i7000000000000000000000000000000000000
χ6312-120−2−2i7−2+2i72+2i72−2i70-660000000000000001+i7−1−i71−i7−1+i7000000000000000000000000000000000000
χ6412-120−2+2i7−2−2i72−2i72+2i706-6000000000000000−1+i71−i7−1−i71+i7000000000000000000000000000000000000
χ6512-120−2+2i7−2−2i72−2i72+2i70-660000000000000001−i7−1+i71+i7−1−i7000000000000000000000000000000000000

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