Finite Group Databasebeta

← Group #13051081

Character table — Group #13051081

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11233334444466777788888121212121212121212121414242424242424242424242828282828282828282856565656565656565656
order1227714142244414143366244441414141428282828282866141428282828282828286666121212121212661212121212121212
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
χ71111111111-1-1111111-111-1-1111111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1
χ81111111111-1-1111111-1-1-111111111-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111
χ91111111111-1-111−1−i32−1+i32−1−i32−1+i32-111-1-1111111-1-1-1-1−1−i32−1+i32-1-11111-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ101111111111-1-111−1−i32−1+i32−1−i32−1+i32-1-1-111111111-1-1-1-1−1−i32−1+i32-1-1-1-1-1-11111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ111111111111-1-111−1+i32−1−i32−1+i32−1−i32-111-1-1111111-1-1-1-1−1+i32−1−i32-1-11111-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ121111111111-1-111−1+i32−1−i32−1+i32−1−i32-1-1-111111111-1-1-1-1−1+i32−1−i32-1-1-1-1-1-11111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ131111111-1-1111111111-1i−ii−i-1-1-1-111111111-1-1ii−i−iii−i−i-1-1-1-1111111-1-1i−ii−ii−ii−i
χ141111111-1-1111111111-1−ii−ii-1-1-1-111111111-1-1−i−iii−i−iii-1-1-1-1111111-1-1−ii−ii−ii−ii
χ151111111-1-111111−1−i32−1+i32−1−i32−1+i32-1i−ii−i-1-1-1-1111111−1−i32−1+i32-1-1ii−i−iii−i−i1+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i32ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ161111111-1-111111−1−i32−1+i32−1−i32−1+i32-1−ii−ii-1-1-1-1111111−1−i32−1+i32-1-1−i−iii−i−iii1+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i32−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ171111111-1-111111−1+i32−1−i32−1+i32−1−i32-1i−ii−i-1-1-1-1111111−1+i32−1−i32-1-1ii−i−iii−i−i1−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i32ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ181111111-1-111111−1+i32−1−i32−1+i32−1−i32-1−ii−ii-1-1-1-1111111−1+i32−1−i32-1-1−i−iii−i−iii1−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i32−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
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χ201111111-1-11-1-11111111−iii−i-1-1-1-111-1-1-1-11111−i−iiiii−i−i-1-1-1-111-1-1-1-111−iii−i−iii−i
χ211111111-1-11-1-111−1−i32−1+i32−1−i32−1+i321i−i−ii-1-1-1-111-1-1-1-1−1−i32−1+i3211ii−i−i−i−iii1+i321+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79
χ221111111-1-11-1-111−1−i32−1+i32−1−i32−1+i321−iii−i-1-1-1-111-1-1-1-1−1−i32−1+i3211−i−iiiii−i−i1+i321+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79
χ231111111-1-11-1-111−1+i32−1−i32−1+i32−1−i321i−i−ii-1-1-1-111-1-1-1-1−1+i32−1−i3211ii−i−i−i−iii1−i321−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83
χ241111111-1-11-1-111−1+i32−1−i32−1+i32−1−i321−iii−i-1-1-1-111-1-1-1-1−1+i32−1−i3211−i−iiiii−i−i1−i321−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79ζ19+ζ31+ζ43+ζ55+ζ67+ζ79−ζ19−ζ31−ζ43−ζ55−ζ67−ζ79−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83ζ11+ζ23+ζ47+ζ59+ζ71+ζ83−ζ11−ζ23−ζ47−ζ59−ζ71−ζ83
χ2522222222-2-2002222220000022-2-2-2-200002200000000002-22-2-2-200000000000000
χ2622222222-2-20022−1−i3−1+i3−1−i3−1+i30000022-2-2-2-20000−1−i3−1+i30000000000−1−i31+i3−1+i31−i31+i31−i300000000000000
χ2722222222-2-20022−1+i3−1−i3−1+i3−1−i30000022-2-2-2-20000−1+i3−1−i30000000000−1+i31−i3−1−i31+i31−i31+i300000000000000
χ282222222-22-20022222200000-2-222-2-20000220000000000-22-22-2-200000000000000
χ292222222-22-20022−1−i3−1+i3−1−i3−1+i300000-2-222-2-20000−1−i3−1+i300000000001+i3−1−i31−i3−1+i31+i31−i300000000000000
χ302222222-22-20022−1+i3−1−i3−1+i3−1−i300000-2-222-2-20000−1+i3−1−i300000000001−i3−1+i31+i3−1−i31−i31+i300000000000000
χ31333−1−i72−1+i72−1−i72−1+i7233333−1−i72−1+i72000033333−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i7200−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i7200000000000000000000
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
χ33333−1−i72−1+i72−1−i72−1+i72333-3-3−1−i72−1+i720000-333-3-3−1−i72−1+i72−1−i72−1+i72−1−i72−1+i721+i721+i721−i721−i72001+i721−i72−1−i72−1+i72−1−i72−1+i721+i721−i721+i721−i7200000000000000000000
χ34333−1−i72−1+i72−1−i72−1+i72333-3-3−1−i72−1+i720000-3-3-333−1−i72−1+i72−1−i72−1+i72−1−i72−1+i721+i721+i721−i721−i72001+i721−i721+i721−i721+i721−i72−1−i72−1+i72−1−i72−1+i7200000000000000000000
χ35333−1−i72−1+i72−1−i72−1+i72-3-3333−1−i72−1+i720000-33i−3i3i−3i1+i721−i721+i721−i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i72001+i721−i72ζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ8300000000000000000000
χ36333−1−i72−1+i72−1−i72−1+i72-3-3333−1−i72−1+i720000-3−3i3i−3i3i1+i721−i721+i721−i72−1−i72−1+i72−1−i72−1−i72−1+i72−1+i72001+i721−i72−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ8300000000000000000000
χ37333−1−i72−1+i72−1−i72−1+i72-3-33-3-3−1−i72−1+i72000033i−3i−3i3i1+i721−i721+i721−i72−1−i72−1+i721+i721+i721−i721−i7200−1−i72−1+i72ζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ8300000000000000000000
χ38333−1−i72−1+i72−1−i72−1+i72-3-33-3-3−1−i72−1+i7200003−3i3i3i−3i1+i721−i721+i721−i72−1−i72−1+i721+i721+i721−i721−i7200−1−i72−1+i72−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ8300000000000000000000
χ39333−1+i72−1−i72−1+i72−1−i7233333−1+i72−1−i72000033333−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1+i72−1−i72−1−i7200−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i72−1+i72−1−i7200000000000000000000
χ40333−1+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
χ41333−1+i72−1−i72−1+i72−1−i72333-3-3−1+i72−1−i720000-333-3-3−1+i72−1−i72−1+i72−1−i72−1+i72−1−i721−i721−i721+i721+i72001−i721+i72−1+i72−1−i72−1+i72−1−i721−i721+i721−i721+i7200000000000000000000
χ42333−1+i72−1−i72−1+i72−1−i72333-3-3−1+i72−1−i720000-3-3-333−1+i72−1−i72−1+i72−1−i72−1+i72−1−i721−i721−i721+i721+i72001−i721+i721−i721+i721−i721+i72−1+i72−1−i72−1+i72−1−i7200000000000000000000
χ43333−1+i72−1−i72−1+i72−1−i72-3-3333−1+i72−1−i720000-33i−3i3i−3i1−i721+i721−i721+i72−1+i72−1−i72−1+i72−1+i72−1−i72−1−i72001−i721+i72ζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ79ζ19+ζ31+ζ47+ζ55+ζ59+ζ83ζ11+ζ23+ζ43+ζ67+ζ71+ζ79−ζ19−ζ31−ζ47−ζ55−ζ59−ζ83−ζ11−ζ23−ζ43−ζ67−ζ71−ζ7900000000000000000000
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χ4744-4444400000-4-44444000000000000000-4-4000000000000000000000000000000
χ4844-4444400000-4-4−2−2i3−2+2i3−2−2i3−2+2i30000000000000002+2i32−2i3000000000000000000000000000000
χ4944-4444400000-4-4−2+2i3−2−2i3−2+2i3−2−2i30000000000000002−2i32+2i3000000000000000000000000000000
χ504-4044-4-40002-20044-4-4000000000002-22-20000000000000000002-22-20000000000
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χ58666−1+i7−1−i7−1+i7−1−i76-6-600−1+i7−1−i7000000000−1+i7−1−i71−i71+i71−i71+i7000000000000000000000000000000000000
χ59666−1+i7−1−i7−1+i7−1−i7-66-600−1+i7−1−i70000000001−i71+i7−1+i7−1−i71−i71+i7000000000000000000000000000000000000
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+2i72−2i70006-600000000000000000−1−i71+i7−1+i71−i700000000000000000000000000000000
χ6312-120−2−2i7−2+2i72+2i72−2i7000-66000000000000000001+i7−1−i71−i7−1+i700000000000000000000000000000000
χ6412-120−2+2i7−2−2i72−2i72+2i70006-600000000000000000−1+i71−i7−1−i71+i700000000000000000000000000000000
χ6512-120−2+2i7−2−2i72−2i72+2i7000-66000000000000000001−i7−1+i71+i7−1−i700000000000000000000000000000000

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