Finite Group Databasebeta

← Group #13051727

Character table — Group #13051727

Order 1344.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1122244446666777781212121212121414141414142424242428282828282828282828282828282828282828285656565656565656
order12244244471428283366814282828282866121212121428565624446666121212121212121212121212266824242424
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1
χ31111111111111−1−i32−1+i32−1−i32−1+i321111111−1−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+i321−1−i32−1+i321−1−i32−1+i32−1−i32−1+i32
χ41111111111111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321111-1-1-1-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321+i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32-11+i321−i32-1−1−i32−1+i321+i321−i32
χ51111111111111−1+i32−1−i32−1+i32−1−i321111111−1+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−i321−1+i32−1−i321−1+i32−1−i32−1+i32−1−i32
χ61111111111111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321111-1-1-1-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321−i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32-11−i321+i32-1−1+i32−1−i321−i321+i32
χ71111111-1-111111111-111-1-1-1-111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ81111111-1-111111111-111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ91111111-1-11111−1−i32−1+i32−1−i32−1+i32-111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-11111−1−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−i32-11+i321−i32-11+i321−i321+i321−i32
χ101111111-1-11111−1−i32−1+i32−1−i32−1+i32-111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i3211-1-1-1-1-1-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321+i321−i321−i321−i321+i321+i321−i321−i321−1−i32−1+i3211+i321−i32−1−i32−1+i32
χ111111111-1-11111−1+i32−1−i32−1+i32−1−i32-111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-11111−1+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+i32-11−i321+i32-11−i321+i321−i321+i32
χ121111111-1-11111−1+i32−1−i32−1+i32−1−i32-111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i3211-1-1-1-1-1-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321−i321−i321+i321+i321+i321−i321−i321+i321+i321−1+i32−1−i3211−i321+i32−1+i32−1−i32
χ1311111-1-11111111111-1111111111111-1-1-1-111-1-1-1-111-1-11-1-11-1-11111-1-1-11-1-111
χ1411111-1-11111111111-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-111-1111111111-1-1-1-1-1
χ1511111-1-1111111−1−i32−1+i32−1−i32−1+i32-1111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-111-1-11+i321−i32−1−i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-11+i321−i3211+i321−i32−1−i32−1+i32
χ1611111-1-1111111−1−i32−1+i32−1−i32−1+i32-1111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1-1-1111+i321−i321+i321−i321+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32-11+i321−i321+i321−i32
χ1711111-1-1111111−1+i32−1−i32−1+i32−1−i32-1111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-111-1-11−i321+i32−1+i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-11−i321+i3211−i321+i32−1+i32−1−i32
χ1811111-1-1111111−1+i32−1−i32−1+i32−1−i32-1111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-1-1-1-1-1111−i321+i321−i321+i321−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32-11−i321+i321−i321+i32
χ1911111-1-1-1-111111111111-1-1-1-1111111-1-11111-1-1-1-111-1-11-1-11-1-1-1-1-1-1111-111-1-1
χ2011111-1-1-1-111111111111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-1-111-111-1-1-1-1-1-1-111111
χ2111111-1-1-1-11111−1−i32−1+i32−1−i32−1+i32111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-11111-1-11+i321−i32−1−i32−1+i321+i321−i32−1−i321+i321+i32−1+i321−i321−i321+i321+i321−i321−i321−1−i32−1+i32-1−1−i32−1+i321+i321−i32
χ2211111-1-1-1-11111−1−i32−1+i32−1−i32−1+i32111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-111-1-1111+i321−i321+i321−i321+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i321+i321+i321−i321−i32-11+i321−i321−1−i32−1+i32−1−i32−1+i32
χ2311111-1-1-1-11111−1+i32−1−i32−1+i32−1−i32111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-11111-1-11−i321+i32−1+i32−1−i321−i321+i32−1+i321−i321−i32−1−i321+i321+i321−i321−i321+i321+i321−1+i32−1−i32-1−1+i32−1−i321−i321+i32
χ2411111-1-1-1-11111−1+i32−1−i32−1+i32−1−i32111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-1-111-1-1111−i321+i321−i321+i321−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i321−i321−i321+i321+i32-11−i321+i321−1+i32−1−i32−1+i32−1−i32
χ25222-2-2000022-2-2222202-2000022-2-2-2-20000002-200000002-202-2000000000000
χ26222-2-2000022-2-2222202-2000022-2-2-2-2000000-220000000-220-22000000000000
χ27222-2-2000022-2-2−1−i3−1+i3−1−i3−1+i302-20000−1−i3−1+i31+i31+i31−i31−i30000002-20000000−1−i31+i30−1+i31−i3000000000000
χ28222-2-2000022-2-2−1−i3−1+i3−1−i3−1+i302-20000−1−i3−1+i31+i31+i31−i31−i3000000-2200000001+i3−1−i301−i3−1+i3000000000000
χ29222-2-2000022-2-2−1+i3−1−i3−1+i3−1−i302-20000−1+i3−1−i31−i31−i31+i31+i30000002-20000000−1+i31−i30−1−i31+i3000000000000
χ30222-2-2000022-2-2−1+i3−1−i3−1+i3−1−i302-20000−1+i3−1−i31−i31−i31+i31+i3000000-2200000001−i3−1+i301+i3−1−i3000000000000
χ3122-22-20000222222220-2-20000-2-22-22-200002-200002200-200-200000000000000
χ3222-22-20000222222220-2-20000-2-22-22-20000-220000-2-200200200000000000000
χ3322-22-200002222−1−i3−1+i3−1−i3−1+i30-2-200001+i31−i3−1−i31+i3−1+i31−i300002-20000−1−i3−1+i3001+i3001−i300000000000000
χ3422-22-200002222−1−i3−1+i3−1−i3−1+i30-2-200001+i31−i3−1−i31+i3−1+i31−i30000-2200001+i31−i300−1−i300−1+i300000000000000
χ3522-22-200002222−1+i3−1−i3−1+i3−1−i30-2-200001−i31+i3−1+i31−i3−1−i31+i300002-20000−1+i3−1−i3001−i3001+i300000000000000
χ3622-22-200002222−1+i3−1−i3−1+i3−1−i30-2-200001−i31+i3−1+i31−i3−1−i31+i30000-2200001−i31+i300−1+i300−1−i300000000000000
χ3722-2-222-20022-2-222220-220000-2-2-22-222-20000002200-2-2000000000000000000
χ3822-2-222-20022-2-2−1−i3−1+i3−1−i3−1+i30-2200001+i31−i31+i3−1−i31−i3−1+i32-2000000−1−i3−1+i3001+i31−i3000000000000000000
χ3922-2-222-20022-2-2−1+i3−1−i3−1+i3−1−i30-2200001−i31+i31−i3−1+i31+i3−1−i32-2000000−1+i3−1−i3001−i31+i3000000000000000000
χ4022-2-22-220022-2-222220-220000-2-2-22-22-22000000-2-20022000000000000000000
χ4122-2-22-220022-2-2−1−i3−1+i3−1−i3−1+i30-2200001+i31−i31+i3−1−i31−i3−1+i3-220000001+i31−i300−1−i3−1+i3000000000000000000
χ4222-2-22-220022-2-2−1+i3−1−i3−1+i3−1−i30-2200001−i31+i31−i3−1+i31+i3−1−i3-220000001−i31+i300−1+i3−1−i3000000000000000000
χ434-4000002i−2i4-40044-4-40002i2i−2i−2i000000000000000000000000002i−2i2i−2i00000000
χ444-4000002i−2i4-400−2−2i3−2+2i32+2i32−2i30002i2i−2i−2i000000000000000000000000002ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ7900000000
χ454-4000002i−2i4-400−2+2i3−2−2i32−2i32+2i30002i2i−2i−2i000000000000000000000000002ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ8300000000
χ464-400000−2i2i4-40044-4-4000−2i−2i2i2i00000000000000000000000000−2i2i−2i2i00000000
χ474-400000−2i2i4-400−2−2i3−2+2i32+2i32−2i3000−2i−2i2i2i00000000000000000000000000−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ83−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ7900000000
χ484-400000−2i2i4-400−2+2i3−2−2i32−2i32+2i3000−2i−2i2i2i00000000000000000000000000−2ζ19−2ζ31−2ζ43−2ζ55−2ζ67−2ζ792ζ19+2ζ31+2ζ43+2ζ55+2ζ67+2ζ79−2ζ11−2ζ23−2ζ47−2ζ59−2ζ71−2ζ832ζ11+2ζ23+2ζ47+2ζ59+2ζ71+2ζ8300000000
χ49666666666-1-1-1-100006-1-1-1-1-1-1000000-1-1-1-10000000000000000000000000000
χ506666666-6-6-1-1-1-10000-6-1-11111000000-1-1110000000000000000000000000000
χ5166666-6-666-1-1-1-10000-6-1-1-1-1-1-100000011110000000000000000000000000000
χ5266666-6-6-6-6-1-1-1-100006-1-1111100000011-1-10000000000000000000000000000
χ5366-6-666-600-1-111000001-17−77−7000000-117−70000000000000000000000000000
χ5466-6-666-600-1-111000001-1−77−77000000-11−770000000000000000000000000000
χ5566-6-66-6600-1-111000001-17−77−70000001-1−770000000000000000000000000000
χ5666-6-66-6600-1-111000001-1−77−770000001-17−70000000000000000000000000000
χ57121212-12-120000-2-22200000-22000000000000000000000000000000000000000000
χ581212-1212-120000-2-2-2-20000022000000000000000000000000000000000000000000
χ5912-12000006i−6i-2227−270000000ζ2−ζ10+ζ11+ζ19+ζ22+ζ23−ζ26+ζ31−ζ34−ζ38+ζ43+ζ46+ζ47+ζ50+ζ55+ζ58+ζ59−ζ62+ζ67+ζ71+ζ74+ζ79−ζ82+ζ83−ζ2+ζ10+ζ11+ζ19−ζ22+ζ23+ζ26+ζ31+ζ34+ζ38+ζ43−ζ46+ζ47−ζ50+ζ55−ζ58+ζ59+ζ62+ζ67+ζ71−ζ74+ζ79+ζ82+ζ83−ζ2+ζ10−ζ11−ζ19−ζ22−ζ23+ζ26−ζ31+ζ34+ζ38−ζ43−ζ46−ζ47−ζ50−ζ55−ζ58−ζ59+ζ62−ζ67−ζ71−ζ74−ζ79+ζ82−ζ83ζ2−ζ10−ζ11−ζ19+ζ22−ζ23−ζ26−ζ31−ζ34−ζ38−ζ43+ζ46−ζ47+ζ50−ζ55+ζ58−ζ59−ζ62−ζ67−ζ71+ζ74−ζ79−ζ82−ζ8300000000000000000000000000000000000000
χ6012-12000006i−6i-22−27270000000−ζ2+ζ10+ζ11+ζ19−ζ22+ζ23+ζ26+ζ31+ζ34+ζ38+ζ43−ζ46+ζ47−ζ50+ζ55−ζ58+ζ59+ζ62+ζ67+ζ71−ζ74+ζ79+ζ82+ζ83ζ2−ζ10+ζ11+ζ19+ζ22+ζ23−ζ26+ζ31−ζ34−ζ38+ζ43+ζ46+ζ47+ζ50+ζ55+ζ58+ζ59−ζ62+ζ67+ζ71+ζ74+ζ79−ζ82+ζ83ζ2−ζ10−ζ11−ζ19+ζ22−ζ23−ζ26−ζ31−ζ34−ζ38−ζ43+ζ46−ζ47+ζ50−ζ55+ζ58−ζ59−ζ62−ζ67−ζ71+ζ74−ζ79−ζ82−ζ83−ζ2+ζ10−ζ11−ζ19−ζ22−ζ23+ζ26−ζ31+ζ34+ζ38−ζ43−ζ46−ζ47−ζ50−ζ55−ζ58−ζ59+ζ62−ζ67−ζ71−ζ74−ζ79+ζ82−ζ8300000000000000000000000000000000000000
χ6112-1200000−6i6i-2227−270000000−ζ2+ζ10−ζ11−ζ19−ζ22−ζ23+ζ26−ζ31+ζ34+ζ38−ζ43−ζ46−ζ47−ζ50−ζ55−ζ58−ζ59+ζ62−ζ67−ζ71−ζ74−ζ79+ζ82−ζ83ζ2−ζ10−ζ11−ζ19+ζ22−ζ23−ζ26−ζ31−ζ34−ζ38−ζ43+ζ46−ζ47+ζ50−ζ55+ζ58−ζ59−ζ62−ζ67−ζ71+ζ74−ζ79−ζ82−ζ83ζ2−ζ10+ζ11+ζ19+ζ22+ζ23−ζ26+ζ31−ζ34−ζ38+ζ43+ζ46+ζ47+ζ50+ζ55+ζ58+ζ59−ζ62+ζ67+ζ71+ζ74+ζ79−ζ82+ζ83−ζ2+ζ10+ζ11+ζ19−ζ22+ζ23+ζ26+ζ31+ζ34+ζ38+ζ43−ζ46+ζ47−ζ50+ζ55−ζ58+ζ59+ζ62+ζ67+ζ71−ζ74+ζ79+ζ82+ζ8300000000000000000000000000000000000000
χ6212-1200000−6i6i-22−27270000000ζ2−ζ10−ζ11−ζ19+ζ22−ζ23−ζ26−ζ31−ζ34−ζ38−ζ43+ζ46−ζ47+ζ50−ζ55+ζ58−ζ59−ζ62−ζ67−ζ71+ζ74−ζ79−ζ82−ζ83−ζ2+ζ10−ζ11−ζ19−ζ22−ζ23+ζ26−ζ31+ζ34+ζ38−ζ43−ζ46−ζ47−ζ50−ζ55−ζ58−ζ59+ζ62−ζ67−ζ71−ζ74−ζ79+ζ82−ζ83−ζ2+ζ10+ζ11+ζ19−ζ22+ζ23+ζ26+ζ31+ζ34+ζ38+ζ43−ζ46+ζ47−ζ50+ζ55−ζ58+ζ59+ζ62+ζ67+ζ71−ζ74+ζ79+ζ82+ζ83ζ2−ζ10+ζ11+ζ19+ζ22+ζ23−ζ26+ζ31−ζ34−ζ38+ζ43+ζ46+ζ47+ζ50+ζ55+ζ58+ζ59−ζ62+ζ67+ζ71+ζ74+ζ79−ζ82+ζ8300000000000000000000000000000000000000

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