Finite Group Databasebeta

← Group #13025376

Character table — Group #13025376

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122444444888888888888888810101010161620203232323240404040404040404040808080808080
order1222445881010101616202040404040808080808080808044444488202020208888161616161616248888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1
χ311111111111111111111111111111111-1-111-1-1-1-11111111111-1-1-1-1-1-1
χ411111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-111-1-11111ii−i−i-1-1ii−i−i-1-1ii−i−i
χ61111111111111111111111111111-1-1-1-111-1-11111−i−iii-1-1−i−iii-1-1−i−iii
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1ii−i−i11−i−iii
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1−i−iii11ii−i−i
χ9111111111111-1-1111111-1-1-1-1-1-1-1-111111-111-1-1111111-1-1-1-1-1-1-111-11-1
χ10111111111111-1-1111111-1-1-1-1-1-1-1-111111-111-1-111-1-1-1-1-1-11111-11-11-11
χ11111111111111-1-1111111-1-1-1-1-1-1-1-11111-111111-1-11111-1-1-1-1-1-11-1-11-11
χ12111111111111-1-1111111-1-1-1-1-1-1-1-11111-111111-1-1-1-1-1-1-1-111111-11-11-1
χ13111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111ii−i−i11−i−iii1-1i−i−ii
χ14111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111−i−iii11ii−i−i1-1−iii−i
χ15111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1ii−i−i11−i−iii-11−iii−i
χ16111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1−i−iii11ii−i−i-11i−i−ii
χ172222222-2-22220022-2-2-2-200000000222200-2-200002-22-2000000000000
χ182222222-2-22220022-2-2-2-200000000222200-2-20000-22-22000000000000
χ192222222-2-22220022-2-2-2-200000000-2-2-2-2002200002i−2i−2i2i000000000000
χ202222222-2-22220022-2-2-2-200000000-2-2-2-200220000−2i2i2i−2i000000000000
χ2122-2-22-222-2-2-2200-22-2-222000000002i−2i2i−2i002i−2i0000000000−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78000000
χ2222-2-22-222-2-2-2200-22-2-222000000002i−2i2i−2i002i−2i00000000002ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ78000000
χ2322-2-22-222-2-2-2200-22-2-22200000000−2i2i−2i2i00−2i2i0000000000−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74000000
χ2422-2-22-222-2-2-2200-22-2-22200000000−2i2i−2i2i00−2i2i00000000002ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ74000000
χ2522-2-22-22-22-2-222i−2i-2222-2-22i2i2i2i−2i−2i−2i−2i2i−2i2i−2i00−2i2i000000002-20000000000
χ2622-2-22-22-22-2-222i−2i-2222-2-22i2i2i2i−2i−2i−2i−2i−2i2i−2i2i002i−2i00000000-220000000000
χ2722-2-22-22-22-2-22−2i2i-2222-2-2−2i−2i−2i−2i2i2i2i2i2i−2i2i−2i00−2i2i00000000-220000000000
χ2822-2-22-22-22-2-22−2i2i-2222-2-2−2i−2i−2i−2i2i2i2i2i−2i2i−2i2i002i−2i000000002-20000000000
χ29444444-144-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-100004400-1-1-1-10000000000000000
χ30444444-144-1-1-144-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-4-40011110000000000000000
χ31444444-144-1-1-1-4-4-1-1-1-1-1-11111111100004-40011-1-10000000000000000
χ32444444-144-1-1-1-4-4-1-1-1-1-1-1111111110000-4400-1-1110000000000000000
χ334444-4-440044400-4-400000000000044-4-4000000000000000000000000
χ344444-4-440044400-4-4000000000000-4-444000000000000000000000000
χ3544-4-44-4-1-4411-14i−4i1-1-1-111−i−i−i−iiiii00000000i5−i55−50000000000000000
χ3644-4-44-4-1-4411-14i−4i1-1-1-111−i−i−i−iiiii00000000−i5i5−550000000000000000
χ3744-4-44-4-1-4411-1−4i4i1-1-1-111iiii−i−i−i−i00000000i5−i5−550000000000000000
χ3844-4-44-4-1-4411-1−4i4i1-1-1-111iiii−i−i−i−i00000000−i5i55−50000000000000000
χ3944-4-4-44400-4-44004-40000000000004i−4i−4i4i000000000000000000000000
χ4044-4-4-44400-4-44004-4000000000000−4i4i4i−4i000000000000000000000000
χ41888888-2-8-8-2-2-200-2-22222000000000000000000000000000000000000
χ428888-8-8-200-2-2-2002200001010−10−101010−10−100000000000000000000000000000
χ438888-8-8-200-2-2-200220000−10−101010−10−1010100000000000000000000000000000
χ4488-8-88-8-28-822-2002-222-2-2000000000000000000000000000000000000
χ4588-8-8-88-20022-200-220000i10i10−i10−i10−i10−i10i10i100000000000000000000000000000
χ4688-8-8-88-20022-200-220000−i10−i10i10i10i10i10−i10−i100000000000000000000000000000
χ478-88-8008008-8-800000000000000000000000000000000000000000000
χ488-88-800-200-222000010−1010−10ζ11+ζ29+ζ47−ζ57−ζ59−ζ61−ζ63+ζ73−ζ11−ζ29−ζ47+ζ57+ζ59+ζ61+ζ63−ζ73ζ9−ζ13−ζ27+ζ31−ζ41+ζ43+ζ77−ζ79−ζ9+ζ13+ζ27−ζ31+ζ41−ζ43−ζ77+ζ79ζ11+ζ29+ζ47−ζ57−ζ59−ζ61−ζ63+ζ73−ζ11−ζ29−ζ47+ζ57+ζ59+ζ61+ζ63−ζ73ζ9−ζ13−ζ27+ζ31−ζ41+ζ43+ζ77−ζ79−ζ9+ζ13+ζ27−ζ31+ζ41−ζ43−ζ77+ζ790000000000000000000000000000
χ498-88-800-200-222000010−1010−10−ζ11−ζ29−ζ47+ζ57+ζ59+ζ61+ζ63−ζ73ζ11+ζ29+ζ47−ζ57−ζ59−ζ61−ζ63+ζ73−ζ9+ζ13+ζ27−ζ31+ζ41−ζ43−ζ77+ζ79ζ9−ζ13−ζ27+ζ31−ζ41+ζ43+ζ77−ζ79−ζ11−ζ29−ζ47+ζ57+ζ59+ζ61+ζ63−ζ73ζ11+ζ29+ζ47−ζ57−ζ59−ζ61−ζ63+ζ73−ζ9+ζ13+ζ27−ζ31+ζ41−ζ43−ζ77+ζ79ζ9−ζ13−ζ27+ζ31−ζ41+ζ43+ζ77−ζ790000000000000000000000000000
χ508-88-800-200-2220000−1010−1010ζ9−ζ13−ζ27+ζ31−ζ41+ζ43+ζ77−ζ79−ζ9+ζ13+ζ27−ζ31+ζ41−ζ43−ζ77+ζ79−ζ11−ζ29−ζ47+ζ57+ζ59+ζ61+ζ63−ζ73ζ11+ζ29+ζ47−ζ57−ζ59−ζ61−ζ63+ζ73ζ9−ζ13−ζ27+ζ31−ζ41+ζ43+ζ77−ζ79−ζ9+ζ13+ζ27−ζ31+ζ41−ζ43−ζ77+ζ79−ζ11−ζ29−ζ47+ζ57+ζ59+ζ61+ζ63−ζ73ζ11+ζ29+ζ47−ζ57−ζ59−ζ61−ζ63+ζ730000000000000000000000000000
χ518-88-800-200-2220000−1010−1010−ζ9+ζ13+ζ27−ζ31+ζ41−ζ43−ζ77+ζ79ζ9−ζ13−ζ27+ζ31−ζ41+ζ43+ζ77−ζ79ζ11+ζ29+ζ47−ζ57−ζ59−ζ61−ζ63+ζ73−ζ11−ζ29−ζ47+ζ57+ζ59+ζ61+ζ63−ζ73−ζ9+ζ13+ζ27−ζ31+ζ41−ζ43−ζ77+ζ79ζ9−ζ13−ζ27+ζ31−ζ41+ζ43+ζ77−ζ79ζ11+ζ29+ζ47−ζ57−ζ59−ζ61−ζ63+ζ73−ζ11−ζ29−ζ47+ζ57+ζ59+ζ61+ζ63−ζ730000000000000000000000000000
χ528-8-8800800-88-800000000000000000000000000000000000000000000
χ538-8-8800-2002-22000010−10−1010ζ9−ζ13+ζ27−ζ31−ζ41−ζ43+ζ77+ζ79−ζ9+ζ13−ζ27+ζ31+ζ41+ζ43−ζ77−ζ79ζ11−ζ29+ζ47+ζ57−ζ59+ζ61−ζ63−ζ73−ζ11+ζ29−ζ47−ζ57+ζ59−ζ61+ζ63+ζ73−ζ9+ζ13−ζ27+ζ31+ζ41+ζ43−ζ77−ζ79ζ9−ζ13+ζ27−ζ31−ζ41−ζ43+ζ77+ζ79−ζ11+ζ29−ζ47−ζ57+ζ59−ζ61+ζ63+ζ73ζ11−ζ29+ζ47+ζ57−ζ59+ζ61−ζ63−ζ730000000000000000000000000000
χ548-8-8800-2002-22000010−10−1010−ζ9+ζ13−ζ27+ζ31+ζ41+ζ43−ζ77−ζ79ζ9−ζ13+ζ27−ζ31−ζ41−ζ43+ζ77+ζ79−ζ11+ζ29−ζ47−ζ57+ζ59−ζ61+ζ63+ζ73ζ11−ζ29+ζ47+ζ57−ζ59+ζ61−ζ63−ζ73ζ9−ζ13+ζ27−ζ31−ζ41−ζ43+ζ77+ζ79−ζ9+ζ13−ζ27+ζ31+ζ41+ζ43−ζ77−ζ79ζ11−ζ29+ζ47+ζ57−ζ59+ζ61−ζ63−ζ73−ζ11+ζ29−ζ47−ζ57+ζ59−ζ61+ζ63+ζ730000000000000000000000000000
χ558-8-8800-2002-220000−101010−10−ζ11+ζ29−ζ47−ζ57+ζ59−ζ61+ζ63+ζ73ζ11−ζ29+ζ47+ζ57−ζ59+ζ61−ζ63−ζ73ζ9−ζ13+ζ27−ζ31−ζ41−ζ43+ζ77+ζ79−ζ9+ζ13−ζ27+ζ31+ζ41+ζ43−ζ77−ζ79ζ11−ζ29+ζ47+ζ57−ζ59+ζ61−ζ63−ζ73−ζ11+ζ29−ζ47−ζ57+ζ59−ζ61+ζ63+ζ73−ζ9+ζ13−ζ27+ζ31+ζ41+ζ43−ζ77−ζ79ζ9−ζ13+ζ27−ζ31−ζ41−ζ43+ζ77+ζ790000000000000000000000000000
χ568-8-8800-2002-220000−101010−10ζ11−ζ29+ζ47+ζ57−ζ59+ζ61−ζ63−ζ73−ζ11+ζ29−ζ47−ζ57+ζ59−ζ61+ζ63+ζ73−ζ9+ζ13−ζ27+ζ31+ζ41+ζ43−ζ77−ζ79ζ9−ζ13+ζ27−ζ31−ζ41−ζ43+ζ77+ζ79−ζ11+ζ29−ζ47−ζ57+ζ59−ζ61+ζ63+ζ73ζ11−ζ29+ζ47+ζ57−ζ59+ζ61−ζ63−ζ73ζ9−ζ13+ζ27−ζ31−ζ41−ζ43+ζ77+ζ79−ζ9+ζ13−ζ27+ζ31+ζ41+ζ43−ζ77−ζ790000000000000000000000000000

Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.