Finite Group Databasebeta

← Group #13025331

Character table — Group #13025331

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111224444448888888888888888881010101016202020202020323232324040404040404040404040404040808080
order1222445881010102216162020404040408080808080808080444428888881010101044888888161616161616488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-11-1-1
χ3111111111111111111111111111111-1-1-1-11ii−i−i-1-11111-1-1iii−i−i−i-1-1ii−i−i-1i−i
χ4111111111111111111111111111111-1-1-1-11−i−iii-1-11111-1-1−i−i−iiii-1-1−i−iii-1−ii
χ511111111111111-1-1111111-1-1-1-1-1-1-1-11111-111111111-1-111111111-1-1-1-1-1-1-1-1-1
χ611111111111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-11111-111
χ711111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-111-1-1-1-1iii−i−i−i11−i−iii1−ii
χ811111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-111-1-1-1-1−i−i−iiii11ii−i−i1i−i
χ9111111111111-1-111111111111111111111-1111111-1-1-1-1-1-11-1-11-1-1111111-1-1-1
χ10111111111111-1-111111111111111111111-1-1-1-1-111-1-1-1-1-1-1-111-11111-1-1-1-1-111
χ11111111111111-1-11111111111111111-1-1-1-1-1ii−i−i-1-1-1-1-1-111i−i−i−iii-1-1ii−i−i1−ii
χ12111111111111-1-11111111111111111-1-1-1-1-1−i−iii-1-1-1-1-1-111−iiii−i−i-1-1−i−iii1i−i
χ13111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111-1-111-1-11-1-11-1-1-1-1-1-1-1-1111
χ14111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-111-1-111-1-1-111-111-1-111111-1-1
χ15111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11ii−i−i-1-1-1-11111i−i−i−iii11−i−iii-1i−i
χ16111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11−i−iii-1-1-1-11111−iiii−i−i11ii−i−i-1−ii
χ172222222-2-2222000022-2-2-2-200000000222202222-2-2000000-200-200000000000
χ182222222-2-2222000022-2-2-2-20000000022220-2-2-2-2-2-2000000200200000000000
χ192222222-2-2222000022-2-2-2-200000000-2-2-2-202i2i−2i−2i22000000−2i002i00000000000
χ202222222-2-2222000022-2-2-2-200000000-2-2-2-20−2i−2i2i2i220000002i00−2i00000000000
χ2122-2-22-222-2-2-222-200-22-2-222000000002i2i−2i−2i000002i−2i2-2002i−2i000000000000000
χ2222-2-22-222-2-2-222-200-22-2-22200000000−2i−2i2i2i00000−2i2i2-200−2i2i000000000000000
χ2322-2-22-222-2-2-22-2200-22-2-222000000002i2i−2i−2i000002i−2i-2200−2i2i000000000000000
χ2422-2-22-222-2-2-22-2200-22-2-22200000000−2i−2i2i2i00000−2i2i-22002i−2i000000000000000
χ2522-2-22-22-22-2-220000-2222-2-2000000002i2i−2i−2i00000−2i2i0000000−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ740−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78000000000
χ2622-2-22-22-22-2-220000-2222-2-2000000002i2i−2i−2i00000−2i2i00000002ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ7402ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ78000000000
χ2722-2-22-22-22-2-220000-2222-2-200000000−2i−2i2i2i000002i−2i0000000−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ780−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74000000000
χ2822-2-22-22-22-2-220000-2222-2-200000000−2i−2i2i2i000002i−2i00000002ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ7802ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ74000000000
χ2922-2-2-22200-2-22002−22-200002222−2−2−2−22i−2i2i−2i0−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ7800000000000000i2−i21+i−1−i1−i−1+i000
χ3022-2-2-22200-2-22002−22-200002222−2−2−2−22i−2i2i−2i02ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ7800000000000000i2−i2−1−i1+i−1+i1−i000
χ3122-2-2-22200-2-22002−22-200002222−2−2−2−2−2i2i−2i2i0−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ7400000000000000−i2i2−1+i1−i−1−i1+i000
χ3222-2-2-22200-2-22002−22-200002222−2−2−2−2−2i2i−2i2i02ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ7400000000000000−i2i21−i−1+i1+i−1−i000
χ3322-2-2-22200-2-2200−222-20000−2−2−2−222222i−2i2i−2i0−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ7800000000000000−i2i2−1−i1+i−1+i1−i000
χ3422-2-2-22200-2-2200−222-20000−2−2−2−222222i−2i2i−2i02ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ7800000000000000−i2i21+i−1−i1−i−1+i000
χ3522-2-2-22200-2-2200−222-20000−2−2−2−22222−2i2i−2i2i0−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ7400000000000000i2−i21−i−1+i1+i−1−i000
χ3622-2-2-22200-2-2200−222-20000−2−2−2−22222−2i2i−2i2i02ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ7400000000000000i2−i2−1+i1−i−1−i1+i000
χ37444444-144-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-100004000000-1-1-1-100000000000000000
χ38444444-144-1-1-144-4-4-1-1-1-1-1-1111111110000-4000000-1-11100000000000000000
χ39444444-144-1-1-1-4-444-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-4000000111100000000000000000
χ40444444-144-1-1-1-4-4-4-4-1-1-1-1-1-1111111110000400000011-1-100000000000000000
χ414444-4-44004440000-4-40000000000004-4-440000000000000000000000000000
χ424444-4-44004440000-4-4000000000000-444-40000000000000000000000000000
χ4344-4-44-4-14-411-14-4001-111-1-155−5−555−5−500000000000-115−500000000000000000
χ4444-4-44-4-14-411-14-4001-111-1-1−5−555−5−55500000000000-11−5500000000000000000
χ4544-4-44-4-14-411-1-44001-111-1-155−5−555−5−5000000000001-1−5500000000000000000
χ4644-4-44-4-14-411-1-44001-111-1-1−5−555−5−555000000000001-15−500000000000000000
χ47888888-2-8-8-2-2-20000-2-222220000000000000000000000000000000000000000
χ488888-8-8-200-2-2-200002200001010−10−10−10−10101000000000000000000000000000000000
χ498888-8-8-200-2-2-20000220000−10−1010101010−10−1000000000000000000000000000000000
χ5088-8-88-8-2-8822-200002-2-2-2220000000000000000000000000000000000000000
χ5188-8-8-88-20022-20042−42-220000−2−2−2−2222200000000000000000000000000000000
χ5288-8-8-88-20022-200−4242-2200002222−2−2−2−200000000000000000000000000000000
χ538-88-8008008-8-800000000000000000000000000000000000000000000000000
χ548-88-800-200-22200000010−1010−10ζ11+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+ζ79ζ9−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−ζ7300000000000000000000000000000000
χ558-88-800-200-22200000010−1010−10−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−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+ζ7300000000000000000000000000000000
χ568-88-800-200-222000000−1010−1010ζ9−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+ζ73−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+ζ7900000000000000000000000000000000
χ578-88-800-200-222000000−1010−1010−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−ζ73ζ11+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−ζ7900000000000000000000000000000000
χ588-8-8800800-88-800000000000000000000000000000000000000000000000000
χ598-8-8800-2002-2200000010−10−1010ζ9+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−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−ζ7900000000000000000000000000000000
χ608-8-8800-2002-2200000010−10−1010−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−ζ73ζ11+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+ζ7900000000000000000000000000000000
χ618-8-8800-2002-22000000−101010−10−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+ζ79−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+ζ7300000000000000000000000000000000
χ628-8-8800-2002-22000000−101010−10ζ11+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−ζ79ζ9+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−ζ7300000000000000000000000000000000

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