Finite Group Databasebeta

← Group #13026703

Character table — Group #13026703

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11222224444444444488888888888888888101010101616161616161616202020204040404040404040404040404080808080
order1224488245810202040404040810161616162040408080808080808080224410204040808080802488444444448161616164488
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-1-1-1-1-1i−ii−i
χ411111111111111111111111111111111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-1-1-1-1-1−ii−ii
χ511111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11-1-1-1-11111
χ711111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i-11111−ii−ii
χ811111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii-11111i−ii−i
χ91111111-1-1111111111-1111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1-111-1-111-1-1
χ101111111-1-1111111111-1111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111-111-1-1-1-111
χ111111111-1-1111111111-1111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1ii−i−i−i−iii1-1-111i−i−ii
χ121111111-1-1111111111-1111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1−i−iiiii−i−i1-1-111−iii−i
χ131111111-1-1111111111-11-1-111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-111-1-111
χ141111111-1-1111111111-11-1-111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-11111-1-1
χ151111111-1-1111111111-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1ii−i−i−i−iii111-1-1−iii−i
χ161111111-1-1111111111-11-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1−i−iiiii−i−i111-1-1i−i−ii
χ1722222-2-2222-2222-2-2-2-2-2200002-2-200000000222222-2-2000022-2-200000000-200000000
χ1822222-2-2222-2222-2-2-2-2-2200002-2-200000000-2-2-2-222-2-20000-2-22200000000200000000
χ1922222-2-2-2-22-2222-2-2-2-22200002-2-2000000002222-2-2220000-2-2-2-200000000200000000
χ2022222-2-2-2-22-2222-2-2-2-22200002-2-200000000-2-2-2-2-2-2220000222200000000-200000000
χ2122-22-2002-2202-2-200000-2i2−i2i2−i2200i2i2i2i2−i2−i2−i2−i22-2-222-200i2i2−i2−i2-2200000000000i2−i2i2−i20000
χ2222-22-2002-2202-2-200000-2i2−i2i2−i2200i2i2i2i2−i2−i2−i2−i2-222-22-200i2i2−i2−i22-200000000000−i2i2−i2i20000
χ2322-22-2002-2202-2-200000-2−i2i2−i2i2200−i2−i2−i2−i2i2i2i2i22-2-222-200−i2−i2i2i2-2200000000000−i2i2−i2i20000
χ2422-22-2002-2202-2-200000-2−i2i2−i2i2200−i2−i2−i2−i2i2i2i2i2-222-22-200−i2−i2i2i22-200000000000i2−i2i2−i20000
χ2522-22-200-22202-2-200000-2i2−i2−i2i2200−i2−i2−i2−i2i2i2i2i22-2-22-2200i2i2−i2−i22-200000000000i2−i2−i2i20000
χ2622-22-200-22202-2-200000-2i2−i2−i2i2200−i2−i2−i2−i2i2i2i2i2-222-2-2200i2i2−i2−i2-2200000000000−i2i2i2−i20000
χ2722-22-200-22202-2-200000-2−i2i2i2−i2200i2i2i2i2−i2−i2−i2−i22-2-22-2200−i2−i2i2i22-200000000000−i2i2i2−i20000
χ2822-22-200-22202-2-200000-2−i2i2i2−i2200i2i2i2i2−i2−i2−i2−i2-222-2-2200−i2−i2i2i2-2200000000000i2−i2−i2i20000
χ2922-2-2222002-222222220-20000-2-2-2000000002-22-200000000002-2002i−2i002i−2i000000000
χ3022-2-2222002-222222220-20000-2-2-2000000002-22-200000000002-200−2i2i00−2i2i000000000
χ3122-2-2222002-222222220-20000-2-2-200000000-22-220000000000-22002-200-22000000000
χ3222-2-2222002-222222220-20000-2-2-200000000-22-220000000000-2200-22002-2000000000
χ3322-2-22-2-20022222-2-2-2-20-20000-222000000002-22-20000000000-222i−2i002i−2i00000000000
χ3422-2-22-2-20022222-2-2-2-20-20000-222000000002-22-20000000000-22−2i2i00−2i2i00000000000
χ3522-2-22-2-20022222-2-2-2-20-20000-22200000000-22-2200000000002-22-200-2200000000000
χ3622-2-22-2-20022222-2-2-2-20-20000-22200000000-22-2200000000002-2-22002-200000000000
χ37444444444-14-1-1-1-1-1-1-14-14444-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1000000000000000000000
χ38444444444-14-1-1-1-1-1-1-14-1-4-4-4-4-1-1-1111111110000-1-1-1-11111000000000000000000000
χ394444444-4-4-14-1-1-1-1-1-1-1-4-144-4-4-1-1-11111111100001111-1-1-1-1000000000000000000000
χ404444444-4-4-14-1-1-1-1-1-1-1-4-1-4-444-1-1-1-1-1-1-1-1-1-1-1000011111111000000000000000000000
χ4144444-4-444-1-4-1-1-11111-4-10000-111i5i5−i5−i5i5i5−i5−i50000-1-111i5−i5i5−i5000000000000000000000
χ4244444-4-444-1-4-1-1-11111-4-10000-111−i5−i5i5i5−i5−i5i5i50000-1-111−i5i5−i5i5000000000000000000000
χ4344444-4-4-4-4-1-4-1-1-111114-10000-111i5i5−i5−i5i5i5−i5−i5000011-1-1−i5i5−i5i5000000000000000000000
χ4444444-4-4-4-4-1-4-1-1-111114-10000-111−i5−i5i5i5−i5−i5i5i5000011-1-1i5−i5i5−i5000000000000000000000
χ45444-4-40000404-4-40000040000-4000000000044-4-400000000000000000000000000000
χ46444-4-40000404-4-40000040000-40000000000-4-44400000000000000000000000000000
χ4744-44-4004-4-10-111i5i5−i5−i5012i2−2i22i2−2i2-1i5−i5ζ14+ζ42+ζ46+ζ58ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78ζ26+ζ62+ζ74+ζ78−ζ14−ζ42−ζ46−ζ58−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78−ζ26−ζ62−ζ74−ζ780000-11i5−i5ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78000000000000000000000
χ4844-44-4004-4-10-111i5i5−i5−i501−2i22i2−2i22i2-1i5−i5−ζ14−ζ42−ζ46−ζ58−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78−ζ26−ζ62−ζ74−ζ78ζ14+ζ42+ζ46+ζ58ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78ζ26+ζ62+ζ74+ζ780000-11i5−i5−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78000000000000000000000
χ4944-44-4004-4-10-111−i5−i5i5i5012i2−2i22i2−2i2-1−i5i5ζ26+ζ62+ζ74+ζ78ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58ζ14+ζ42+ζ46+ζ58−ζ26−ζ62−ζ74−ζ78−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58−ζ14−ζ42−ζ46−ζ580000-11−i5i5ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58000000000000000000000
χ5044-44-4004-4-10-111−i5−i5i5i501−2i22i2−2i22i2-1−i5i5−ζ26−ζ62−ζ74−ζ78−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58−ζ14−ζ42−ζ46−ζ58ζ26+ζ62+ζ74+ζ78ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58ζ14+ζ42+ζ46+ζ580000-11−i5i5−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58000000000000000000000
χ5144-44-400-44-10-111i5i5−i5−i5012i2−2i2−2i22i2-1i5−i5−ζ14−ζ42−ζ46−ζ58−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78−ζ26−ζ62−ζ74−ζ78ζ14+ζ42+ζ46+ζ58ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78ζ26+ζ62+ζ74+ζ7800001-1−i5i5ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78000000000000000000000
χ5244-44-400-44-10-111i5i5−i5−i501−2i22i22i2−2i2-1i5−i5ζ14+ζ42+ζ46+ζ58ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78ζ26+ζ62+ζ74+ζ78−ζ14−ζ42−ζ46−ζ58−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78−ζ26−ζ62−ζ74−ζ7800001-1−i5i5−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78000000000000000000000
χ5344-44-400-44-10-111−i5−i5i5i5012i2−2i2−2i22i2-1−i5i5−ζ26−ζ62−ζ74−ζ78−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58−ζ14−ζ42−ζ46−ζ58ζ26+ζ62+ζ74+ζ78ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58ζ14+ζ42+ζ46+ζ5800001-1i5−i5ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58000000000000000000000
χ5444-44-400-44-10-111−i5−i5i5i501−2i22i22i2−2i2-1−i5i5ζ26+ζ62+ζ74+ζ78ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58ζ14+ζ42+ζ46+ζ58−ζ26−ζ62−ζ74−ζ78−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58−ζ14−ζ42−ζ46−ζ5800001-1i5−i5−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58000000000000000000000
χ55888-8-80000-20-2222i52i5−2i5−2i50-200002−2i52i500000000000000000000000000000000000000000
χ56888-8-80000-20-222−2i5−2i52i52i50-2000022i5−2i500000000000000000000000000000000000000000
χ5788-8-888800-2-8-2-2-2-2-2-2-202000022200000000000000000000000000000000000000000
χ5888-8-88-8-800-28-2-2-222220200002-2-200000000000000000000000000000000000000000
χ598-80004i2−4i20080-8004i2−4i24i2−4i200000000000000000000000000000000000000000000000000
χ608-80004i2−4i200-2022i5−2i52ζ14+2ζ42+2ζ46+2ζ58−2ζ14−2ζ42−2ζ46−2ζ582ζ26+2ζ62+2ζ74+2ζ78−2ζ26−2ζ62−2ζ74−2ζ78000000000−ζ11−ζ13−ζ31−ζ57+ζ59+ζ73+ζ77+ζ79ζ11+ζ13+ζ31+ζ57−ζ59−ζ73−ζ77−ζ79ζ9+ζ27−ζ29−ζ41−ζ43+ζ47+ζ61−ζ63−ζ9−ζ27+ζ29+ζ41+ζ43−ζ47−ζ61+ζ63−ζ11+ζ13+ζ31−ζ57+ζ59+ζ73−ζ77−ζ79ζ11−ζ13−ζ31+ζ57−ζ59−ζ73+ζ77+ζ79ζ9+ζ27+ζ29−ζ41−ζ43−ζ47−ζ61+ζ63−ζ9−ζ27−ζ29+ζ41+ζ43+ζ47+ζ61−ζ63000000000000000000000000000000000
χ618-80004i2−4i200-2022i5−2i52ζ14+2ζ42+2ζ46+2ζ58−2ζ14−2ζ42−2ζ46−2ζ582ζ26+2ζ62+2ζ74+2ζ78−2ζ26−2ζ62−2ζ74−2ζ78000000000ζ11+ζ13+ζ31+ζ57−ζ59−ζ73−ζ77−ζ79−ζ11−ζ13−ζ31−ζ57+ζ59+ζ73+ζ77+ζ79−ζ9−ζ27+ζ29+ζ41+ζ43−ζ47−ζ61+ζ63ζ9+ζ27−ζ29−ζ41−ζ43+ζ47+ζ61−ζ63ζ11−ζ13−ζ31+ζ57−ζ59−ζ73+ζ77+ζ79−ζ11+ζ13+ζ31−ζ57+ζ59+ζ73−ζ77−ζ79−ζ9−ζ27−ζ29+ζ41+ζ43+ζ47+ζ61−ζ63ζ9+ζ27+ζ29−ζ41−ζ43−ζ47−ζ61+ζ63000000000000000000000000000000000
χ628-80004i2−4i200-202−2i52i52ζ26+2ζ62+2ζ74+2ζ78−2ζ26−2ζ62−2ζ74−2ζ782ζ14+2ζ42+2ζ46+2ζ58−2ζ14−2ζ42−2ζ46−2ζ58000000000ζ9+ζ27−ζ29−ζ41−ζ43+ζ47+ζ61−ζ63−ζ9−ζ27+ζ29+ζ41+ζ43−ζ47−ζ61+ζ63ζ11+ζ13+ζ31+ζ57−ζ59−ζ73−ζ77−ζ79−ζ11−ζ13−ζ31−ζ57+ζ59+ζ73+ζ77+ζ79ζ9+ζ27+ζ29−ζ41−ζ43−ζ47−ζ61+ζ63−ζ9−ζ27−ζ29+ζ41+ζ43+ζ47+ζ61−ζ63ζ11−ζ13−ζ31+ζ57−ζ59−ζ73+ζ77+ζ79−ζ11+ζ13+ζ31−ζ57+ζ59+ζ73−ζ77−ζ79000000000000000000000000000000000
χ638-80004i2−4i200-202−2i52i52ζ26+2ζ62+2ζ74+2ζ78−2ζ26−2ζ62−2ζ74−2ζ782ζ14+2ζ42+2ζ46+2ζ58−2ζ14−2ζ42−2ζ46−2ζ58000000000−ζ9−ζ27+ζ29+ζ41+ζ43−ζ47−ζ61+ζ63ζ9+ζ27−ζ29−ζ41−ζ43+ζ47+ζ61−ζ63−ζ11−ζ13−ζ31−ζ57+ζ59+ζ73+ζ77+ζ79ζ11+ζ13+ζ31+ζ57−ζ59−ζ73−ζ77−ζ79−ζ9−ζ27−ζ29+ζ41+ζ43+ζ47+ζ61−ζ63ζ9+ζ27+ζ29−ζ41−ζ43−ζ47−ζ61+ζ63−ζ11+ζ13+ζ31−ζ57+ζ59+ζ73−ζ77−ζ79ζ11−ζ13−ζ31+ζ57−ζ59−ζ73+ζ77+ζ79000000000000000000000000000000000
χ648-8000−4i24i20080-800−4i24i2−4i24i200000000000000000000000000000000000000000000000000
χ658-8000−4i24i200-2022i5−2i5−2ζ14−2ζ42−2ζ46−2ζ582ζ14+2ζ42+2ζ46+2ζ58−2ζ26−2ζ62−2ζ74−2ζ782ζ26+2ζ62+2ζ74+2ζ78000000000−ζ11+ζ13+ζ31−ζ57+ζ59+ζ73−ζ77−ζ79ζ11−ζ13−ζ31+ζ57−ζ59−ζ73+ζ77+ζ79ζ9+ζ27+ζ29−ζ41−ζ43−ζ47−ζ61+ζ63−ζ9−ζ27−ζ29+ζ41+ζ43+ζ47+ζ61−ζ63ζ11+ζ13+ζ31+ζ57−ζ59−ζ73−ζ77−ζ79−ζ11−ζ13−ζ31−ζ57+ζ59+ζ73+ζ77+ζ79−ζ9−ζ27+ζ29+ζ41+ζ43−ζ47−ζ61+ζ63ζ9+ζ27−ζ29−ζ41−ζ43+ζ47+ζ61−ζ63000000000000000000000000000000000
χ668-8000−4i24i200-2022i5−2i5−2ζ14−2ζ42−2ζ46−2ζ582ζ14+2ζ42+2ζ46+2ζ58−2ζ26−2ζ62−2ζ74−2ζ782ζ26+2ζ62+2ζ74+2ζ78000000000ζ11−ζ13−ζ31+ζ57−ζ59−ζ73+ζ77+ζ79−ζ11+ζ13+ζ31−ζ57+ζ59+ζ73−ζ77−ζ79−ζ9−ζ27−ζ29+ζ41+ζ43+ζ47+ζ61−ζ63ζ9+ζ27+ζ29−ζ41−ζ43−ζ47−ζ61+ζ63−ζ11−ζ13−ζ31−ζ57+ζ59+ζ73+ζ77+ζ79ζ11+ζ13+ζ31+ζ57−ζ59−ζ73−ζ77−ζ79ζ9+ζ27−ζ29−ζ41−ζ43+ζ47+ζ61−ζ63−ζ9−ζ27+ζ29+ζ41+ζ43−ζ47−ζ61+ζ63000000000000000000000000000000000
χ678-8000−4i24i200-202−2i52i5−2ζ26−2ζ62−2ζ74−2ζ782ζ26+2ζ62+2ζ74+2ζ78−2ζ14−2ζ42−2ζ46−2ζ582ζ14+2ζ42+2ζ46+2ζ58000000000ζ9+ζ27+ζ29−ζ41−ζ43−ζ47−ζ61+ζ63−ζ9−ζ27−ζ29+ζ41+ζ43+ζ47+ζ61−ζ63ζ11−ζ13−ζ31+ζ57−ζ59−ζ73+ζ77+ζ79−ζ11+ζ13+ζ31−ζ57+ζ59+ζ73−ζ77−ζ79−ζ9−ζ27+ζ29+ζ41+ζ43−ζ47−ζ61+ζ63ζ9+ζ27−ζ29−ζ41−ζ43+ζ47+ζ61−ζ63−ζ11−ζ13−ζ31−ζ57+ζ59+ζ73+ζ77+ζ79ζ11+ζ13+ζ31+ζ57−ζ59−ζ73−ζ77−ζ79000000000000000000000000000000000
χ688-8000−4i24i200-202−2i52i5−2ζ26−2ζ62−2ζ74−2ζ782ζ26+2ζ62+2ζ74+2ζ78−2ζ14−2ζ42−2ζ46−2ζ582ζ14+2ζ42+2ζ46+2ζ58000000000−ζ9−ζ27−ζ29+ζ41+ζ43+ζ47+ζ61−ζ63ζ9+ζ27+ζ29−ζ41−ζ43−ζ47−ζ61+ζ63−ζ11+ζ13+ζ31−ζ57+ζ59+ζ73−ζ77−ζ79ζ11−ζ13−ζ31+ζ57−ζ59−ζ73+ζ77+ζ79ζ9+ζ27−ζ29−ζ41−ζ43+ζ47+ζ61−ζ63−ζ9−ζ27+ζ29+ζ41+ζ43−ζ47−ζ61+ζ63ζ11+ζ13+ζ31+ζ57−ζ59−ζ73−ζ77−ζ79−ζ11−ζ13−ζ31−ζ57+ζ59+ζ73+ζ77+ζ79000000000000000000000000000000000

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