Finite Group Databasebeta

← Group #13014110

Character table — Group #13014110

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112244444488888888161616161616161616161616161620202020404040404040404040404040404080808080
order12442424510202024101010202020441010202020202020202020208888224488161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ511111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1
χ611111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i−i−iii
χ811111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiiiii−i−i
χ911-1-11-1-1111-1-1-111-1-111-1i−i-1-111iiii−i−i−i−iii−i−i1-11-1i−i−ζ26−ζ42−ζ58−ζ74−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74ζ26+ζ42+ζ58+ζ74−ζ14−ζ46−ζ62−ζ78−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78ζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74
χ1011-1-11-1-1111-1-1-111-1-111-1i−i-1-111iiii−i−i−i−iii−i−i1-11-1i−iζ26+ζ42+ζ58+ζ74ζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74−ζ26−ζ42−ζ58−ζ74ζ14+ζ46+ζ62+ζ78ζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78ζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74
χ1111-1-11-1-1111-1-1-111-1-111-1i−i-1-111iiii−i−i−i−i−i−iii-11-11−ii−ζ14−ζ46−ζ62−ζ78−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78ζ14+ζ46+ζ62+ζ78−ζ26−ζ42−ζ58−ζ74−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74ζ26+ζ42+ζ58+ζ74ζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74ζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78
χ1211-1-11-1-1111-1-1-111-1-111-1i−i-1-111iiii−i−i−i−i−i−iii-11-11−iiζ14+ζ46+ζ62+ζ78ζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78−ζ14−ζ46−ζ62−ζ78ζ26+ζ42+ζ58+ζ74ζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74−ζ26−ζ42−ζ58−ζ74−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78
χ1311-1-11-1-1111-1-1-111-1-111-1−ii-1-111−i−i−i−iiiiiii−i−i-11-11i−i−ζ26−ζ42−ζ58−ζ74−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74ζ26+ζ42+ζ58+ζ74−ζ14−ζ46−ζ62−ζ78−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78ζ14+ζ46+ζ62+ζ78ζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78ζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74
χ1411-1-11-1-1111-1-1-111-1-111-1−ii-1-111−i−i−i−iiiiiii−i−i-11-11i−iζ26+ζ42+ζ58+ζ74ζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74−ζ26−ζ42−ζ58−ζ74ζ14+ζ46+ζ62+ζ78ζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78−ζ14−ζ46−ζ62−ζ78−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74
χ1511-1-11-1-1111-1-1-111-1-111-1−ii-1-111−i−i−i−iiiii−i−iii1-11-1−ii−ζ14−ζ46−ζ62−ζ78−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78ζ14+ζ46+ζ62+ζ78−ζ26−ζ42−ζ58−ζ74−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74ζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74−ζ14−ζ46−ζ62−ζ78ζ14+ζ46+ζ62+ζ78
χ1611-1-11-1-1111-1-1-111-1-111-1−ii-1-111−i−i−i−iiiii−i−iii1-11-1−iiζ14+ζ46+ζ62+ζ78ζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78−ζ14−ζ46−ζ62−ζ78ζ26+ζ42+ζ58+ζ74ζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74−ζ26−ζ42−ζ58−ζ74ζ26+ζ42+ζ58+ζ74−ζ26−ζ42−ζ58−ζ74ζ14+ζ46+ζ62+ζ78−ζ14−ζ46−ζ62−ζ78
χ17222222222222-2-222222200-2-2-2-20000000022220000-2-2000000000000
χ18222222222222-2-222222200-2-2-2-200000000-2-2-2-2000022000000000000
χ1922-2-22-2-2222-2-22-22-2-222-20022-2-2000000002i2i−2i−2i0000−2i2i000000000000
χ2022-2-22-2-2222-2-22-22-2-222-20022-2-200000000−2i−2i2i2i00002i−2i000000000000
χ2144444444-1-1-1-144-1-1-1-1-1-144-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ2244444444-1-1-1-144-1-1-1-1-1-1-4-4-1-1-1-1111111110000000000000000000000
χ2344444444-1-1-1-1-4-4-1-1-1-1-1-100111155−5−555−5−50000000000000000000000
χ2444444444-1-1-1-1-4-4-1-1-1-1-1-1001111−5−555−5−5550000000000000000000000
χ25444444-4-44444004-4-4-4-44000000000000000000000000000000000000
χ26444444-4-4-1-1-1-100-11111-1005−55−5−ζ12+ζ28−ζ44+ζ76ζ12−ζ28+ζ44−ζ76ζ12−ζ28−ζ44+ζ76−ζ12+ζ28+ζ44−ζ76−ζ12+ζ28−ζ44+ζ76ζ12−ζ28+ζ44−ζ76ζ12−ζ28−ζ44+ζ76−ζ12+ζ28+ζ44−ζ760000000000000000000000
χ27444444-4-4-1-1-1-100-11111-1005−55−5ζ12−ζ28+ζ44−ζ76−ζ12+ζ28−ζ44+ζ76−ζ12+ζ28+ζ44−ζ76ζ12−ζ28−ζ44+ζ76ζ12−ζ28+ζ44−ζ76−ζ12+ζ28−ζ44+ζ76−ζ12+ζ28+ζ44−ζ76ζ12−ζ28−ζ44+ζ760000000000000000000000
χ28444444-4-4-1-1-1-100-11111-100−55−55ζ12−ζ28−ζ44+ζ76−ζ12+ζ28+ζ44−ζ76ζ12−ζ28+ζ44−ζ76−ζ12+ζ28−ζ44+ζ76ζ12−ζ28−ζ44+ζ76−ζ12+ζ28+ζ44−ζ76ζ12−ζ28+ζ44−ζ76−ζ12+ζ28−ζ44+ζ760000000000000000000000
χ29444444-4-4-1-1-1-100-11111-100−55−55−ζ12+ζ28+ζ44−ζ76ζ12−ζ28−ζ44+ζ76−ζ12+ζ28−ζ44+ζ76ζ12−ζ28+ζ44−ζ76−ζ12+ζ28+ζ44−ζ76ζ12−ζ28−ζ44+ζ76−ζ12+ζ28−ζ44+ζ76ζ12−ζ28+ζ44−ζ760000000000000000000000
χ304444-4-400444400-40000-40000000000000000002-2-2200000000000000
χ314444-4-400444400-40000-4000000000000000000-222-200000000000000
χ3244-4-44-44-444-4-400444-4-4-4000000000000000000000000000000000000
χ3344-4-44-44-4-1-11100-1-1-1111005−5−55−ζ8−ζ24+ζ56+ζ72ζ8+ζ24−ζ56−ζ72−ζ8+ζ24−ζ56+ζ72ζ8−ζ24+ζ56−ζ72ζ8+ζ24−ζ56−ζ72−ζ8−ζ24+ζ56+ζ72ζ8−ζ24+ζ56−ζ72−ζ8+ζ24−ζ56+ζ720000000000000000000000
χ3444-4-44-44-4-1-11100-1-1-1111005−5−55ζ8+ζ24−ζ56−ζ72−ζ8−ζ24+ζ56+ζ72ζ8−ζ24+ζ56−ζ72−ζ8+ζ24−ζ56+ζ72−ζ8−ζ24+ζ56+ζ72ζ8+ζ24−ζ56−ζ72−ζ8+ζ24−ζ56+ζ72ζ8−ζ24+ζ56−ζ720000000000000000000000
χ3544-4-44-44-4-1-11100-1-1-111100−555−5−ζ8+ζ24−ζ56+ζ72ζ8−ζ24+ζ56−ζ72ζ8+ζ24−ζ56−ζ72−ζ8−ζ24+ζ56+ζ72ζ8−ζ24+ζ56−ζ72−ζ8+ζ24−ζ56+ζ72−ζ8−ζ24+ζ56+ζ72ζ8+ζ24−ζ56−ζ720000000000000000000000
χ3644-4-44-44-4-1-11100-1-1-111100−555−5ζ8−ζ24+ζ56−ζ72−ζ8+ζ24−ζ56+ζ72−ζ8−ζ24+ζ56+ζ72ζ8+ζ24−ζ56−ζ72−ζ8+ζ24−ζ56+ζ72ζ8−ζ24+ζ56−ζ72ζ8+ζ24−ζ56−ζ72−ζ8−ζ24+ζ56+ζ720000000000000000000000
χ3744-4-44-4-44-1-1114-4-111-1-1100-1-111i5i5−i5−i5−i5−i5i5i50000000000000000000000
χ3844-4-44-4-44-1-1114-4-111-1-1100-1-111−i5−i5i5i5i5i5−i5−i50000000000000000000000
χ3944-4-44-4-44-1-111-44-111-1-114i−4i11-1-1−i−i−i−iiiii0000000000000000000000
χ4044-4-44-4-44-1-111-44-111-1-11−4i4i11-1-1iiii−i−i−i−i0000000000000000000000
χ4144-4-4-440044-4-400-40000400000000000000000022-2-200000000000000
χ4244-4-4-440044-4-400-400004000000000000000000-2-22200000000000000
χ434-44i−4i00004-44i−4i0000000000000000000000−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78000000−ζ11−ζ27−ζ31−ζ43−ζ47−ζ59−ζ63−ζ79ζ11+ζ27+ζ31+ζ43+ζ47+ζ59+ζ63+ζ79−ζ11−ζ27+ζ31−ζ43+ζ47−ζ59+ζ63+ζ79ζ11+ζ27−ζ31+ζ43−ζ47+ζ59−ζ63−ζ79−ζ9+ζ13+ζ29−ζ41−ζ57+ζ61−ζ73+ζ77ζ9−ζ13−ζ29+ζ41+ζ57−ζ61+ζ73−ζ77ζ9+ζ13+ζ29+ζ41+ζ57+ζ61+ζ73+ζ77−ζ9−ζ13−ζ29−ζ41−ζ57−ζ61−ζ73−ζ770000
χ444-44i−4i00004-44i−4i0000000000000000000000−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78000000ζ11+ζ27+ζ31+ζ43+ζ47+ζ59+ζ63+ζ79−ζ11−ζ27−ζ31−ζ43−ζ47−ζ59−ζ63−ζ79ζ11+ζ27−ζ31+ζ43−ζ47+ζ59−ζ63−ζ79−ζ11−ζ27+ζ31−ζ43+ζ47−ζ59+ζ63+ζ79ζ9−ζ13−ζ29+ζ41+ζ57−ζ61+ζ73−ζ77−ζ9+ζ13+ζ29−ζ41−ζ57+ζ61−ζ73+ζ77−ζ9−ζ13−ζ29−ζ41−ζ57−ζ61−ζ73−ζ77ζ9+ζ13+ζ29+ζ41+ζ57+ζ61+ζ73+ζ770000
χ454-44i−4i00004-44i−4i00000000000000000000002ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ78000000−ζ11−ζ27+ζ31−ζ43+ζ47−ζ59+ζ63+ζ79ζ11+ζ27−ζ31+ζ43−ζ47+ζ59−ζ63−ζ79ζ11+ζ27+ζ31+ζ43+ζ47+ζ59+ζ63+ζ79−ζ11−ζ27−ζ31−ζ43−ζ47−ζ59−ζ63−ζ79−ζ9−ζ13−ζ29−ζ41−ζ57−ζ61−ζ73−ζ77ζ9+ζ13+ζ29+ζ41+ζ57+ζ61+ζ73+ζ77−ζ9+ζ13+ζ29−ζ41−ζ57+ζ61−ζ73+ζ77ζ9−ζ13−ζ29+ζ41+ζ57−ζ61+ζ73−ζ770000
χ464-44i−4i00004-44i−4i00000000000000000000002ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ78000000ζ11+ζ27−ζ31+ζ43−ζ47+ζ59−ζ63−ζ79−ζ11−ζ27+ζ31−ζ43+ζ47−ζ59+ζ63+ζ79−ζ11−ζ27−ζ31−ζ43−ζ47−ζ59−ζ63−ζ79ζ11+ζ27+ζ31+ζ43+ζ47+ζ59+ζ63+ζ79ζ9+ζ13+ζ29+ζ41+ζ57+ζ61+ζ73+ζ77−ζ9−ζ13−ζ29−ζ41−ζ57−ζ61−ζ73−ζ77ζ9−ζ13−ζ29+ζ41+ζ57−ζ61+ζ73−ζ77−ζ9+ζ13+ζ29−ζ41−ζ57+ζ61−ζ73+ζ770000
χ474-4−4i4i00004-4−4i4i0000000000000000000000−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74000000−ζ9+ζ13+ζ29−ζ41−ζ57+ζ61−ζ73+ζ77ζ9−ζ13−ζ29+ζ41+ζ57−ζ61+ζ73−ζ77−ζ9−ζ13−ζ29−ζ41−ζ57−ζ61−ζ73−ζ77ζ9+ζ13+ζ29+ζ41+ζ57+ζ61+ζ73+ζ77ζ11+ζ27+ζ31+ζ43+ζ47+ζ59+ζ63+ζ79−ζ11−ζ27−ζ31−ζ43−ζ47−ζ59−ζ63−ζ79−ζ11−ζ27+ζ31−ζ43+ζ47−ζ59+ζ63+ζ79ζ11+ζ27−ζ31+ζ43−ζ47+ζ59−ζ63−ζ790000
χ484-4−4i4i00004-4−4i4i0000000000000000000000−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74000000ζ9−ζ13−ζ29+ζ41+ζ57−ζ61+ζ73−ζ77−ζ9+ζ13+ζ29−ζ41−ζ57+ζ61−ζ73+ζ77ζ9+ζ13+ζ29+ζ41+ζ57+ζ61+ζ73+ζ77−ζ9−ζ13−ζ29−ζ41−ζ57−ζ61−ζ73−ζ77−ζ11−ζ27−ζ31−ζ43−ζ47−ζ59−ζ63−ζ79ζ11+ζ27+ζ31+ζ43+ζ47+ζ59+ζ63+ζ79ζ11+ζ27−ζ31+ζ43−ζ47+ζ59−ζ63−ζ79−ζ11−ζ27+ζ31−ζ43+ζ47−ζ59+ζ63+ζ790000
χ494-4−4i4i00004-4−4i4i00000000000000000000002ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ74000000ζ9+ζ13+ζ29+ζ41+ζ57+ζ61+ζ73+ζ77−ζ9−ζ13−ζ29−ζ41−ζ57−ζ61−ζ73−ζ77−ζ9+ζ13+ζ29−ζ41−ζ57+ζ61−ζ73+ζ77ζ9−ζ13−ζ29+ζ41+ζ57−ζ61+ζ73−ζ77−ζ11−ζ27+ζ31−ζ43+ζ47−ζ59+ζ63+ζ79ζ11+ζ27−ζ31+ζ43−ζ47+ζ59−ζ63−ζ79−ζ11−ζ27−ζ31−ζ43−ζ47−ζ59−ζ63−ζ79ζ11+ζ27+ζ31+ζ43+ζ47+ζ59+ζ63+ζ790000
χ504-4−4i4i00004-4−4i4i00000000000000000000002ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ74000000−ζ9−ζ13−ζ29−ζ41−ζ57−ζ61−ζ73−ζ77ζ9+ζ13+ζ29+ζ41+ζ57+ζ61+ζ73+ζ77ζ9−ζ13−ζ29+ζ41+ζ57−ζ61+ζ73−ζ77−ζ9+ζ13+ζ29−ζ41−ζ57+ζ61−ζ73+ζ77ζ11+ζ27−ζ31+ζ43−ζ47+ζ59−ζ63−ζ79−ζ11−ζ27+ζ31−ζ43+ζ47−ζ59+ζ63+ζ79ζ11+ζ27+ζ31+ζ43+ζ47+ζ59+ζ63+ζ79−ζ11−ζ27−ζ31−ζ43−ζ47−ζ59−ζ63−ζ790000
χ518888-8-800-2-2-2-200225−2525−252000000000000000000000000000000000000
χ528888-8-800-2-2-2-2002−2525−25252000000000000000000000000000000000000
χ5388-8-8-8800-2-22200225−25−2525-2000000000000000000000000000000000000
χ5488-8-8-8800-2-222002−252525−25-2000000000000000000000000000000000000
χ5516-1616i−16i0000-44−4i4i00000000000000000000000000000000000000000000
χ5616-16−16i16i0000-444i−4i00000000000000000000000000000000000000000000

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