Finite Group Databasebeta

← Group #13014318

Character table — Group #13014318

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size1111224444448888881616161616161616161616161616162020202040404040404040404040808080808080
order1244242451020201010102020208884040404040404040404040408888241616161616161616448888
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i
χ4111111111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii
χ5111111111111111111-1-11-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ6111111111111111111-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ8111111111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ922222222222222222200-200000000-2-2-2-22222-2-200000000000000
χ1022222222222222222200-200000000-2-2-2-2-2-2-2-22200000000000000
χ1122-2-22-22-222-2-2222-2-2-20000000000000002i2i−2i−2i0000000000001−i−1+i1+i−1−i
χ1222-2-22-22-222-2-2222-2-2-20000000000000002i2i−2i−2i000000000000−1+i1−i−1−i1+i
χ1322-2-22-22-222-2-2222-2-2-2000000000000000−2i−2i2i2i0000000000001+i−1−i1−i−1+i
χ1422-2-22-22-222-2-2222-2-2-2000000000000000−2i−2i2i2i000000000000−1−i1+i−1+i1−i
χ1522-2-22-2-2222-2-22-2-222-200000000000000000002-222−2−222−2−2000000
χ1622-2-22-2-2222-2-22-2-222-200000000000000000002-2−2−222−2−222000000
χ1722-2-22-2-2222-2-22-2-222-20000000000000000000-22i2i2−i2−i2−i2−i2i2i2000000
χ1822-2-22-2-2222-2-22-2-222-20000000000000000000-22−i2−i2i2i2i2i2−i2−i2000000
χ1944444444-1-1-1-1-1-1-1-1-1-100-45555−5−5−5−5111100000000000000000000
χ2044444444-1-1-1-1-1-1-1-1-1-100-4−5−5−5−55555111100000000000000000000
χ2144444444-1-1-1-1-1-1-1-1-1-1444-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2244444444-1-1-1-1-1-1-1-1-1-1-4-4411111111-1-1-1-100000000000000000000
χ23444444-4-444444-4-4-4-4400000000000000000000000000000000000
χ24444444-4-4-1-1-1-1-11111-1000−ζ8+ζ24−ζ56+ζ72−ζ8+ζ24−ζ56+ζ72ζ8−ζ24+ζ56−ζ72ζ8−ζ24+ζ56−ζ72−ζ8−ζ24+ζ56+ζ72−ζ8−ζ24+ζ56+ζ72ζ8+ζ24−ζ56−ζ72ζ8+ζ24−ζ56−ζ7255−5−500000000000000000000
χ25444444-4-4-1-1-1-1-11111-1000−ζ8−ζ24+ζ56+ζ72−ζ8−ζ24+ζ56+ζ72ζ8+ζ24−ζ56−ζ72ζ8+ζ24−ζ56−ζ72ζ8−ζ24+ζ56−ζ72ζ8−ζ24+ζ56−ζ72−ζ8+ζ24−ζ56+ζ72−ζ8+ζ24−ζ56+ζ72−5−55500000000000000000000
χ26444444-4-4-1-1-1-1-11111-1000ζ8−ζ24+ζ56−ζ72ζ8−ζ24+ζ56−ζ72−ζ8+ζ24−ζ56+ζ72−ζ8+ζ24−ζ56+ζ72ζ8+ζ24−ζ56−ζ72ζ8+ζ24−ζ56−ζ72−ζ8−ζ24+ζ56+ζ72−ζ8−ζ24+ζ56+ζ7255−5−500000000000000000000
χ27444444-4-4-1-1-1-1-11111-1000ζ8+ζ24−ζ56−ζ72ζ8+ζ24−ζ56−ζ72−ζ8−ζ24+ζ56+ζ72−ζ8−ζ24+ζ56+ζ72−ζ8+ζ24−ζ56+ζ72−ζ8+ζ24−ζ56+ζ72ζ8−ζ24+ζ56−ζ72ζ8−ζ24+ζ56−ζ72−5−55500000000000000000000
χ284444-4-4004444-40000-4000000000000000000000000000002-20000
χ294444-4-4004444-40000-400000000000000000000000000000-220000
χ3044-4-4-440044-4-4-4000042i−2i02i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ3144-4-4-440044-4-4-400004−2i2i0−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ3244-4-4-4400-1-11115−55−5-12i−2i0−ζ12−ζ28+ζ44−ζ76ζ12+ζ28−ζ44+ζ76−ζ12−ζ28−ζ44+ζ76ζ12+ζ28+ζ44−ζ76ζ12−ζ28−ζ44−ζ76−ζ12+ζ28+ζ44+ζ76−ζ12+ζ28−ζ44−ζ76ζ12−ζ28+ζ44+ζ76−ζ8−ζ24+ζ56+ζ72ζ8+ζ24−ζ56−ζ72−ζ8+ζ24−ζ56+ζ72ζ8−ζ24+ζ56−ζ7200000000000000000000
χ3344-4-4-4400-1-11115−55−5-12i−2i0−ζ12−ζ28−ζ44+ζ76ζ12+ζ28+ζ44−ζ76−ζ12−ζ28+ζ44−ζ76ζ12+ζ28−ζ44+ζ76−ζ12+ζ28−ζ44−ζ76ζ12−ζ28+ζ44+ζ76ζ12−ζ28−ζ44−ζ76−ζ12+ζ28+ζ44+ζ76ζ8+ζ24−ζ56−ζ72−ζ8−ζ24+ζ56+ζ72ζ8−ζ24+ζ56−ζ72−ζ8+ζ24−ζ56+ζ7200000000000000000000
χ3444-4-4-4400-1-11115−55−5-1−2i2i0ζ12+ζ28−ζ44+ζ76−ζ12−ζ28+ζ44−ζ76ζ12+ζ28+ζ44−ζ76−ζ12−ζ28−ζ44+ζ76−ζ12+ζ28+ζ44+ζ76ζ12−ζ28−ζ44−ζ76ζ12−ζ28+ζ44+ζ76−ζ12+ζ28−ζ44−ζ76−ζ8−ζ24+ζ56+ζ72ζ8+ζ24−ζ56−ζ72−ζ8+ζ24−ζ56+ζ72ζ8−ζ24+ζ56−ζ7200000000000000000000
χ3544-4-4-4400-1-11115−55−5-1−2i2i0ζ12+ζ28+ζ44−ζ76−ζ12−ζ28−ζ44+ζ76ζ12+ζ28−ζ44+ζ76−ζ12−ζ28+ζ44−ζ76ζ12−ζ28+ζ44+ζ76−ζ12+ζ28−ζ44−ζ76−ζ12+ζ28+ζ44+ζ76ζ12−ζ28−ζ44−ζ76ζ8+ζ24−ζ56−ζ72−ζ8−ζ24+ζ56+ζ72ζ8−ζ24+ζ56−ζ72−ζ8+ζ24−ζ56+ζ7200000000000000000000
χ3644-4-4-4400-1-1111−55−55-12i−2i0ζ12−ζ28−ζ44−ζ76−ζ12+ζ28+ζ44+ζ76−ζ12+ζ28−ζ44−ζ76ζ12−ζ28+ζ44+ζ76−ζ12−ζ28−ζ44+ζ76ζ12+ζ28+ζ44−ζ76−ζ12−ζ28+ζ44−ζ76ζ12+ζ28−ζ44+ζ76ζ8−ζ24+ζ56−ζ72−ζ8+ζ24−ζ56+ζ72−ζ8−ζ24+ζ56+ζ72ζ8+ζ24−ζ56−ζ7200000000000000000000
χ3744-4-4-4400-1-1111−55−55-12i−2i0−ζ12+ζ28−ζ44−ζ76ζ12−ζ28+ζ44+ζ76ζ12−ζ28−ζ44−ζ76−ζ12+ζ28+ζ44+ζ76−ζ12−ζ28+ζ44−ζ76ζ12+ζ28−ζ44+ζ76−ζ12−ζ28−ζ44+ζ76ζ12+ζ28+ζ44−ζ76−ζ8+ζ24−ζ56+ζ72ζ8−ζ24+ζ56−ζ72ζ8+ζ24−ζ56−ζ72−ζ8−ζ24+ζ56+ζ7200000000000000000000
χ3844-4-4-4400-1-1111−55−55-1−2i2i0−ζ12+ζ28+ζ44+ζ76ζ12−ζ28−ζ44−ζ76ζ12−ζ28+ζ44+ζ76−ζ12+ζ28−ζ44−ζ76ζ12+ζ28+ζ44−ζ76−ζ12−ζ28−ζ44+ζ76ζ12+ζ28−ζ44+ζ76−ζ12−ζ28+ζ44−ζ76ζ8−ζ24+ζ56−ζ72−ζ8+ζ24−ζ56+ζ72−ζ8−ζ24+ζ56+ζ72ζ8+ζ24−ζ56−ζ7200000000000000000000
χ3944-4-4-4400-1-1111−55−55-1−2i2i0ζ12−ζ28+ζ44+ζ76−ζ12+ζ28−ζ44−ζ76−ζ12+ζ28+ζ44+ζ76ζ12−ζ28−ζ44−ζ76ζ12+ζ28−ζ44+ζ76−ζ12−ζ28+ζ44−ζ76ζ12+ζ28+ζ44−ζ76−ζ12−ζ28−ζ44+ζ76−ζ8+ζ24−ζ56+ζ72ζ8−ζ24+ζ56−ζ72ζ8+ζ24−ζ56−ζ72−ζ8−ζ24+ζ56+ζ7200000000000000000000
χ404-44i−4i00004-44i−4i000000000000000000000−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ7800−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−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+ζ79000000
χ414-44i−4i00004-44i−4i000000000000000000000−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ7800ζ9−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+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−ζ79000000
χ424-44i−4i00004-44i−4i0000000000000000000002ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ7800ζ9+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+ζ79000000
χ434-44i−4i00004-44i−4i0000000000000000000002ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ7800−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−ζ79000000
χ444-4−4i4i00004-4−4i4i000000000000000000000−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ7400−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+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+ζ77000000
χ454-4−4i4i00004-4−4i4i000000000000000000000−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ7400ζ11+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−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−ζ77000000
χ464-4−4i4i00004-4−4i4i0000000000000000000002ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ7400−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−ζ77000000
χ474-4−4i4i00004-4−4i4i0000000000000000000002ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ7400ζ11+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+ζ77000000
χ488888-8-800-2-2-2-2225−25−2525200000000000000000000000000000000000
χ498888-8-800-2-2-2-22−252525−25200000000000000000000000000000000000
χ5088-8-88-88-8-2-222-2-2-222200000000000000000000000000000000000
χ5188-8-88-8-88-2-222-222-2-2200000000000000000000000000000000000
χ5216-1616i−16i0000-44−4i4i00000000000000000000000000000000000000000
χ5316-16−16i16i0000-444i−4i00000000000000000000000000000000000000000

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