Finite Group Databasebeta

← Group #13104142

Character table — Group #13104142

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size11222444444448888888888888888888825254040404050505050505050505050508080808080808080
order1248855551010101051020202020202040404040404040404040404022224448816161616161616161010101020202020
χ11111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1
χ5111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111111-1-1-1-111-1-111-1-1
χ6111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-111-1-1-1-1111111-1-1-1-111
χ7111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111-1-1
χ8111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111111-1-1-1-1-1-111-1-111
χ9222222222222222222222222222222222-2-20000-2-2-20000000000000000
χ10222-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-22200002-2-20000000000000000
χ1122-2002222222222-2-2-2-2-2-2000000000000220000-20022−2−222−2−200000000
χ1222-2002222222222-2-2-2-2-2-2000000000000220000-200−2−222−2−22200000000
χ1322-2002222222222-2-2-2-2-2-2000000000000-2-2000020022−2−2−2−22200000000
χ1422-2002222222222-2-2-2-2-2-2000000000000-2-20000200−2−22222−2−200000000
χ152-202−22222-2-2-2-22-2000000222222−2−2−2−2−2−22-2000002−2−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ7700000000
χ162-202−22222-2-2-2-22-2000000222222−2−2−2−2−2−22-2000002−2ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ7700000000
χ172-202−22222-2-2-2-22-2000000222222−2−2−2−2−2−2-2200000−22−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ7900000000
χ182-202−22222-2-2-2-22-2000000222222−2−2−2−2−2−2-2200000−22ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ7900000000
χ192-20−222222-2-2-2-22-2000000−2−2−2−2−2−22222222-200000−22−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ7900000000
χ202-20−222222-2-2-2-22-2000000−2−2−2−2−2−22222222-200000−22ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ7900000000
χ212-20−222222-2-2-2-22-2000000−2−2−2−2−2−2222222-22000002−2−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ7700000000
χ222-20−222222-2-2-2-22-2000000−2−2−2−2−2−2222222-22000002−2ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ77−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77−ζ9−ζ31−ζ41−ζ47−ζ57−ζ63−ζ73−ζ79ζ9+ζ31+ζ41+ζ47+ζ57+ζ63+ζ73+ζ79−ζ11−ζ13−ζ27−ζ29−ζ43−ζ59−ζ61−ζ77ζ11+ζ13+ζ27+ζ29+ζ43+ζ59+ζ61+ζ7700000000
χ2344444−1+5−1−53−523+523−523+52−1+5−1−5-1-13−523+52−1+5−1−5-1-1-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−500220000000000000−1+52−1−52−1+52−1−520000
χ2444444−1+5−1−53−523+523−523+52−1+5−1−5-1-13−523+52−1+5−1−5-1-1-1-1−1+53−523+52−1−5-1-1−1+53−523+52−1−500-2-200000000000001−521+521−521+520000
χ25444443−523+52−1−5−1+5−1−5−1+53−523+52-1-1−1−5−1+53−523+52-1-1-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+52000022000000000000000−1+52−1−52−1+52−1−52
χ26444443−523+52−1−5−1+5−1−5−1+53−523+52-1-1−1−5−1+53−523+52-1-1-1-13−52−1−5−1+53+52-1-13−52−1−5−1+53+520000-2-20000000000000001−521+521−521+52
χ27444443+523−52−1+5−1−5−1+5−1−53+523−52-1-1−1+5−1−53+523−52-1-1-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−52000022000000000000000−1−52−1+52−1−52−1+52
χ28444443+523−52−1+5−1−5−1+5−1−53+523−52-1-1−1+5−1−53+523−52-1-1-1-13+52−1+5−1−53−52-1-13+52−1+5−1−53−520000-2-20000000000000001+521−521+521−52
χ2944444−1−5−1+53+523−523+523−52−1−5−1+5-1-13+523−52−1−5−1+5-1-1-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+500220000000000000−1−52−1+52−1−52−1+520000
χ3044444−1−5−1+53+523−523+523−52−1−5−1+5-1-13+523−52−1−5−1+5-1-1-1-1−1−53+523−52−1+5-1-1−1−53+523−52−1+500-2-200000000000001+521−521+521−520000
χ31444-4-4−1+5−1−53−523+523−523+52−1+5−1−5-1-13−523+52−1+5−1−5-1-1111−5−3+52−3−521+5111−5−3+52−3−521+5002-20000000000000−1+52−1−521−521+520000
χ32444-4-4−1+5−1−53−523+523−523+52−1+5−1−5-1-13−523+52−1+5−1−5-1-1111−5−3+52−3−521+5111−5−3+52−3−521+500-2200000000000001−521+52−1+52−1−520000
χ33444-4-43−523+52−1−5−1+5−1−5−1+53−523+52-1-1−1−5−1+53−523+52-1-111−3+521+51−5−3−5211−3+521+51−5−3−5200002-2000000000000000−1+52−1−521−521+52
χ34444-4-43−523+52−1−5−1+5−1−5−1+53−523+52-1-1−1−5−1+53−523+52-1-111−3+521+51−5−3−5211−3+521+51−5−3−520000-220000000000000001−521+52−1+52−1−52
χ35444-4-43+523−52−1+5−1−5−1+5−1−53+523−52-1-1−1+5−1−53+523−52-1-111−3−521−51+5−3+5211−3−521−51+5−3+5200002-2000000000000000−1−52−1+521+521−52
χ36444-4-43+523−52−1+5−1−5−1+5−1−53+523−52-1-1−1+5−1−53+523−52-1-111−3−521−51+5−3+5211−3−521−51+5−3+520000-220000000000000001+521−52−1−52−1+52
χ37444-4-4−1−5−1+53+523−523+523−52−1−5−1+5-1-13+523−52−1−5−1+5-1-1111+5−3−52−3+521−5111+5−3−52−3+521−5002-20000000000000−1−52−1+521+521−520000
χ38444-4-4−1−5−1+53+523−523+523−52−1−5−1+5-1-13+523−52−1−5−1+5-1-1111+5−3−52−3+521−5111+5−3−52−3+521−500-2200000000000001+521−52−1−52−1+520000
χ3988888-2-2-2-2-2-2-2-233-2-2-2-23333-2-2-2-233-2-2-2-20000000000000000000000000
χ40888-8-8-2-2-2-2-2-2-2-233-2-2-2-233-3-32222-3-322220000000000000000000000000
χ4188-800-2-2-2-2-2-2-2-2332222-3-35i−5i00005i−5i00000000000000000000000000000
χ4288-800-2-2-2-2-2-2-2-2332222-3-3−5i5i0000−5i5i00000000000000000000000000000
χ4388-800−2+25−2−253−53+53−53+5−2+25−2−25-2-2−3+5−3−52−252+25220000000000000000000000000000000000000
χ4488-8003−53+5−2−25−2+25−2−25−2+253−53+5-2-22+252−25−3+5−3−5220000000000000000000000000000000000000
χ4588-8003+53−5−2+25−2−25−2+25−2−253+53−5-2-22−252+25−3−5−3+5220000000000000000000000000000000000000
χ4688-800−2−25−2+253+53−53+53−5−2−25−2+25-2-2−3−5−3+52+252−25220000000000000000000000000000000000000
χ478-8042−42-2-2-2-222223-300005i−5i−ζ14−4ζ26−4ζ42−ζ46−4ζ58−ζ62−4ζ74−ζ784ζ14+ζ26+ζ42+4ζ46+ζ58+4ζ62+ζ74+4ζ78−2−2−2−2ζ14+4ζ26+4ζ42+ζ46+4ζ58+ζ62+4ζ74+ζ78−4ζ14−ζ26−ζ42−4ζ46−ζ58−4ζ62−ζ74−4ζ7822220000000000000000000000000
χ488-8042−42-2-2-2-222223-30000−5i5i4ζ14+ζ26+ζ42+4ζ46+ζ58+4ζ62+ζ74+4ζ78−ζ14−4ζ26−4ζ42−ζ46−4ζ58−ζ62−4ζ74−ζ78−2−2−2−2−4ζ14−ζ26−ζ42−4ζ46−ζ58−4ζ62−ζ74−4ζ78ζ14+4ζ26+4ζ42+ζ46+4ζ58+ζ62+4ζ74+ζ7822220000000000000000000000000
χ498-8042−42−2+25−2−253−53+5−3+5−3−52−252+25-22000000−2−2−2ζ14+2ζ26−2ζ46+2ζ742ζ14−2ζ26−ζ42+2ζ46−ζ58+ζ62−2ζ74+ζ78ζ14−ζ26−2ζ42+ζ46−2ζ58+2ζ62−ζ74+2ζ782ζ42+2ζ58−2ζ62−2ζ78222ζ14−2ζ26+2ζ46−2ζ74−2ζ14+2ζ26+ζ42−2ζ46+ζ58−ζ62+2ζ74−ζ78−ζ14+ζ26+2ζ42−ζ46+2ζ58−2ζ62+ζ74−2ζ78−2ζ42−2ζ58+2ζ62+2ζ780000000000000000000000000
χ508-8042−423−53+5−2−25−2+252+252−25−3+5−3−5-22000000−2−22ζ14−2ζ26−ζ42+2ζ46−ζ58+ζ62−2ζ74+ζ782ζ42+2ζ58−2ζ62−2ζ78−2ζ14+2ζ26−2ζ46+2ζ74ζ14−ζ26−2ζ42+ζ46−2ζ58+2ζ62−ζ74+2ζ7822−2ζ14+2ζ26+ζ42−2ζ46+ζ58−ζ62+2ζ74−ζ78−2ζ42−2ζ58+2ζ62+2ζ782ζ14−2ζ26+2ζ46−2ζ74−ζ14+ζ26+2ζ42−ζ46+2ζ58−2ζ62+ζ74−2ζ780000000000000000000000000
χ518-8042−423+53−5−2+25−2−252−252+25−3−5−3+5-22000000−2−2ζ14−ζ26−2ζ42+ζ46−2ζ58+2ζ62−ζ74+2ζ78−2ζ14+2ζ26−2ζ46+2ζ742ζ42+2ζ58−2ζ62−2ζ782ζ14−2ζ26−ζ42+2ζ46−ζ58+ζ62−2ζ74+ζ7822−ζ14+ζ26+2ζ42−ζ46+2ζ58−2ζ62+ζ74−2ζ782ζ14−2ζ26+2ζ46−2ζ74−2ζ42−2ζ58+2ζ62+2ζ78−2ζ14+2ζ26+ζ42−2ζ46+ζ58−ζ62+2ζ74−ζ780000000000000000000000000
χ528-8042−42−2−25−2+253+53−5−3−5−3+52+252−25-22000000−2−22ζ42+2ζ58−2ζ62−2ζ78ζ14−ζ26−2ζ42+ζ46−2ζ58+2ζ62−ζ74+2ζ782ζ14−2ζ26−ζ42+2ζ46−ζ58+ζ62−2ζ74+ζ78−2ζ14+2ζ26−2ζ46+2ζ7422−2ζ42−2ζ58+2ζ62+2ζ78−ζ14+ζ26+2ζ42−ζ46+2ζ58−2ζ62+ζ74−2ζ78−2ζ14+2ζ26+ζ42−2ζ46+ζ58−ζ62+2ζ74−ζ782ζ14−2ζ26+2ζ46−2ζ740000000000000000000000000
χ538-80−4242-2-2-2-222223-300005i−5iζ14+4ζ26+4ζ42+ζ46+4ζ58+ζ62+4ζ74+ζ78−4ζ14−ζ26−ζ42−4ζ46−ζ58−4ζ62−ζ74−4ζ782222−ζ14−4ζ26−4ζ42−ζ46−4ζ58−ζ62−4ζ74−ζ784ζ14+ζ26+ζ42+4ζ46+ζ58+4ζ62+ζ74+4ζ78−2−2−2−20000000000000000000000000
χ548-80−4242-2-2-2-222223-30000−5i5i−4ζ14−ζ26−ζ42−4ζ46−ζ58−4ζ62−ζ74−4ζ78ζ14+4ζ26+4ζ42+ζ46+4ζ58+ζ62+4ζ74+ζ7822224ζ14+ζ26+ζ42+4ζ46+ζ58+4ζ62+ζ74+4ζ78−ζ14−4ζ26−4ζ42−ζ46−4ζ58−ζ62−4ζ74−ζ78−2−2−2−20000000000000000000000000
χ558-80−4242−2+25−2−253−53+5−3+5−3−52−252+25-22000000222ζ14−2ζ26+2ζ46−2ζ74−2ζ14+2ζ26+ζ42−2ζ46+ζ58−ζ62+2ζ74−ζ78−ζ14+ζ26+2ζ42−ζ46+2ζ58−2ζ62+ζ74−2ζ78−2ζ42−2ζ58+2ζ62+2ζ78−2−2−2ζ14+2ζ26−2ζ46+2ζ742ζ14−2ζ26−ζ42+2ζ46−ζ58+ζ62−2ζ74+ζ78ζ14−ζ26−2ζ42+ζ46−2ζ58+2ζ62−ζ74+2ζ782ζ42+2ζ58−2ζ62−2ζ780000000000000000000000000
χ568-80−42423−53+5−2−25−2+252+252−25−3+5−3−5-2200000022−2ζ14+2ζ26+ζ42−2ζ46+ζ58−ζ62+2ζ74−ζ78−2ζ42−2ζ58+2ζ62+2ζ782ζ14−2ζ26+2ζ46−2ζ74−ζ14+ζ26+2ζ42−ζ46+2ζ58−2ζ62+ζ74−2ζ78−2−22ζ14−2ζ26−ζ42+2ζ46−ζ58+ζ62−2ζ74+ζ782ζ42+2ζ58−2ζ62−2ζ78−2ζ14+2ζ26−2ζ46+2ζ74ζ14−ζ26−2ζ42+ζ46−2ζ58+2ζ62−ζ74+2ζ780000000000000000000000000
χ578-80−42423+53−5−2+25−2−252−252+25−3−5−3+5-2200000022−ζ14+ζ26+2ζ42−ζ46+2ζ58−2ζ62+ζ74−2ζ782ζ14−2ζ26+2ζ46−2ζ74−2ζ42−2ζ58+2ζ62+2ζ78−2ζ14+2ζ26+ζ42−2ζ46+ζ58−ζ62+2ζ74−ζ78−2−2ζ14−ζ26−2ζ42+ζ46−2ζ58+2ζ62−ζ74+2ζ78−2ζ14+2ζ26−2ζ46+2ζ742ζ42+2ζ58−2ζ62−2ζ782ζ14−2ζ26−ζ42+2ζ46−ζ58+ζ62−2ζ74+ζ780000000000000000000000000
χ588-80−4242−2−25−2+253+53−5−3−5−3+52+252−25-2200000022−2ζ42−2ζ58+2ζ62+2ζ78−ζ14+ζ26+2ζ42−ζ46+2ζ58−2ζ62+ζ74−2ζ78−2ζ14+2ζ26+ζ42−2ζ46+ζ58−ζ62+2ζ74−ζ782ζ14−2ζ26+2ζ46−2ζ74−2−22ζ42+2ζ58−2ζ62−2ζ78ζ14−ζ26−2ζ42+ζ46−2ζ58+2ζ62−ζ74+2ζ782ζ14−2ζ26−ζ42+2ζ46−ζ58+ζ62−2ζ74+ζ78−2ζ14+2ζ26−2ζ46+2ζ740000000000000000000000000

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