Finite Group Databasebeta

← Group #65093

Character table — Group #65093

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222222222222444444444444444455558888888810101010101020202020
order1222445588881010101010104444202020204040404040404040444420202020202020202288882244
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ4111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111
χ611111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1
χ711111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1
χ811111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111
χ91-11-11-111ii−i−i-1-1-1-111i−i1-111-1-1iiii−i−i−i−i11-1-1ii−i−i11-1-11-1ii−i−i1-1i−i
χ101-11-11-111ii−i−i-1-1-1-111i−i1-111-1-1iiii−i−i−i−i-1-111ii−i−i11-1-1-11−i−iii-11−ii
χ111-11-11-111ii−i−i-1-1-1-111−ii-1111-1-1iiii−i−i−i−i11-1-1−i−iii-1-1111-1ii−i−i-11−ii
χ121-11-11-111ii−i−i-1-1-1-111−ii-1111-1-1iiii−i−i−i−i-1-111−i−iii-1-111-11−i−iii1-1i−i
χ131-11-11-111−i−iii-1-1-1-111i−i-1111-1-1−i−i−i−iiiii11-1-1ii−i−i-1-1111-1−i−iii-11i−i
χ141-11-11-111−i−iii-1-1-1-111i−i-1111-1-1−i−i−i−iiiii-1-111ii−i−i-1-111-11ii−i−i1-1−ii
χ151-11-11-111−i−iii-1-1-1-111−ii1-111-1-1−i−i−i−iiiii11-1-1−i−iii11-1-11-1−i−iii1-1−ii
χ161-11-11-111−i−iii-1-1-1-111−ii1-111-1-1−i−i−i−iiiii-1-111−i−iii11-1-1-11ii−i−i-11i−i
χ17222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−520000000000
χ18222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200001−521+521−521+521−521+521−521+520000000000
χ19222222−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−5222-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+520000−1+52−1−52−1+52−1−521−521+521−521+520000000000
χ20222222−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52-2-222−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+5200001−521+521−521+52−1+52−1−52−1+52−1−520000000000
χ21222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+520000000000
χ22222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200001+521−521+521−521+521−521+521−520000000000
χ23222222−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+5222-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−520000−1−52−1+52−1−52−1+521+521−521+521−520000000000
χ24222222−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52-2-222−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−5200001+521−521+521−52−1−52−1+52−1−52−1+520000000000
χ252222-2-22200002222220000-2-2-2-200000000222200000000-2-200000000
χ262222-2-22200002222220000-2-2-2-200000000-2-2-2-2000000002200000000
χ2722-2-20022i2−i2i2−i2-2-222-2-200000000i2−i2i2−i2i2−i2i2−i22i−2i2i−2i00000000002−22−20000
χ2822-2-20022i2−i2i2−i2-2-222-2-200000000i2−i2i2−i2i2−i2i2−i2−2i2i−2i2i0000000000−22−220000
χ2922-2-20022−i2i2−i2i2-2-222-2-200000000−i2i2−i2i2−i2i2−i2i22i−2i2i−2i0000000000−22−220000
χ3022-2-20022−i2i2−i2i2-2-222-2-200000000−i2i2−i2i2−i2i2−i2i2−2i2i−2i2i00000000002−22−20000
χ312-22-22-2−1+52−1−522i2i−2i−2i1−521+521−521+52−1+52−1−522i−2i2-2−1+52−1−521−521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ140000−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ14−1+52−1−521−521+520000000000
χ322-22-22-2−1+52−1−522i2i−2i−2i1−521+521−521+52−1+52−1−52−2i2i-22−1+52−1−521−521+52−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ140000ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ141−521+52−1+52−1−520000000000
χ332-22-22-2−1+52−1−52−2i−2i2i2i1−521+521−521+52−1+52−1−522i−2i-22−1+52−1−521−521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ140000−ζ22−ζ38−ζ6−ζ14ζ22+ζ38ζ6+ζ141−521+52−1+52−1−520000000000
χ342-22-22-2−1+52−1−52−2i−2i2i2i1−521+521−521+52−1+52−1−52−2i2i2-2−1+52−1−521−521+52ζ22+ζ38ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38−ζ6−ζ14−ζ6−ζ140000ζ22+ζ38ζ6+ζ14−ζ22−ζ38−ζ6−ζ14−1+52−1−521−521+520000000000
χ352-22-22-2−1−52−1+522i2i−2i−2i1+521−521+521−52−1−52−1+522i−2i2-2−1−52−1+521+521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ380000−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ38−1−52−1+521+521−520000000000
χ362-22-22-2−1−52−1+522i2i−2i−2i1+521−521+521−52−1−52−1+52−2i2i-22−1−52−1+521+521−52−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ380000ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ381+521−52−1−52−1+520000000000
χ372-22-22-2−1−52−1+52−2i−2i2i2i1+521−521+521−52−1−52−1+522i−2i-22−1−52−1+521+521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ380000−ζ6−ζ14−ζ22−ζ38ζ6+ζ14ζ22+ζ381+521−52−1−52−1+520000000000
χ382-22-22-2−1−52−1+52−2i−2i2i2i1+521−521+521−52−1−52−1+52−2i2i2-2−1−52−1+521+521−52ζ6+ζ14ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14−ζ22−ζ38−ζ22−ζ380000ζ6+ζ14ζ22+ζ38−ζ6−ζ14−ζ22−ζ38−1−52−1+521+521−520000000000
χ392-22-2-22220000-2-2-2-2220000-2-2220000000022-2-200000000-2200000000
χ402-22-2-22220000-2-2-2-2220000-2-22200000000-2-222000000002-200000000
χ412-2-2200222−2−2222-2-2-2-2000000002−22−2−22−222i−2i−2i2i0000000000−i2i2i2−i20000
χ422-2-2200222−2−2222-2-2-2-2000000002−22−2−22−22−2i2i2i−2i0000000000i2−i2−i2i20000
χ432-2-220022−222−222-2-2-2-200000000−22−222−22−22i−2i−2i2i0000000000i2−i2−i2i20000
χ442-2-220022−222−222-2-2-2-200000000−22−222−22−2−2i2i2i−2i0000000000−i2i2i2−i20000
χ454444-4-4−1+5−1−50000−1+5−1−5−1+5−1−5−1+5−1−500001−51+51−51+5000000000000000000000000000000
χ464444-4-4−1−5−1+50000−1−5−1+5−1−5−1+5−1−5−1+500001+51−51+51−5000000000000000000000000000000
χ4744-4-400−1+5−1−52i2−2i22i2−2i21−51+5−1+5−1−51−51+500000000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ390000000000000000000000
χ4844-4-400−1+5−1−5−2i22i2−2i22i21−51+5−1+5−1−51−51+500000000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ390000000000000000000000
χ4944-4-400−1−5−1+52i2−2i22i2−2i21+51−5−1−5−1+51+51−500000000ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ370000000000000000000000
χ5044-4-400−1−5−1+5−2i22i2−2i22i21+51−5−1−5−1+51+51−500000000−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ370000000000000000000000
χ514-44-4-44−1+5−1−500001−51+51−51+5−1+5−1−500001−51+5−1+5−1−5000000000000000000000000000000
χ524-44-4-44−1−5−1+500001+51−51+51−5−1−5−1+500001+51−5−1−5−1+5000000000000000000000000000000
χ534-4-4400−1+5−1−522−22−2222−1+5−1−51−51+51−51+500000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ390000000000000000000000
χ544-4-4400−1+5−1−5−222222−22−1+5−1−51−51+51−51+500000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ390000000000000000000000
χ554-4-4400−1−5−1+522−22−2222−1−5−1+51+51−51+51−500000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ370000000000000000000000
χ564-4-4400−1−5−1+5−222222−22−1−5−1+51+51−51+51−500000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ370000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.