Finite Group Databasebeta

← Group #12253491

Character table — Group #12253491

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1122222444444488888888888888888888888881010161616161616161616161616162020203232323232324040404040404040808080
order1225510104444410102224444202020202020202020202020202020202020228881010101010102020202044440404040404024444444888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-11111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111-11-11111111111111111111111-1-1-11111-1-111-1-1111-1-1-1-1-1-1-1111-1111-1-1-1
χ41111111111111111-11-111111111111111111111-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1111
χ511111111111111-1-1111-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-111111111111-1-1-1-111-1-111-1-11-1-1
χ611111111111111-1-1111-1-11111-1-1-1-1-1-1-1-1111111-1-11-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-111-1-111-111
χ711111111111111-1-1-11-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-111-1-1111-1-11111-11-1-1-11-1-1-111
χ811111111111111-1-1-11-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-111111-1111-1111-1-1
χ91111111-1-1111111-11-111-1-1-1-1-11111-1-1-1-111111111-11-111-1-111-1-111111-1-111-1-11-11-11-11-1-11-1
χ101111111-1-1111111-11-111-1-1-1-1-11111-1-1-1-1111111-1-1-11-111-1-111-1-111-1-1-1-1-111-1-1-11-11-11-111-11
χ111111111-1-1111111-1-1-1-11-1-1-1-1-11111-1-1-1-1111111111-1111-1-1-1-1-1-1-1-111111-1-111-1-11-1-1-11-11-11
χ121111111-1-1111111-1-1-1-11-1-1-1-1-11111-1-1-1-1111111-1-11-1111-1-1-1-1-1-1-1-1-1-1-111-1-11111-1111-11-11-1
χ131111111-1-111111-111-11-11-1-1-1-1-1-1-1-1111111111111-1-11-1-11111-1-111111-1-1-1-1111-1-111-1-11-1-11
χ141111111-1-111111-111-11-11-1-1-1-1-1-1-1-11111111111-1-1-1-11-1-11111-1-111-1-1-1-1-1-1-111-111-1-111-111-1
χ151111111-1-111111-11-1-1-1-11-1-1-1-1-1-1-1-111111111111111-1-1-111-1-1-1-1-1-11111111-1-1-1-1-11-1-1-1111-1
χ161111111-1-111111-11-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-111-1-1-1-1-1-1-1-1-11111-1-1111-1111-1-1-11
χ172222222002-2-222020000-200000000-2-2-2-222-2-2-2-22200000220000002-2-20000000002000-2000
χ182222222002-2-222020000-200000000-2-2-2-222-2-2-2-2-2-20000022000000-222000000000-20002000
χ192222222002-2-2220-20000200000000222222-2-2-2-22200000-2-20000002-2-2000000000-20002000
χ202222222002-2-2220-20000200000000222222-2-2-2-2-2-200000-2-2000000-2220000000002000-2000
χ21222222200-22-22220000-200000-2-2-2-20000-2-222-2-2220002200000000-22-2000000002000-20000
χ22222222200-22-22220000-200000-2-2-2-20000-2-222-2-2-2-200022000000002-2200000000-200020000
χ23222222200-22-222-2000020000022220000-2-222-2-222000-2-200000000-22-200000000-200020000
χ24222222200-22-222-2000020000022220000-2-222-2-2-2-2000-2-2000000002-22000000002000-20000
χ25222222222-2-2222000-2000222200000000-2-2-2-22222000000000-2-200-2-220000000-2000200000
χ26222222222-2-2222000-2000222200000000-2-2-2-222-2-2000000000-2-20022-200000002000-200000
χ272222222-2-2-2-22220002000-2-2-2-200000000-2-2-2-222220000000002200-2-2200000002000-200000
χ282222222-2-2-2-22220002000-2-2-2-200000000-2-2-2-222-2-2000000000220022-20000000-2000200000
χ29222−1+52−1−52−1+52−1−5222222−1+52−1−522222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−5200222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000−1+52−1−52−1+52−1−52−1+52−1−5200000000000
χ30222−1+52−1−52−1+52−1−5222222−1+52−1−5222-22-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−5200-2-2-2−1+52−1−52−1+52−1−521−521+52−1+52−1−521−521+520001−521+521−521+521−521+5200000000000
χ31222−1+52−1−52−1+52−1−5222222−1+52−1−52-2-2222-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1−52002-2-21−521+521−521+52−1+52−1−52−1+52−1−52−1+52−1−52000−1+52−1−521−521+521−521+5200000000000
χ32222−1+52−1−52−1+52−1−5222222−1+52−1−52-2-2-22-2-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1−5200-2221−521+521−521+521−521+52−1+52−1−521−521+520001−521+52−1+52−1−52−1+52−1−5200000000000
χ33222−1+52−1−52−1+52−1−52-2-2222−1+52−1−522-22-222-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1−5200-22-2−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1−520001−521+52−1+52−1−521−521+5200000000000
χ34222−1+52−1−52−1+52−1−52-2-2222−1+52−1−522-2-2-2-22-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1−52002-22−1+52−1−521−521+521−521+521−521+521−521+52000−1+52−1−521−521+52−1+52−1−5200000000000
χ35222−1+52−1−52−1+52−1−52-2-2222−1+52−1−52-222-22-221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−5200-2-221−521+52−1+52−1−52−1+52−1−521−521+52−1+52−1−520001−521+521−521+52−1+52−1−5200000000000
χ36222−1+52−1−52−1+52−1−52-2-2222−1+52−1−52-22-2-2-2-221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52−1+52−1−520022-21−521+52−1+52−1−521−521+521−521+521−521+52000−1+52−1−52−1+52−1−521−521+5200000000000
χ37222−1−52−1+52−1−52−1+5222222−1−52−1+522222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+5200222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52000−1−52−1+52−1−52−1+52−1−52−1+5200000000000
χ38222−1−52−1+52−1−52−1+5222222−1−52−1+5222-22-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+5200-2-2-2−1−52−1+52−1−52−1+521+521−52−1−52−1+521+521−520001+521−521+521−521+521−5200000000000
χ39222−1−52−1+52−1−52−1+5222222−1−52−1+52-2-2222-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1+52002-2-21+521−521+521−52−1−52−1+52−1−52−1+52−1−52−1+52000−1−52−1+521+521−521+521−5200000000000
χ40222−1−52−1+52−1−52−1+5222222−1−52−1+52-2-2-22-2-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1+5200-2221+521−521+521−521+521−52−1−52−1+521+521−520001+521−52−1−52−1+52−1−52−1+5200000000000
χ41222−1−52−1+52−1−52−1+52-2-2222−1−52−1+522-22-222-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1+5200-22-2−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1+520001+521−52−1−52−1+521+521−5200000000000
χ42222−1−52−1+52−1−52−1+52-2-2222−1−52−1+522-2-2-2-22-21+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1+52002-22−1−52−1+521+521−521+521−521+521−521+521−52000−1−52−1+521+521−52−1−52−1+5200000000000
χ43222−1−52−1+52−1−52−1+52-2-2222−1−52−1+52-222-22-221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+5200-2-221+521−52−1−52−1+52−1−52−1+521+521−52−1−52−1+520001+521−521+521−52−1−52−1+5200000000000
χ44222−1−52−1+52−1−52−1+52-2-2222−1−52−1+52-22-2-2-2-221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52−1−52−1+520022-21+521−52−1−52−1+521+521−521+521−521+521−52000−1−52−1+52−1−52−1+521+521−5200000000000
χ45444−1+5−1−5−1+5−1−5004-4-4−1+5−1−5040000-4000000001−51−51+51+5−1+5−1−51−51+51−51+50000000−1+5−1−500000000000000000000000000
χ46444−1+5−1−5−1+5−1−5004-4-4−1+5−1−50-40000400000000−1+5−1+5−1−5−1−5−1+5−1−51−51+51−51+500000001−51+500000000000000000000000000
χ47444−1+5−1−5−1+5−1−500-44-4−1+5−1−540000-4000001−51−51+51+500001−51+5−1+5−1−51−51+500000−1+5−1−50000000000000000000000000000
χ48444−1+5−1−5−1+5−1−500-44-4−1+5−1−5-40000400000−1+5−1+5−1−5−1−500001−51+5−1+5−1−51−51+5000001−51+50000000000000000000000000000
χ49444−1+5−1−5−1+5−1−544-4-44−1+5−1−5000-4000−1+5−1+5−1−5−1−5000000001−51+51−51+5−1+5−1−5000000000001−51+50000000000000000000000
χ50444−1+5−1−5−1+5−1−5-4-4-4-44−1+5−1−500040001−51−51+51+5000000001−51+51−51+5−1+5−1−500000000000−1+5−1−50000000000000000000000
χ51444−1−5−1+5−1−5−1+5004-4-4−1−5−1+5040000-4000000001+51+51−51−5−1−5−1+51+51−51+51−50000000−1−5−1+500000000000000000000000000
χ52444−1−5−1+5−1−5−1+5004-4-4−1−5−1+50-40000400000000−1−5−1−5−1+5−1+5−1−5−1+51+51−51+51−500000001+51−500000000000000000000000000
χ53444−1−5−1+5−1−5−1+500-44-4−1−5−1+540000-4000001+51+51−51−500001+51−5−1−5−1+51+51−500000−1−5−1+50000000000000000000000000000
χ54444−1−5−1+5−1−5−1+500-44-4−1−5−1+5-40000400000−1−5−1−5−1+5−1+500001+51−5−1−5−1+51+51−5000001+51−50000000000000000000000000000
χ55444−1−5−1+5−1−5−1+544-4-44−1−5−1+5000-4000−1−5−1−5−1+5−1+5000000001+51−51+51−5−1−5−1+5000000000001+51−50000000000000000000000
χ56444−1−5−1+5−1−5−1+5-4-4-4-44−1−5−1+500040001+51+51−51−5000000001+51−51+51−5−1−5−1+500000000000−1−5−1+50000000000000000000000
χ5744-4444400000-4-40020-2000000000000000000004-400000002200-2-20000000002000-2000000
χ5844-4444400000-4-40020-200000000000000000000-4400000002200-2-2000000000-20002000000
χ5944-4444400000-4-400-202000000000000000000004-40000000-2-20022000000000-20002000000
χ6044-4444400000-4-400-20200000000000000000000-440000000-2-200220000000002000-2000000
χ6188-8−2+25−2−25−2+25−2−25000002−252+250040-400000000000000000000000000000−1+5−1−5001−51+500000000000000000000
χ6288-8−2+25−2−25−2+25−2−25000002−252+2500-404000000000000000000000000000001−51+500−1+5−1−500000000000000000000
χ6388-8−2−25−2+25−2−25−2+25000002+252−250040-400000000000000000000000000000−1−5−1+5001+51−500000000000000000000
χ6488-8−2−25−2+25−2−25−2+25000002+252−2500-404000000000000000000000000000001+51−500−1−5−1+500000000000000000000
χ658-8088-8-84-40000000000004-44-40000000000000000000000000000000000000000000000000
χ668-8088-8-8-44000000000000-44-440000000000000000000000000000000000000000000000000
χ678-80−2+25−2−252−252+254-4000000000000−1+51−5−1−51+5−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ700000000000000000000000000000000000000000
χ688-80−2+25−2−252−252+254-4000000000000−1+51−5−1−51+52ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ700000000000000000000000000000000000000000
χ698-80−2+25−2−252−252+25-440000000000001−5−1+51+5−1−5−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ700000000000000000000000000000000000000000
χ708-80−2+25−2−252−252+25-440000000000001−5−1+51+5−1−52ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ700000000000000000000000000000000000000000
χ718-80−2−25−2+252+252−254-4000000000000−1−51+5−1+51−52ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ1900000000000000000000000000000000000000000
χ728-80−2−25−2+252+252−254-4000000000000−1−51+5−1+51−5−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ1900000000000000000000000000000000000000000
χ738-80−2−25−2+252+252−25-440000000000001+5−1−51−5−1+52ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ1900000000000000000000000000000000000000000
χ748-80−2−25−2+252+252−25-440000000000001+5−1−51−5−1+5−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ1900000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1).