Finite Group Databasebeta

← Group #12253483

Character table — Group #12253483

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1122222444444488888888888888888888888881010161616161616161616161616162020203232323232324040404040404040808080
order1225510104444410102224444202020202020202020202020202020202020228881010101010102020202044440404040404022244444888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-11111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111-11-11111111111111111111111-1-1-11111-1-111-1-1111-1-1-1-1-1-111-11-1111-1-1-1
χ41111111111111111-11-111111111111111111111-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1111
χ5111111111111111-11-11-1-11111-1-1-1-1-1-1-1-1111111111-1-111-1-111-1-11111111-1-1-1-11-11-111-1-11-1-1
χ6111111111111111-11-11-1-11111-1-1-1-1-1-1-1-1111111-1-11-1-111-1-111-1-111-1-1-111-1-1-1-1-11-11-1-111-111
χ7111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-1-1-1-1111-1-111111-1-1-1-11-1-1-111
χ8111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-11111-1111-1-1
χ91111111-1-111111-111-111-1-1-1-1-11111-1-1-1-111111111-11-1-1-11111-1-111111-1-111-1-1-1-1111-11-1-11-1
χ101111111-1-111111-111-111-1-1-1-1-11111-1-1-1-1111111-1-1-11-1-1-11111-1-111-1-1-1-1-111-1-111-1-1-11-111-11
χ111111111-1-111111-11-1-1-11-1-1-1-1-11111-1-1-1-1111111111-11-1-111-1-1-1-1-1-111111-1-111-1-1-11-1-11-11-11
χ121111111-1-111111-11-1-1-11-1-1-1-1-11111-1-1-1-1111111-1-11-11-1-111-1-1-1-1-1-1-1-1-111-1-111111-111-11-11-1
χ131111111-1-111111-1-1111-11-1-1-1-1-1-1-1-1111111111111-1-11-1-1-1-1111111111-1-1-1-111-111-11-1-11-1-11
χ141111111-1-111111-1-1111-11-1-1-1-1-1-1-1-11111111111-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1111-1-11-111-111-1
χ151111111-1-111111-1-1-11-1-11-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-111-1-11111111-1-1-11-1-1-1-1-1111-1
χ161111111-1-111111-1-1-11-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-111-1-1-1-1-11111-1-11-111111-1-1-11
χ172222222002-2-222000200-200000000-2-2-2-222-2-2-2-22200000000022002-2-20000000200000-2000
χ182222222002-2-222000200-200000000-2-2-2-222-2-2-2-2-2-20000000002200-2220000000-2000002000
χ192222222002-2-222000-200200000000222222-2-2-2-222000000000-2-2002-2-20000000-2000002000
χ202222222002-2-222000-200200000000222222-2-2-2-2-2-2000000000-2-200-2220000000200000-2000
χ21222222200-22-22202000-200000-2-2-2-20000-2-222-2-2220000022000000-22-2000000000200-20000
χ22222222200-22-22202000-200000-2-2-2-20000-2-222-2-2-2-200000220000002-22000000000-20020000
χ23222222200-22-2220-200020000022220000-2-222-2-22200000-2-2000000-22-2000000000-20020000
χ24222222200-22-2220-200020000022220000-2-222-2-2-2-200000-2-20000002-22000000000200-20000
χ25222222222-2-2222-2000000222200000000-2-2-2-22222000-2-200000000-2-22000000-20000200000
χ26222222222-2-2222-2000000222200000000-2-2-2-222-2-2000-2-20000000022-200000020000-200000
χ272222222-2-2-2-22222000000-2-2-2-200000000-2-2-2-222220002200000000-2-2200000020000-200000
χ282222222-2-2-2-22222000000-2-2-2-200000000-2-2-2-222-2-2000220000000022-2000000-20000200000
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+52−1−522-22-22-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1−52002-2-2−1+52−1−521−521+52−1+52−1−521−521+52−1+52−1−52000−1+52−1−521−521+521−521+5200000000000
χ32222−1+52−1−52−1+52−1−5222222−1+52−1−522-2-2-2-2-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1−5200-222−1+52−1−521−521+521−521+521−521+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+52−1−52-222-222-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1−5200-22-21−521+52−1+52−1−52−1+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+52−1−52-22-2-2-22-21−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1−52002-221−521+52−1+52−1−521−521+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+52−1−52-2-2222-221−521−521+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+521−521+52−1+52−1−52−1+52−1−52−1+52−1−520001−521+521−521+52−1+52−1−5200000000000
χ36222−1+52−1−52−1+52−1−52-2-2222−1+52−1−52-2-2-22-2-221−521−521+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+521−521+521−521+52−1+52−1−521−521+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+522-22-22-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1+52002-2-2−1−52−1+521+521−52−1−52−1+521+521−52−1−52−1+52000−1−52−1+521+521−521+521−5200000000000
χ40222−1−52−1+52−1−52−1+5222222−1−52−1+522-2-2-2-2-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1+5200-222−1−52−1+521+521−521+521−521+521−521+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+52-222-222-21+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+5200-22-21+521−52−1−52−1+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+52-22-2-2-22-21+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+52002-221+521−52−1−52−1+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+52-2-2222-221+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+521−521+521−52−1−52−1+52−1−52−1+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+52-2-2-22-2-221+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+521−521+521−521+521−52−1−52−1+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+5−1−5000400-4000000001−51−51+51+5−1+5−1−51−51+51−51+500000000000−1+5−1−50000000000000000000000
χ46444−1+5−1−5−1+5−1−5004-4-4−1+5−1−5000-400400000000−1+5−1+5−1−5−1−5−1+5−1−51−51+51−51+5000000000001−51+50000000000000000000000
χ47444−1+5−1−5−1+5−1−500-44-4−1+5−1−504000-4000001−51−51+51+500001−51+5−1+5−1−51−51+50000000−1+5−1−500000000000000000000000000
χ48444−1+5−1−5−1+5−1−500-44-4−1+5−1−50-4000400000−1+5−1+5−1−5−1−500001−51+5−1+5−1−51−51+500000001−51+500000000000000000000000000
χ49444−1+5−1−5−1+5−1−544-4-44−1+5−1−5-4000000−1+5−1+5−1−5−1−5000000001−51+51−51+5−1+5−1−5000001−51+50000000000000000000000000000
χ50444−1+5−1−5−1+5−1−5-4-4-4-44−1+5−1−540000001−51−51+51+5000000001−51+51−51+5−1+5−1−500000−1+5−1−50000000000000000000000000000
χ51444−1−5−1+5−1−5−1+5004-4-4−1−5−1+5000400-4000000001+51+51−51−5−1−5−1+51+51−51+51−500000000000−1−5−1+50000000000000000000000
χ52444−1−5−1+5−1−5−1+5004-4-4−1−5−1+5000-400400000000−1−5−1−5−1+5−1+5−1−5−1+51+51−51+51−5000000000001+51−50000000000000000000000
χ53444−1−5−1+5−1−5−1+500-44-4−1−5−1+504000-4000001+51+51−51−500001+51−5−1−5−1+51+51−50000000−1−5−1+500000000000000000000000000
χ54444−1−5−1+5−1−5−1+500-44-4−1−5−1+50-4000400000−1−5−1−5−1+5−1+500001+51−5−1−5−1+51+51−500000001+51−500000000000000000000000000
χ55444−1−5−1+5−1−5−1+544-4-44−1−5−1+5-4000000−1−5−1−5−1+5−1+5000000001+51−51+51−5−1−5−1+5000001+51−50000000000000000000000000000
χ56444−1−5−1+5−1−5−1+5-4-4-4-44−1−5−1+540000001+51+51−51−5000000001+51−51+51−5−1−5−1+500000−1−5−1+50000000000000000000000000000
χ5744-4444400000-4-40020-2000000000000000000004-400000002200-2-20000000000020-2000000
χ5844-4444400000-4-40020-200000000000000000000-4400000002200-2-200000000000-202000000
χ5944-4444400000-4-400-202000000000000000000004-40000000-2-2002200000000000-202000000
χ6044-4444400000-4-400-20200000000000000000000-440000000-2-200220000000000020-2000000
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
χ658-8088-8-84i−4i0000000000004i−4i4i−4i0000000000000000000000000000000000000000000000000
χ668-8088-8-8−4i4i000000000000−4i4i−4i4i0000000000000000000000000000000000000000000000000
χ678-80−2+25−2−252−252+254i−4i000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ1800000000000000000000000000000000000000000
χ688-80−2+25−2−252−252+254i−4i000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ1800000000000000000000000000000000000000000
χ698-80−2+25−2−252−252+25−4i4i0000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ1800000000000000000000000000000000000000000
χ708-80−2+25−2−252−252+25−4i4i0000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ1800000000000000000000000000000000000000000
χ718-80−2−25−2+252+252−254i−4i000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000000000000
χ728-80−2−25−2+252+252−254i−4i000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000000000000
χ738-80−2−25−2+252+252−25−4i4i0000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000000000000
χ748-80−2−25−2+252+252−25−4i4i0000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.