Finite Group Databasebeta

← Group #12253420

Character table — Group #12253420

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1122222444444488888888888888888888888881010161616161616161616161616162020203232323232324040404040404040808080
order1225510102244410102244444101010101010101020202020202020202020224481010202020202020202022420202020404022444444448
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-11111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111-111-11111111111111111111111-1-1-1-1-111-1-11111111-1-1-1-1-1-11-111-1111-1-1-1
χ4111111111111111-111-111111111111111111111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1111
χ511111111111111-111-11-1-1-1-1-1-11111-1-1-1-111111111-1-11111111-1-1-1-1111-1-1-1-111-111-111-1-1-1-11
χ611111111111111-111-11-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-11111-1
χ711111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-111-1-1-1-1-1-11111111-1-1-1-11-1-11-1-111-1
χ811111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-111-1-1-1-1-1-1-1-1-11111-1-111-111-111-1-11
χ9111111111-1-111111-1-111-111111111-1-1-1-1-1-1-1-111111-1-111-1-11111-1-111111-1-1-1-1-11-111-11-11-1-1
χ10111111111-1-111111-1-111-111111111-1-1-1-1-1-1-1-111-1-11-1-111-1-11111-1-1-1-1-111-1-1-1-11-11-1-11-11-111
χ11111111111-1-11111-1-1-1-11-111111111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-111-1-1111-1-11111-1-1-11-1-11-1-111
χ12111111111-1-11111-1-1-1-11-111111111-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-11111111-111-111-1-1
χ13111111111-1-1111-11-111-11-1-1-1-111111111-1-1-1-11111-11-111-1-111-1-111111-1-111-1-111-1-11-1-11-11-1
χ14111111111-1-1111-11-111-11-1-1-1-111111111-1-1-1-111-1-1-11-111-1-111-1-111-1-1-1-1-111-1-1-1-111-111-11-11
χ15111111111-1-1111-1-1-11-1-11-1-1-1-111111111-1-1-1-111111-11-1-1-1-1-1-1-1-11111111-1-1111-1-1-1-1-1-111-11
χ16111111111-1-1111-1-1-11-1-11-1-1-1-111111111-1-1-1-111-1-11-11-1-1-1-1-1-1-1-111-1-1-111-1-111-1111111-1-11-1
χ1722222222-200-222000200-2000022-2-222220000-2-22200000000000-2-22-2-20000002000000-2000
χ1822222222-200-222000200-2000022-2-222220000-2-2-2-200000000000-2-2-222000000-20000002000
χ1922222222-200-222000-2002000022-2-2-2-2-2-20000-2-22200000000000222-2-2000000-20000002000
χ2022222222-200-222000-2002000022-2-2-2-2-2-20000-2-2-2-20000000000022-2220000002000000-2000
χ212222222-2200-22220000-202222-2-22200000000-2-222000000000-2-200-22-2000000000200-20000
χ222222222-2200-22220000-202222-2-22200000000-2-2-2-2000000000-2-2002-22000000000-20020000
χ232222222-2200-222-2000020-2-2-2-2-2-22200000000-2-2220000000002200-22-2000000000-20020000
χ242222222-2200-222-2000020-2-2-2-2-2-22200000000-2-2-2-200000000022002-22000000000200-20000
χ252222222-2-22222200-200000000-2-2-2-200002222222200000-2-2000000-2-2200000000-200200000
χ262222222-2-22222200-200000000-2-2-2-20000222222-2-200000-2-200000022-200000000200-200000
χ272222222-2-2-2-222200200000000-2-2-2-20000-2-2-2-222220000022000000-2-2200000000200-200000
χ282222222-2-2-2-222200200000000-2-2-2-20000-2-2-2-222-2-2000002200000022-200000000-200200000
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+52−1−522-222-222−1+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+52−1−5200-2-2-21−521+52−1+52−1−521−521+52−1+52−1−52−1+52−1−520001−521+521−521+521−521+5200000000000
χ31222−1+52−1−52−1+52−1−5222222−1+52−1−52-222-22-2-21−521−521+521+52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−5200-2-22−1+52−1−52−1+52−1−52−1+52−1−521−521+521−521+520001−521+521−521+52−1+52−1−5200000000000
χ32222−1+52−1−52−1+52−1−5222222−1+52−1−52-2-22-2-2-2-21−521−521+521+52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−520022-21−521+52−1+52−1−521−521+521−521+521−521+52000−1+52−1−52−1+52−1−521−521+5200000000000
χ33222−1+52−1−52−1+52−1−5222-2-22−1+52−1−5222-2-222-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−52002-2-2−1+52−1−521−521+52−1+52−1−52−1+52−1−521−521+52000−1+52−1−521−521+521−521+5200000000000
χ34222−1+52−1−52−1+52−1−5222-2-22−1+52−1−522-2-2-2-22-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+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
χ35222−1+52−1−52−1+52−1−5222-2-22−1+52−1−52-22-222-221−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+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
χ36222−1+52−1−52−1+52−1−5222-2-22−1+52−1−52-2-2-22-2-221−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52002-221−521+521−521+521−521+521−521+52−1+52−1−52000−1+52−1−521−521+52−1+52−1−5200000000000
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+522-222-222−1−52−1−52−1+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+5200-2-2-21+521−52−1−52−1+521+521−52−1−52−1+52−1−52−1+520001+521−521+521−521+521−5200000000000
χ39222−1−52−1+52−1−52−1+5222222−1−52−1+52-222-22-2-21+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+5200-2-22−1−52−1+52−1−52−1+52−1−52−1+521+521−521+521−520001+521−521+521−52−1−52−1+5200000000000
χ40222−1−52−1+52−1−52−1+5222222−1−52−1+52-2-22-2-2-2-21+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+520022-21+521−52−1−52−1+521+521−521+521−521+521−52000−1−52−1+52−1−52−1+521+521−5200000000000
χ41222−1−52−1+52−1−52−1+5222-2-22−1−52−1+5222-2-222-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+52002-2-2−1−52−1+521+521−52−1−52−1+52−1−52−1+521+521−52000−1−52−1+521+521−521+521−5200000000000
χ42222−1−52−1+52−1−52−1+5222-2-22−1−52−1+522-2-2-2-22-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+5200-2221+521−521+521−521+521−52−1−52−1+521+521−520001+521−52−1−52−1+52−1−52−1+5200000000000
χ43222−1−52−1+52−1−52−1+5222-2-22−1−52−1+52-22-222-221+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+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
χ44222−1−52−1+52−1−52−1+5222-2-22−1−52−1+52-2-2-22-2-221+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+52002-221+521−521+521−521+521−521+521−52−1−52−1+52000−1−52−1+521+521−52−1−52−1+5200000000000
χ45444−1+5−1−5−1+5−1−54-400-4−1+5−1−5000400-40000−1+5−1−51−51+5−1+5−1+5−1−5−1−500001−51+500000000000001−51+500000000000000000000
χ46444−1+5−1−5−1+5−1−54-400-4−1+5−1−5000-40040000−1+5−1−51−51+51−51−51+51+500001−51+50000000000000−1+5−1−500000000000000000000
χ47444−1+5−1−5−1+5−1−5-4400-4−1+5−1−540000-40−1+5−1+5−1−5−1−51−51+5−1+5−1−5000000001−51+5000000000001−51+50000000000000000000000
χ48444−1+5−1−5−1+5−1−5-4400-4−1+5−1−5-40000401−51−51+51+51−51+5−1+5−1−5000000001−51+500000000000−1+5−1−50000000000000000000000
χ49444−1+5−1−5−1+5−1−5-4-4444−1+5−1−500-4000000001−51+51−51+50000−1+5−1+5−1−5−1−5−1+5−1−500000001−51+500000000000000000000000000
χ50444−1+5−1−5−1+5−1−5-4-4-4-44−1+5−1−5004000000001−51+51−51+500001−51−51+51+5−1+5−1−50000000−1+5−1−500000000000000000000000000
χ51444−1−5−1+5−1−5−1+54-400-4−1−5−1+5000400-40000−1−5−1+51+51−5−1−5−1−5−1+5−1+500001+51−500000000000001+51−500000000000000000000
χ52444−1−5−1+5−1−5−1+54-400-4−1−5−1+5000-40040000−1−5−1+51+51−51+51+51−51−500001+51−50000000000000−1−5−1+500000000000000000000
χ53444−1−5−1+5−1−5−1+5-4400-4−1−5−1+540000-40−1−5−1−5−1+5−1+51+51−5−1−5−1+5000000001+51−5000000000001+51−50000000000000000000000
χ54444−1−5−1+5−1−5−1+5-4400-4−1−5−1+5-40000401+51+51−51−51+51−5−1−5−1+5000000001+51−500000000000−1−5−1+50000000000000000000000
χ55444−1−5−1+5−1−5−1+5-4-4444−1−5−1+500-4000000001+51−51+51−50000−1−5−1−5−1+5−1+5−1−5−1+500000001+51−500000000000000000000000000
χ56444−1−5−1+5−1−5−1+5-4-4-4-44−1−5−1+5004000000001+51−51+51−500001+51+51−51−5−1−5−1+50000000−1−5−1+500000000000000000000000000
χ5744-4444400000-4-40200-2000000000000000000004-40002200-2-200000000000000200-2000000
χ5844-4444400000-4-40200-200000000000000000000-440002200-2-200000000000000-2002000000
χ5944-4444400000-4-40-2002000000000000000000004-4000-2-2002200000000000000-2002000000
χ6044-4444400000-4-40-200200000000000000000000-44000-2-2002200000000000000200-2000000
χ6188-8−2+25−2−25−2+25−2−25000002−252+250400-40000000000000000000000000−1+5−1−5001−51+5000000000000000000000000
χ6288-8−2+25−2−25−2+25−2−25000002−252+250-400400000000000000000000000001−51+500−1+5−1−5000000000000000000000000
χ6388-8−2−25−2+25−2−25−2+25000002+252−250400-40000000000000000000000000−1−5−1+5001+51−5000000000000000000000000
χ6488-8−2−25−2+25−2−25−2+25000002+252−250-400400000000000000000000000001+51−500−1−5−1+5000000000000000000000000
χ658-8088-8-8004i−4i00000000000000000000004i−4i4i−4i0000000000000000000000000000000000000
χ668-8088-8-800−4i4i0000000000000000000000−4i4i−4i4i0000000000000000000000000000000000000
χ678-80−2+25−2−252−252+25004i−4i00000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ180000−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ70000000000000000000000000000000000000
χ688-80−2+25−2−252−252+25004i−4i0000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ1800002ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ70000000000000000000000000000000000000
χ698-80−2+25−2−252−252+2500−4i4i00000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ1800002ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ70000000000000000000000000000000000000
χ708-80−2+25−2−252−252+2500−4i4i0000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ180000−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ70000000000000000000000000000000000000
χ718-80−2−25−2+252+252−25004i−4i0000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ140000−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ190000000000000000000000000000000000000
χ728-80−2−25−2+252+252−25004i−4i00000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ1400002ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ190000000000000000000000000000000000000
χ738-80−2−25−2+252+252−2500−4i4i0000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ1400002ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ190000000000000000000000000000000000000
χ748-80−2−25−2+252+252−2500−4i4i00000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ140000−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ190000000000000000000000000000000000000

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