Finite Group Databasebeta

← Group #12253412

Character table — Group #12253412

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1122222444444488888888888888888888888881010161616161616161616161616162020203232323232324040404040404040808080
order1225510102244410102222444101010101010101010101010202020202020224481010101020202020202022420202020404022444444448
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-11111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111-1-11111111111111111111111-1-1-111-1-1-1-11111111-1-1-1-1-1-11-111-1111-1-1-1
χ411111111111111111-1-111111111111111111111-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1111
χ5111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111111111-1-11111111-1-1-1-1111-1-1-1-11111-1-111-1-1-1-11
χ6111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1
χ7111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-111-1-1-1-1-1-1-1-11111111-1-11-1-1-1-11-1-111-1
χ8111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-11111-111-1-11
χ9111111111-1-1111-11-1111-11111-1-1-1-11111-1-1-1-111111-1-1-1-1111111-1-111111-1-1-1-1-111-11-11-11-1-1
χ10111111111-1-1111-11-1111-11111-1-1-1-11111-1-1-1-111-1-11-1-1-1-1111111-1-1-1-1-111-1-1-1-11-1-11-11-11-111
χ11111111111-1-1111-11-1-1-11-11111-1-1-1-11111-1-1-1-11111-111-1-1-1-1-1-111-1-1111-1-11111-1-11-1-1-11-1-111
χ12111111111-1-1111-11-1-1-11-11111-1-1-1-11111-1-1-1-111-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1111111-1111-111-1-1
χ13111111111-1-1111-1-1111-11-1-1-1-111111111-1-1-1-11111-11-1-1-11111-1-111111-1-111-1-1-11-111-1-11-11-1
χ14111111111-1-1111-1-1111-11-1-1-1-111111111-1-1-1-111-1-1-11-1-1-11111-1-111-1-1-1-1-111-1-11-11-1-111-11-11
χ15111111111-1-1111-1-11-1-1-11-1-1-1-111111111-1-1-1-111111-11-1-1-1-1-1-1-1-11111111-1-111-1-1-11-1-1-111-11
χ16111111111-1-1111-1-11-1-1-11-1-1-1-111111111-1-1-1-111-1-11-11-1-1-1-1-1-1-1-111-1-1-111-1-111111-1111-1-11-1
χ1722222222-200-222002000-20000222222-2-20000-2-22200000000000-2-22-2-20000000002000-2000
χ1822222222-200-222002000-20000222222-2-20000-2-2-2-200000000000-2-2-222000000000-20002000
χ1922222222-200-22200-200020000-2-2-2-222-2-20000-2-22200000000000222-2-2000000000-20002000
χ2022222222-200-22200-200020000-2-2-2-222-2-20000-2-2-2-20000000000022-2220000000002000-2000
χ212222222-2200-22202000-2022220000-2-2220000-2-222000000000-2-200-22-2000000002000-20000
χ222222222-2200-22202000-2022220000-2-2220000-2-2-2-2000000000-2-2002-2200000000-200020000
χ232222222-2200-2220-200020-2-2-2-20000-2-2220000-2-2220000000002200-22-200000000-200020000
χ242222222-2200-2220-200020-2-2-2-20000-2-2220000-2-2-2-200000000022002-22000000002000-20000
χ252222222-2-222222-200000000000000-2-2-2-222222222000-2-200000000-2-22000000-20000200000
χ262222222-2-222222-200000000000000-2-2-2-2222222-2-2000-2-20000000022-200000020000-200000
χ272222222-2-2-2-2222200000000000000-2-2-2-2-2-2-2-222220002200000000-2-2200000020000-200000
χ282222222-2-2-2-2222200000000000000-2-2-2-2-2-2-2-222-2-2000220000000022-2000000-20000200000
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+52−1−52222-2-222−1+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+52−1−521−521+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+52−1−522-2-222-2-21−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5200-2-22−1+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+52−1−522-2-2-2-2-2-21−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−520022-2−1+52−1−521−521+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+52−1−52-22-2222-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1−52002-2-21−521+52−1+52−1−52−1+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+52−1−52-22-2-2-22-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1−521−521−521+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+52−1−52-2-2222-221−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1−5200-22-21−521+52−1+52−1−52−1+52−1−521−521+52−1+52−1−520001−521+52−1+52−1−521−521+5200000000000
χ36222−1+52−1−52−1+52−1−5222-2-22−1+52−1−52-2-22-2-2-221−521−521+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+52222-2-222−1−52−1−52−1+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+521+521−521+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+522-2-222-2-21+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+5200-2-22−1−52−1+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+522-2-2-2-2-2-21+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+520022-2−1−52−1+521+521−521+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+52-22-2222-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1+52002-2-21+521−52−1−52−1+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+52-22-2-2-22-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+52−1−52−1+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+52-2-2222-221+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+5200-22-21+521−52−1−52−1+52−1−52−1+521+521−52−1−52−1+520001+521−52−1−52−1+521+521−5200000000000
χ44222−1−52−1+52−1−52−1+5222-2-22−1−52−1+52-2-22-2-2-221+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+5−1−5004000-40000−1+5−1+5−1−5−1−5−1+5−1−51−51+500001−51+500000000000001−51+500000000000000000000
χ46444−1+5−1−5−1+5−1−54-400-4−1+5−1−500-4000400001−51−51+51+5−1+5−1−51−51+500001−51+50000000000000−1+5−1−500000000000000000000
χ47444−1+5−1−5−1+5−1−5-4400-4−1+5−1−504000-40−1+5−1+5−1−5−1−500001−51+5−1+5−1−500001−51+5000000000001−51+50000000000000000000000
χ48444−1+5−1−5−1+5−1−5-4400-4−1+5−1−50-4000401−51−51+51+500001−51+5−1+5−1−500001−51+500000000000−1+5−1−50000000000000000000000
χ49444−1+5−1−5−1+5−1−5-4-4444−1+5−1−5-4000000000000001−51+51−51+5−1+5−1+5−1−5−1−5−1+5−1−5000001−51+50000000000000000000000000000
χ50444−1+5−1−5−1+5−1−5-4-4-4-44−1+5−1−54000000000000001−51+51−51+51−51−51+51+5−1+5−1−500000−1+5−1−50000000000000000000000000000
χ51444−1−5−1+5−1−5−1+54-400-4−1−5−1+5004000-40000−1−5−1−5−1+5−1+5−1−5−1+51+51−500001+51−500000000000001+51−500000000000000000000
χ52444−1−5−1+5−1−5−1+54-400-4−1−5−1+500-4000400001+51+51−51−5−1−5−1+51+51−500001+51−50000000000000−1−5−1+500000000000000000000
χ53444−1−5−1+5−1−5−1+5-4400-4−1−5−1+504000-40−1−5−1−5−1+5−1+500001+51−5−1−5−1+500001+51−5000000000001+51−50000000000000000000000
χ54444−1−5−1+5−1−5−1+5-4400-4−1−5−1+50-4000401+51+51−51−500001+51−5−1−5−1+500001+51−500000000000−1−5−1+50000000000000000000000
χ55444−1−5−1+5−1−5−1+5-4-4444−1−5−1+5-4000000000000001+51−51+51−5−1−5−1−5−1+5−1+5−1−5−1+5000001+51−50000000000000000000000000000
χ56444−1−5−1+5−1−5−1+5-4-4-4-44−1−5−1+54000000000000001+51−51+51−51+51+51−51−5−1−5−1+500000−1−5−1+50000000000000000000000000000
χ5744-4444400000-4-40002-2000000000000000000004-40000022-2-200000000000000200-2000000
χ5844-4444400000-4-40002-200000000000000000000-440000022-2-200000000000000-2002000000
χ5944-4444400000-4-4000-22000000000000000000004-400000-2-22200000000000000-2002000000
χ6044-4444400000-4-4000-2200000000000000000000-4400000-2-22200000000000000200-2000000
χ6188-8−2+25−2−25−2+25−2−25000002−252+250004-4000000000000000000000000000−1+5−1−51−51+5000000000000000000000000
χ6288-8−2+25−2−25−2+25−2−25000002−252+25000-440000000000000000000000000001−51+5−1+5−1−5000000000000000000000000
χ6388-8−2−25−2+25−2−25−2+25000002+252−250004-4000000000000000000000000000−1−5−1+51+51−5000000000000000000000000
χ6488-8−2−25−2+25−2−25−2+25000002+252−25000-440000000000000000000000000001+51−5−1−5−1+5000000000000000000000000
χ658-8088-8-8004-400000000000000000000004-44-40000000000000000000000000000000000000
χ668-8088-8-800-440000000000000000000000-44-440000000000000000000000000000000000000
χ678-80−2+25−2−252−252+25004-400000000002ζ−2ζ4−2ζ+2ζ42ζ2−2ζ3−2ζ2+2ζ32ζ−2ζ4−2ζ+2ζ42ζ2−2ζ3−2ζ2+2ζ30000−1+51−5−1−51+50000000000000000000000000000000000000
χ688-80−2+25−2−252−252+25004-40000000000−2ζ+2ζ42ζ−2ζ4−2ζ2+2ζ32ζ2−2ζ3−2ζ+2ζ42ζ−2ζ4−2ζ2+2ζ32ζ2−2ζ30000−1+51−5−1−51+50000000000000000000000000000000000000
χ698-80−2+25−2−252−252+2500-4400000000002ζ−2ζ4−2ζ+2ζ42ζ2−2ζ3−2ζ2+2ζ3−2ζ+2ζ42ζ−2ζ4−2ζ2+2ζ32ζ2−2ζ300001−5−1+51+5−1−50000000000000000000000000000000000000
χ708-80−2+25−2−252−252+2500-440000000000−2ζ+2ζ42ζ−2ζ4−2ζ2+2ζ32ζ2−2ζ32ζ−2ζ4−2ζ+2ζ42ζ2−2ζ3−2ζ2+2ζ300001−5−1+51+5−1−50000000000000000000000000000000000000
χ718-80−2−25−2+252+252−25004-400000000002ζ2−2ζ3−2ζ2+2ζ3−2ζ+2ζ42ζ−2ζ42ζ2−2ζ3−2ζ2+2ζ3−2ζ+2ζ42ζ−2ζ40000−1−51+5−1+51−50000000000000000000000000000000000000
χ728-80−2−25−2+252+252−25004-40000000000−2ζ2+2ζ32ζ2−2ζ32ζ−2ζ4−2ζ+2ζ4−2ζ2+2ζ32ζ2−2ζ32ζ−2ζ4−2ζ+2ζ40000−1−51+5−1+51−50000000000000000000000000000000000000
χ738-80−2−25−2+252+252−2500-4400000000002ζ2−2ζ3−2ζ2+2ζ3−2ζ+2ζ42ζ−2ζ4−2ζ2+2ζ32ζ2−2ζ32ζ−2ζ4−2ζ+2ζ400001+5−1−51−5−1+50000000000000000000000000000000000000
χ748-80−2−25−2+252+252−2500-440000000000−2ζ2+2ζ32ζ2−2ζ32ζ−2ζ4−2ζ+2ζ42ζ2−2ζ3−2ζ2+2ζ3−2ζ+2ζ42ζ−2ζ400001+5−1−51−5−1+50000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 5 (ζ5 = 1).