Finite Group Databasebeta

← Group #12077752

Character table — Group #12077752

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size111122222222222244444444488888888888888888888888888888810101616161616161616161616161616161616202020323240404040404040404040404080
order1222444455101010101010420202020202020204444448888882020202020202020202040404040404040404442020202020202020404040404040404024420202444448888884
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-111111111111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-111111111-1-1-1-1-1-1-1-1111-1-1111111-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ5111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-11111-1-1-1-111111111111-1-1-111-1-1-11111-1-1-1
χ6111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-11-1-1111-1-1-1-1111
χ7111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-1-1-1-1111
χ8111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111111-1-1-1
χ91111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-111-1-11111-1-1-1-1111111-1-1-11-111-1-1-1-11
χ101111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-111-1111-11-1-11111-1
χ111111111111111111111111111-1-111-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-111-1-1-1-1-1-11111111-1-11-1-1-11-1-1-11111-1
χ121111111111111111111111111-1-111-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111-1111-1-1-1-11
χ131111111111111111111111111-1-1-1-11111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-1-11-1111-1-111-1
χ141111111111111111111111111-1-1-1-11111-1-111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111-11-1-1-111-1-11
χ151111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1111111111-1-1-11-11-1-111-1-11
χ161111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-111111-11-111-1-111-1
χ1722222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52222222222222−1+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+52−1−52−1−52−1−52−1−52002−1+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+52−1−52−1−52000−1+52−1−520000000000000
χ1822222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52222222-2-2-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+5200-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+520001−521+520000000000000
χ1922222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-2-2-22222-2-21−521−521+521+521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+5200-2−1+52−1+52−1−52−1−521−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520001−521+520000000000000
χ2022222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-2-2-2-2-2-2-2221−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52002−1+52−1+52−1−52−1−521−521+521−521+521−521−521+521+521−521−521+521+52000−1+52−1−520000000000000
χ2122222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-222-2-222-2-2-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+520021−521−521+521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+52000−1+52−1−520000000000000
χ2222222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-222-2-2-2-22222−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-21−521−521+521+52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−520001−521+520000000000000
χ2322222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-22222-2-2221−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-21−521−521+521+521−521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+520001−521+520000000000000
χ2422222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-222-2-222-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+520021−521−521+521+521−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000−1+52−1−520000000000000
χ2522222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52222222222222−1−52−1−52−1+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+52002−1−52−1−52−1+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+52000−1−52−1+520000000000000
χ2622222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52222222-2-2-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−5200-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−520001+521−520000000000000
χ2722222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-2-2-22222-2-21+521+521−521−521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−5200-2−1−52−1−52−1+52−1+521+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520001+521−520000000000000
χ2822222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-2-2-2-2-2-2-2221+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+52002−1−52−1−52−1+52−1+521+521−521+521−521+521+521−521−521+521+521−521−52000−1−52−1+520000000000000
χ2922222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-222-2-222-2-2-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−520021+521+521−521−52−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−52000−1−52−1+520000000000000
χ3022222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-222-2-2-2-22222−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-21+521+521−521−52−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+520001+521−520000000000000
χ3122222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-22222-2-2221+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-21+521+521−521−521+521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−520001+521−520000000000000
χ3222222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-222-2-222-2-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−520021+521+521−521−521+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52000−1−52−1+520000000000000
χ3322222-2-2222222222-22-22-22-22-200002-20000000000-2-2-2-2-2-20000000022000000022000000002-2-200000-2020000000
χ3422222-2-2222222222-22-22-22-22-200002-20000000000-2-2-2-2-2-200000000-2-200000002200000000-2220000020-20000000
χ3522222-2-2222222222-22-22-22-22-20000-2200000000002222-2-200000000220000000-2-2000000002-2-20000020-20000000
χ3622222-2-2222222222-22-22-22-22-20000-2200000000002222-2-200000000-2-20000000-2-200000000-22200000-2020000000
χ372222-222-222222222-2-22-22-22-22002-20000000022220000-2-2000000002200000-2-20000000000-22-2002000-200000000
χ382222-222-222222222-2-22-22-22-22002-20000000022220000-2-200000000-2-200000-2-200000000002-2200-2000200000000
χ392222-222-222222222-2-22-22-22-2200-2200000000-2-2-2-20000-2-2000000002200000220000000000-22-200-2000200000000
χ402222-222-222222222-2-22-22-22-2200-2200000000-2-2-2-20000-2-200000000-2-2000002200000000002-22002000-200000000
χ412222-2-2-2-2222222222-2-2-2-2-2-2-2-22-200000000000000000022000000002202-22-2000000000000-2-220002-20000000000
χ422222-2-2-2-2222222222-2-2-2-2-2-2-2-22-20000000000000000002200000000-2-202-22-200000000000022-2000-220000000000
χ432222-2-2-2-2222222222-2-2-2-2-2-2-2-2-220000000000000000002200000000220-22-22000000000000-2-22000-220000000000
χ442222-2-2-2-2222222222-2-2-2-2-2-2-2-2-220000000000000000002200000000-2-20-22-2200000000000022-20002-20000000000
χ4544444-4-44−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-4−1+51−5−1−51+5−1+51−5−1−51+500004-400000000001−51−51+51+51−51+500000000000000000−1+5−1−500000000000000000000000000
χ4644444-4-44−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-4−1+51−5−1−51+5−1+51−5−1−51+50000-440000000000−1+5−1+5−1−5−1−51−51+5000000000000000001−51+500000000000000000000000000
χ4744444-4-44−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-4−1−51+5−1+51−5−1−51+5−1+51−500004-400000000001+51+51−51−51+51−500000000000000000−1−5−1+500000000000000000000000000
χ4844444-4-44−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-4−1−51+5−1+51−5−1−51+5−1+51−50000-440000000000−1−5−1−5−1+5−1+51+51−5000000000000000001+51−500000000000000000000000000
χ494444-444-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-41−5−1+51+5−1−51−5−1+51+5−1−5004-400000000−1+5−1+5−1−5−1−500001−51+50000000000000001−51+50000000000000000000000000000
χ504444-444-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-41−5−1+51+5−1−51−5−1+51+5−1−500-44000000001−51−51+51+500001−51+5000000000000000−1+5−1−50000000000000000000000000000
χ514444-444-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-41+5−1−51−5−1+51+5−1−51−5−1+5004-400000000−1−5−1−5−1+5−1+500001+51−50000000000000001+51−50000000000000000000000000000
χ524444-444-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-41+5−1−51−5−1+51+5−1−51−5−1+500-44000000001+51+51−51−500001+51−5000000000000000−1−5−1+50000000000000000000000000000
χ534444-4-4-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−541−51−51+51+51−51−51+51+54-4000000000000000000−1+5−1−500000000000−1+51−5−1−51+5000000000000000000000000000000
χ544444-4-4-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−541−51−51+51+51−51−51+51+5-44000000000000000000−1+5−1−5000000000001−5−1+51+5−1−5000000000000000000000000000000
χ554444-4-4-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+541+51+51−51−51+51+51−51−54-4000000000000000000−1−5−1+500000000000−1−51+5−1+51−5000000000000000000000000000000
χ564444-4-4-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+541+51+51−51−51+51+51−51−5-44000000000000000000−1−5−1+5000000000001+5−1−51−5−1+5000000000000000000000000000000
χ5744-4-4000044-4-4-4-44400000000000000000002-2000000000022-2-222-2-24i−4i000000000000000000000000000000002i−2i0
χ5844-4-4000044-4-4-4-44400000000000000000002-2000000000022-2-222-2-2−4i4i00000000000000000000000000000000−2i2i0
χ5944-4-4000044-4-4-4-4440000000000000000000-220000000000-2-222-2-2224i−4i00000000000000000000000000000000−2i2i0
χ6044-4-4000044-4-4-4-4440000000000000000000-220000000000-2-222-2-222−4i4i000000000000000000000000000000002i−2i0
χ614-44-404-40444-44-4-4-400-40-404040000000000000000000000000000000000000000000000000000000000000022−22000
χ624-44-404-40444-44-4-4-400-40-4040400000000000000000000000000000000000000000000000000000000000000−2222000
χ634-44-40-440444-44-4-4-4004040-40-40000000022−220000000000000000000000000000000000022−2222−22000000000000000000
χ644-44-40-440444-44-4-4-4004040-40-400000000−222200000000000000000000000000000000000−2222−2222000000000000000000
χ654-44-40-440−1+5−1−5−1+51−5−1−51+51−51+500−1+50−1−501−501+50000000022−22002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39000000000000000000
χ664-44-40-440−1+5−1−5−1+51−5−1−51+51−51+500−1+50−1−501−501+50000000022−2200−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39000000000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39000000000000000000
χ674-44-40-440−1+5−1−5−1+51−5−1−51+51−51+500−1+50−1−501−501+500000000−2222002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39000000000000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39000000000000000000
χ684-44-40-440−1+5−1−5−1+51−5−1−51+51−51+500−1+50−1−501−501+500000000−222200−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39000000000000000000
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χ834-4-44-400444-44-44-4-40-40-4040400000000000000000000000000000000000000000000000000000000000002i2−2i200000
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χ8588-8-80000−2+25−2−252−252−252+252+25−2+25−2−2500000000000000000004-40000000000−1+5−1+51−51−5−1−5−1−51+51+50000000000000000000000000000000000000
χ8688-8-80000−2+25−2−252−252−252+252+25−2+25−2−250000000000000000000-4400000000001−51−5−1+5−1+51+51+5−1−5−1−50000000000000000000000000000000000000
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χ898-88-808-80−2+25−2−25−2+252−25−2−252+252−252+25002−2502+250−2+250−2−250000000000000000000000000000000000000000000000000000000000000000000
χ908-88-808-80−2−25−2+25−2−252+25−2+252−252+252−25002+2502−250−2−250−2+250000000000000000000000000000000000000000000000000000000000000000000
χ918-8-88-8008−2+25−2−252−25−2+252+25−2−252−252+2502−2502+250−2+250−2−2500000000000000000000000000000000000000000000000000000000000000000000
χ928-8-88-8008−2−25−2+252+25−2−252−25−2+252+252−2502+2502−250−2−250−2+2500000000000000000000000000000000000000000000000000000000000000000000

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