Finite Group Databasebeta

← Group #12086905

Character table — Group #12086905

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111222222222222444444444444444444444448888888888888888888888888881010161616161616161616161620202020203232323240404040404040808080
order1222444455101010101010488888820202020202020204040404040404040248881010101020202020202040404040404040404040404022448404040404040404044488202020204488888448
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1111-1-1-1
χ4111111111111111111111111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111
χ5111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-11111-1-1-1-1111-1-111-1-1-1-11111-1-11-1
χ6111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11-1-11111-1-1-1-1-1-1-11111-1-111-1-1-1-111-11
χ7111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-111-1-1-1-11111111-1-1-1-111-1-1-1-111-11-11
χ8111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-111-1-1-1-11111-1-1-111-1-1111111-1-11-11-1
χ911111111111111111-1-1-1-1111111111111111111-1-1111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111111111-1-1-1-1-1-111-1-11-1-11
χ1011111111111111111-1-1-1-1111111111111111111-1-1111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-111-1-111-111-1
χ1111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1111-1
χ1211111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-11
χ1311111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-11-11111-1-1-1-1111-1-1-1-1111111-1-1-11-1-1
χ1411111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-111-1-111-1-1-1-1111-111
χ1511111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-1-11111111-1-111-1-111-1-1-1-1-1-111
χ1611111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-11111-1-1-1-1111111-1-1
χ1722222222−1+52−1−52−1+52−1−52−1+52−1−52−1+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+52−1−52−1−52−1−52−1−5222222−1+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+52−1−52−1−52−1−52−1−5200222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000−1+52−1−52−1+52−1−520000000000
χ1822222222−1+52−1−52−1+52−1−52−1+52−1−52−1+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+52−1−52−1−52−1−52−1−52222-2-2−1+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+52−1−52−1−52−1−52−1−5200-2-2-21−521−521+521+521−521−521+521+52000001−521+521−521+520000000000
χ1922222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222222-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-2-2-2221−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52002-2-2−1+52−1+52−1−52−1−521−521−521+521+5200000−1+52−1−521−521+520000000000
χ2022222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222222-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-2-2-2-2-21−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−5200-2221−521−521+521+52−1+52−1+52−1−52−1−52000001−521+52−1+52−1−520000000000
χ2122222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522-2-2-2-222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-22221−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+5200-2-22−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000001−521+521−521+520000000000
χ2222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522-2-2-2-222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-22-2-21−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+520022-21−521−521+521+521−521−521+521+5200000−1+52−1−52−1+52−1−520000000000
χ2322222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+5222-222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+5200-22-2−1+52−1+52−1−52−1−521−521−521+521+52000001−521+52−1+52−1−520000000000
χ2422222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+5222-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52002-221−521−521+521+52−1+52−1+52−1−52−1−5200000−1+52−1−521−521+520000000000
χ2522222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+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+5222222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000−1−52−1+52−1−52−1+520000000000
χ2622222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+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+52222-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-2-2-21+521+521−521−521+521+521−521−52000001+521−521+521−520000000000
χ2722222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-2-2-2221+521+521−521−52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52002-2-2−1−52−1−52−1+52−1+521+521+521−521−5200000−1−52−1+521+521−520000000000
χ2822222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-2-2-2-2-21+521+521−521−52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+5200-2221+521+521−521−52−1−52−1−52−1+52−1+52000001+521−52−1−52−1+520000000000
χ2922222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522-2-2-2-222−1−52−1+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+52-2-22221+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−5200-2-22−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000001+521−521+521−520000000000
χ3022222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522-2-2-2-222−1−52−1+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+52-2-22-2-21+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−520022-21+521+521−521−521+521+521−521−5200000−1−52−1+52−1−52−1+520000000000
χ3122222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−5222-222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−5200-22-2−1−52−1−52−1+52−1+521+521+521−521−52000001+521−52−1−52−1+520000000000
χ3222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−5222-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52002-221+521+521−521−52−1−52−1−52−1+52−1+5200000−1−52−1+521+521−520000000000
χ3322222-2-2222222222-2000022-2-22222-2-22222222200-2000000-2-20000-2-2-2-2000000002200000000000-22-2220000000000-2000
χ3422222-2-2222222222-2000022-2-22222-2-22222222200-2000000-2-20000-2-2-2-200000000-2-2000000000002-22-2-200000000002000
χ3522222-2-2222222222-20000-2-2-2-22222-2-2-2-2-2-2-2-2-2-2002000000-2-200002222000000002200000000000-22-2-2-200000000002000
χ3622222-2-2222222222-20000-2-2-2-22222-2-2-2-2-2-2-2-2-2-2002000000-2-20000222200000000-2-2000000000002-22220000000000-2000
χ372222-222-222222222-200000022-2-2-2-222000000002-20002222-2-2-2-2-2-20000000000002200000000000-2-220000002-200000000
χ382222-222-222222222-200000022-2-2-2-222000000002-20002222-2-2-2-2-2-2000000000000-2-20000000000022-2000000-2200000000
χ392222-222-222222222-200000022-2-2-2-22200000000-22000-2-2-2-2-2-222220000000000002200000000000-2-22000000-2200000000
χ402222-222-222222222-200000022-2-2-2-22200000000-22000-2-2-2-2-2-22222000000000000-2-20000000000022-20000002-200000000
χ412222-2-2-2-22222222222i2i−2i−2i00-2-2-2-2-2-2-2-20000000000000000022000000002i2i−2i−2i2i2i−2i−2i22000000000002-2-200000000002i−2i0000
χ422222-2-2-2-22222222222i2i−2i−2i00-2-2-2-2-2-2-2-20000000000000000022000000002i2i−2i−2i2i2i−2i−2i-2-200000000000-2220000000000−2i2i0000
χ432222-2-2-2-2222222222−2i−2i2i2i00-2-2-2-2-2-2-2-2000000000000000002200000000−2i−2i2i2i−2i−2i2i2i22000000000002-2-20000000000−2i2i0000
χ442222-2-2-2-2222222222−2i−2i2i2i00-2-2-2-2-2-2-2-2000000000000000002200000000−2i−2i2i2i−2i−2i2i2i-2-200000000000-22200000000002i−2i0000
χ4544444-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-40000441−51+5−1+5−1−5−1+5−1−51−51+5−1+5−1+5−1+5−1+5−1−5−1−5−1−5−1−500-40000001−51+500001−51−51+51+50000000000000000000000000000000000000000
χ4644444-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-40000-4-41−51+5−1+5−1−5−1+5−1−51−51+51−51−51−51−51+51+51+51+50040000001−51+50000−1+5−1+5−1−5−1−50000000000000000000000000000000000000000
χ4744444-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-40000441+51−5−1−5−1+5−1−5−1+51+51−5−1−5−1−5−1−5−1−5−1+5−1+5−1+5−1+500-40000001+51−500001+51+51−51−50000000000000000000000000000000000000000
χ4844444-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-40000-4-41+51−5−1−5−1+5−1−5−1+51+51−51+51+51+51+51−51−51−51−50040000001+51−50000−1−5−1−5−1+5−1+50000000000000000000000000000000000000000
χ494444-444-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4000000−1+5−1−51−51+51−51+5−1+5−1−5000000004-4000−1+5−1+5−1−5−1−51−51+51−51−51+51+500000000000000000000000000000000000000000000
χ504444-444-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4000000−1+5−1−51−51+51−51+5−1+5−1−500000000-440001−51−51+51+51−51+5−1+5−1+5−1−5−1−500000000000000000000000000000000000000000000
χ514444-444-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4000000−1−5−1+51+51−51+51−5−1−5−1+5000000004-4000−1−5−1−5−1+5−1+51+51−51+51+51−51−500000000000000000000000000000000000000000000
χ524444-444-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4000000−1−5−1+51+51−51+51−5−1−5−1+500000000-440001+51+51−51−51+51−5−1−5−1−5−1+5−1+500000000000000000000000000000000000000000000
χ534444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−544i4i−4i−4i001−51+51−51+51−51+51−51+500000000000000000−1+5−1−500000000−2ζ22−2ζ38−2ζ22−2ζ382ζ22+2ζ382ζ22+2ζ38−2ζ6−2ζ14−2ζ6−2ζ142ζ6+2ζ142ζ6+2ζ1400000000000000000000000000000000
χ544444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−54−4i−4i4i4i001−51+51−51+51−51+51−51+500000000000000000−1+5−1−5000000002ζ22+2ζ382ζ22+2ζ38−2ζ22−2ζ38−2ζ22−2ζ382ζ6+2ζ142ζ6+2ζ14−2ζ6−2ζ14−2ζ6−2ζ1400000000000000000000000000000000
χ554444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+544i4i−4i−4i001+51−51+51−51+51−51+51−500000000000000000−1−5−1+500000000−2ζ6−2ζ14−2ζ6−2ζ142ζ6+2ζ142ζ6+2ζ14−2ζ22−2ζ38−2ζ22−2ζ382ζ22+2ζ382ζ22+2ζ3800000000000000000000000000000000
χ564444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+54−4i−4i4i4i001+51−51+51−51+51−51+51−500000000000000000−1−5−1+5000000002ζ6+2ζ142ζ6+2ζ14−2ζ6−2ζ14−2ζ6−2ζ142ζ22+2ζ382ζ22+2ζ38−2ζ22−2ζ38−2ζ22−2ζ3800000000000000000000000000000000
χ5744-4-400004444-4-4-4-40000022−22000000002222−22−222222−22−220000000000000000000000000004-40000000000000022−2200000000000000
χ5844-4-400004444-4-4-4-40000022−22000000002222−22−222222−22−22000000000000000000000000000-4400000000000000−222200000000000000
χ5944-4-400004444-4-4-4-400000−222200000000−22−222222−22−2222220000000000000000000000000004-400000000000000−222200000000000000
χ6044-4-400004444-4-4-4-400000−222200000000−22−222222−22−222222000000000000000000000000000-440000000000000022−2200000000000000
χ614-44-4400-444-4-444-4-400000000044-4-4000000000000000000000000000000000000000000000000000000000000022−22000000
χ624-44-4400-444-4-444-4-400000000044-4-40000000000000000000000000000000000000000000000000000000000000−2222000000
χ634-44-4-400444-4-444-4-4000000000-4-44400000000000002i2−2i20000000000000000000000000002i2−2i22i2−2i200000000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.