Finite Group Databasebeta

← Group #12090318

Character table — Group #12090318

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111222222222222444444444444444444444448888888888888888888888888881616161616161616161616202020202020323232324040404040404040408080
order1222444455101010101010444888820202020202020204040404040404040488882020202020202020202040404040404040404040404044840404040404040404444882020202022448888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11-111111-1-1
χ4111111111111111111111111111111111111111111-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-11-1-1-1-1-111
χ51111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-111111111-1-11-11-11-1-1-1-11-1
χ61111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1-1-1-111-1-1-11-11-11111-11
χ71111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1111111-1-111-1-111-11111-1-1-1-1-11
χ81111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-111-1-1-1-1111-1-1-1-111111-1
χ91111111111111111-1-1111111111111111111111-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-111
χ101111111111111111-1-1111111111111111111111-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-111-111-1-111-1-1
χ111111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-111111111-111-1-1-1-1
χ121111111111111111-1-1111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-11111
χ131111111111111111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-111-1-1-1-1-1-111-1111-1-1-1111-1
χ141111111111111111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1111-1-1-1111-1-1-11
χ151111111111111111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-1-111111111-1-111-1-11-11-1-1-1-111-11
χ161111111111111111-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-111-1-1-1-11111-1-1-1-11111-1-1-11-11111-1-11-1
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+52−1−52−1−52−1−52−1−52222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000−1+52−1−52−1+52−1−5200000000000
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+52−1−52−1−52−1−52−1−52-2-2-21−521−521+521+521−521−521+521+520000001−521+521−521+5200000000000
χ1922222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+522-2-222−1+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+52-22-2−1+52−1+52−1−52−1−521−521−521+521+52000000−1+52−1−521−521+5200000000000
χ2022222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+522-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+522-221−521−521+521+52−1+52−1+52−1−52−1−520000001−521+52−1+52−1−5200000000000
χ2122222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2-2221−521−521+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+52-2-22−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000001−521+521−521+5200000000000
χ2222222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2-2-2-2-21−521−521+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+5222-21−521−521+521+521−521−521+521+52000000−1+52−1−52−1+52−1−5200000000000
χ2322222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-22-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-222221−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522-2-2−1+52−1+52−1−52−1−521−521−521+521+520000001−521+52−1+52−1−5200000000000
χ2422222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-22-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-222-2-21−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-2221−521−521+521+52−1+52−1+52−1−52−1−52000000−1+52−1−521−521+5200000000000
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+52222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000−1−52−1+52−1−52−1+5200000000000
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+52-2-2-21+521+521−521−521+521+521−521−520000001+521−521+521−5200000000000
χ2722222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−522-2-222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52-22-2−1−52−1−52−1+52−1+521+521+521−521−52000000−1−52−1+521+521−5200000000000
χ2822222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−522-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−522-221+521+521−521−52−1−52−1−52−1+52−1+520000001+521−52−1−52−1+5200000000000
χ2922222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-222222−1−52−1+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+52-2-2-2221+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52-2-22−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000001+521−521+521−5200000000000
χ3022222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-222222−1−52−1+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+52-2-2-2-2-21+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−5222-21+521+521−521−521+521+521−521−52000000−1−52−1+52−1−52−1+5200000000000
χ3122222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-22-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-222221+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+522-2-2−1−52−1−52−1+52−1+521+521+521−521−520000001+521−52−1−52−1+5200000000000
χ3222222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-22-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-222-2-21+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+52-2221+521+521−521−52−1−52−1−52−1+52−1+52000000−1−52−1+521+521−5200000000000
χ3322222-2-222222222200-222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2000000000-2-20000222200000000000000000000022000000-220-20000000
χ3422222-2-222222222200-222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2000000000-2-200002222000000000000000000000-2-20000002-2020000000
χ3522222-2-222222222200-2-2-222-2-22222-2-222222222000000000-2-20000-2-2-2-200000000000000000000022000000-2-2020000000
χ3622222-2-222222222200-2-2-222-2-22222-2-222222222000000000-2-20000-2-2-2-2000000000000000000000-2-2000000220-20000000
χ372222-222-22222222222-2000022-2-2-2-22200000000-20000-2-2-2-2-2-2222200000000000000000000000220022000000-20-2000000
χ382222-222-22222222222-2000022-2-2-2-22200000000-20000-2-2-2-2-2-2222200000000000000000000000-2-200-2-2000000202000000
χ392222-222-222222222-2-2-2000022-2-2-2-22200000000200002222-2-2-2-2-2-2000000000000000000000002200-2-2000000-202000000
χ402222-222-222222222-2-2-2000022-2-2-2-22200000000200002222-2-2-2-2-2-200000000000000000000000-2-2002200000020-2000000
χ412-22-20-2202222-2-2-2-22i−2i02−22−2-2-200002222−2−222−2−20i2−i2000000002i−2i2i−2i2−22−2i2i2−i2−i2i2i2−i2−i2000000000002i−2i002-2000000000i2−i22−200
χ422-22-20-2202222-2-2-2-22i−2i02−22−2-2-200002222−2−222−2−20i2−i2000000002i−2i2i−2i2−22−2i2i2−i2−i2i2i2−i2−i200000000000−2i2i00-22000000000−i2i2−2200
χ432-22-20-2202222-2-2-2-22i−2i0−22−22-2-2000022−2−222−2−2220−i2i2000000002i−2i2i−2i−22−22−i2−i2i2i2−i2−i2i2i2000000000002i−2i002-2000000000−i2i2−2200
χ442-22-20-2202222-2-2-2-22i−2i0−22−22-2-2000022−2−222−2−2220−i2i2000000002i−2i2i−2i−22−22−i2−i2i2i2−i2−i2i2i200000000000−2i2i00-22000000000i2−i22−200
χ452-22-20-2202222-2-2-2-2−2i2i02−22−2-2-200002222−2−222−2−20−i2i200000000−2i2i−2i2i2−22−2−i2−i2i2i2−i2−i2i2i2000000000002i−2i00-22000000000i2−i2−2200
χ462-22-20-2202222-2-2-2-2−2i2i02−22−2-2-200002222−2−222−2−20−i2i200000000−2i2i−2i2i2−22−2−i2−i2i2i2−i2−i2i2i200000000000−2i2i002-2000000000−i2i22−200
χ472-22-20-2202222-2-2-2-2−2i2i0−22−22-2-2000022−2−222−2−2220i2−i200000000−2i2i−2i2i−22−22i2i2−i2−i2i2i2−i2−i2000000000002i−2i00-22000000000−i2i22−200
χ482-22-20-2202222-2-2-2-2−2i2i0−22−22-2-2000022−2−222−2−2220i2−i200000000−2i2i−2i2i−22−22i2i2−i2−i2i2i2−i2−i200000000000−2i2i002-2000000000i2−i2−2200
χ4944444-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500-444-4-41−51+5−1+5−1−5−1+5−1−51−51+51−51−51−51−51+51+51+51+50000000001−51+50000−1+5−1+5−1−5−1−50000000000000000000000000000000000000000
χ5044444-4-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500-4-4-4441−51+5−1+5−1−5−1+5−1−51−51+5−1+5−1+5−1+5−1+5−1−5−1−5−1−5−1−50000000001−51+500001−51−51+51+50000000000000000000000000000000000000000
χ5144444-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500-444-4-41+51−5−1−5−1+5−1−5−1+51+51−51+51+51+51+51−51−51−51−50000000001+51−50000−1−5−1−5−1+5−1+50000000000000000000000000000000000000000
χ5244444-4-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500-4-4-4441+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+50000000001+51−500001+51+51−51−50000000000000000000000000000000000000000
χ534444-444-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−544-40000−1+5−1−51−51+51−51+5−1+5−1−500000000-400001−51−51+51+51−51+5−1+5−1+5−1−5−1−500000000000000000000000000000000000000000000
χ544444-444-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-4-40000−1+5−1−51−51+51−51+5−1+5−1−50000000040000−1+5−1+5−1−5−1−51−51+51−51−51+51+500000000000000000000000000000000000000000000
χ554444-444-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+544-40000−1−5−1+51+51−51+51−5−1−5−1+500000000-400001+51+51−51−51+51−5−1−5−1−5−1+5−1+500000000000000000000000000000000000000000000
χ564444-444-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4-4-40000−1−5−1+51+51−51+51−5−1−5−1+50000000040000−1−5−1−5−1+5−1+51+51−51+51+51−51−500000000000000000000000000000000000000000000
χ574444-4-4-4-4444444440040000-4-4-4-4-4-4-4-40000000000000000044000000000000000000000000000000000000000000000000
χ584444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500400001−51+51−51+51−51+51−51+500000000000000000−1+5−1−500000000−2ζ22+2ζ382ζ22−2ζ38−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000
χ594444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500400001−51+51−51+51−51+51−51+500000000000000000−1+5−1−5000000002ζ22−2ζ38−2ζ22+2ζ382ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000
χ604444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500400001+51−51+51−51+51−51+51−500000000000000000−1−5−1+5000000002ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ382ζ22−2ζ38−2ζ22+2ζ3800000000000000000000000000000000
χ614444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500400001+51−51+51−51+51−51+51−500000000000000000−1−5−1+500000000−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ38−2ζ22+2ζ382ζ22−2ζ3800000000000000000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.