Finite Group Databasebeta

← Group #12090752

Character table — Group #12090752

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222222222222444444444444444888888888888888888888881010101016161616161616161616161616161616161616202020202020202032324040404040808080
order1222444455101010101010444888820202020202020204448820202020202020202020404040404040404088884482020202020202020404040404040404044888888202024488248
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-11-111-1-1-1-1111111111111111111-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1
χ41111111111111111111111111111111-11-111-1-1-1-111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111
χ51111111111111111111-1-1-1-111111111111-1-11111111111-1-1-1-1-1-1-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1111-1-1
χ61111111111111111111-1-1-1-111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11-1-1-111
χ71111111111111111111-1-1-1-111111111-11-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-111-111
χ81111111111111111111-1-1-1-111111111-11-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-111111-1-11-1-1
χ91111111111111111-1-111111111111111-11-1-11111-1-1-1-111111111111111-1-11-1-111-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-1-11
χ101111111111111111-1-111111111111111-11-1-11111-1-1-1-11111111111-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111-1
χ111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-1
χ121111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111-1-11
χ131111111111111111-1-11-1-1-1-1111111111-11111111-1-1-1-111-1-1-1-1-1-1-1-11111-11-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111111-1-1-11-1
χ141111111111111111-1-11-1-1-1-1111111111-11111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-1-1111-11
χ151111111111111111-1-11-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111-11-1-1-1-111111111111111-1-1-1-111-1-1-1-11-1-11-11
χ161111111111111111-1-11-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1111111111111-1-11111-1-1-1-111-111-11-1
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+52−1−52−1−5222222−1+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+52−1−52−1−52−1−52−1−520000222−1+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+52−1−52−1−5200000000−1+52−1−5200000000
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+52−1−52−1−52-22-2221−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000-2-2-2−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000001−521+5200000000
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+52−1−52−1−52222-2-2−1+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+5200002-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52000000001−521+5200000000
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+52−1−52−1−52-22-2-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+520000-222−1+52−1−521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−5200000000−1+52−1−5200000000
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+52−1−52−1−522-22-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000-2-221−521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000000001−521+5200000000
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+52−1−52−1−52-2-2-2-2-21−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52000022-21−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+5200000000−1+52−1−5200000000
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+52−1−52−1−522-2222−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+520000-22-21−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+5200000000−1+52−1−5200000000
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+52−1−52−1−52-2-2-2221−521−521+521+521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+5200002-221−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000001−521+5200000000
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+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+520000222−1−52−1+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+5200000000−1−52−1+5200000000
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+52-22-2221+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+520000-2-2-2−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000001+521−5200000000
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+52222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−5200002-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000000001+521−5200000000
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+52-22-2-2-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−520000-222−1−52−1+521+521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+5200000000−1−52−1+5200000000
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+522-22-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+520000-2-221+521−52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52000000001+521−5200000000
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+52-2-2-2-2-21+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+52000022-21+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5200000000−1−52−1+5200000000
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+522-2222−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−520000-22-21+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−5200000000−1−52−1+5200000000
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+52-2-2-2221+521+521−521−521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−5200002-221+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+52000000001+521−5200000000
χ3322222-2-222222222200-200002-22-22-22-220-200-2-2-2-20000-2-20000000022220000022000000000000000000-2-2002-2000000
χ3422222-2-222222222200-200002-22-22-22-220-200-2-2-2-20000-2-200000000-2-2-2-200000220000000000000000002200-22000000
χ3522222-2-222222222200-200002-22-22-22-2-2020022220000-2-200000000222200000-2-2000000000000000000-2-200-22000000
χ3622222-2-222222222200-200002-22-22-22-2-2020022220000-2-200000000-2-2-2-200000-2-200000000000000000022002-2000000
χ372222-222-22222222222-20000-22-22-22-220-200000002222-2-2000000000000000-2-2000000000000002222-2-2000000-200000
χ382222-222-22222222222-20000-22-22-22-220-200000002222-2-2000000000000000-2-200000000000000-2-2-2-222000000200000
χ392222-222-222222222-2-2-20000-22-22-22-22020000000-2-2-2-2-2-2000000000000000220000000000000022-2-222000000-200000
χ402222-222-222222222-2-2-20000-22-22-22-22020000000-2-2-2-2-2-20000000000000002200000000000000-2-222-2-2000000200000
χ412-22-202-2022-2-22-22-22-20i2i2−i2−i20-20-20202000i2−i200002-22-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000i2−i2i2−i200002-22-200i2−i200000i2−i2000
χ422-22-202-2022-2-22-22-22-20i2i2−i2−i20-20-20202000i2−i200002-22-200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000i2−i2i2−i20000-22-2200−i2i200000−i2i2000
χ432-22-202-2022-2-22-22-22-20−i2−i2i2i20-20-20202000−i2i200002-22-200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000−i2i2−i2i20000-22-2200i2−i200000i2−i2000
χ442-22-202-2022-2-22-22-22-20−i2−i2i2i20-20-20202000−i2i200002-22-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000−i2i2−i2i200002-22-200−i2i200000−i2i2000
χ452-22-202-2022-2-22-22-2-220i2i2−i2−i20-20-20202000−i2i20000-22-2200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000−i2i2−i2i20000-222-200i2−i200000−i2i2000
χ462-22-202-2022-2-22-22-2-220i2i2−i2−i20-20-20202000−i2i20000-22-2200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000−i2i2−i2i200002-2-2200−i2i200000i2−i2000
χ472-22-202-2022-2-22-22-2-220−i2−i2i2i20-20-20202000i2−i20000-22-2200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000i2−i2i2−i200002-2-2200i2−i200000−i2i2000
χ482-22-202-2022-2-22-22-2-220−i2−i2i2i20-20-20202000i2−i20000-22-2200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000i2−i2i2−i20000-222-200−i2i200000i2−i2000
χ4944444-4-44−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−500-40000−1+51−5−1−51+5−1+51−5−1−51+540-4001−51−51+51+500001−51+500000000000000000−1+5−1−5000000000000000000000000000000
χ5044444-4-44−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−500-40000−1+51−5−1−51+5−1+51−5−1−51+5-40400−1+5−1+5−1−5−1−500001−51+5000000000000000001−51+5000000000000000000000000000000
χ5144444-4-44−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+500-40000−1−51+5−1+51−5−1−51+5−1+51−540-4001+51+51−51−500001+51−500000000000000000−1−5−1+5000000000000000000000000000000
χ5244444-4-44−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+500-40000−1−51+5−1+51−5−1−51+5−1+51−5-40400−1−5−1−5−1+5−1+500001+51−5000000000000000001+51−5000000000000000000000000000000
χ534444-444-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−544-400001−5−1+51+5−1−51−5−1+51+5−1−50-40000000−1+5−1+5−1−5−1−51−51+50000000000000001−51+500000000000000000000000000000000
χ544444-444-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-4-4-400001−5−1+51+5−1−51−5−1+51+5−1−50400000001−51−51+51+51−51+5000000000000000−1+5−1−500000000000000000000000000000000
χ554444-444-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+544-400001+5−1−51−5−1+51+5−1−51−5−1+50-40000000−1−5−1−5−1+5−1+51+51−50000000000000001+51−500000000000000000000000000000000
χ564444-444-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-4-4-400001+5−1−51−5−1+51+5−1−51−5−1+50400000001+51+51−51−51+51−5000000000000000−1−5−1+500000000000000000000000000000000
χ574444-4-4-4-4444444440040000-4-4-4-4-4-4-4-40000000000000440000000000000000000000000000000000000000000000000
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+50000000000000−1+5−1−500000000000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000000
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+50000000000000−1+5−1−50000000000000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000000
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+51−51−50000000000000−1−5−1+50000000000000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000000
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+51−51−50000000000000−1−5−1+500000000000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000000
χ6244-4-4400-444-4-4-44-4400000004040-40-40000000000000000000000004-44-40000000000000000000000000000000000000
χ6344-4-4400-444-4-4-44-4400000004040-40-4000000000000000000000000-44-440000000000000000000000000000000000000
χ6444-4-4-400444-4-4-44-440002i2−2i22i2−2i2-40-4040400000000000000002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000000000000000000
χ6544-4-4-400444-4-4-44-44000−2i22i2−2i22i2-40-404040000000000000000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000000000000000000
χ6644-4-4-4004−1+5−1−51−51+51−5−1+51+5−1−50002i2−2i22i2−2i21−501+50−1+50−1−5000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ14000000ζ7+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−ζ390000000000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.