Finite Group Databasebeta

← Group #12090811

Character table — Group #12090811

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101
size1111222222222222222244444444444444444444488888888888888888888888881616161616161616161616162020202020202020202032323232404040404040408080
order1222444455888810101010101044488202020202020202040404040404040402881010101020202020202040404040404040404040404044884040404040404040228888888820202020224448844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111
χ511111111111111111111-1-11111111111111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1
χ611111111111111111111-1-11111111111111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-111
χ711111111111111111111-1-11111111111111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ811111111111111111111-1-11111111111111111111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111-1-111111111-1-1-1-11111-1-1-1-1-1
χ91111111111-1-1-1-1111111111-1-111111111-1-1-1-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1111111-1-1-1-111-1-11-11-11-1-11-1
χ101111111111-1-1-1-1111111111-1-111111111-1-1-1-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-11-11-111-11
χ111111111111-1-1-1-1111111111-1-111111111-1-1-1-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111111111-1-1-1-1-1-111-11-111-1-1-11
χ121111111111-1-1-1-1111111111-1-111111111-1-1-1-1-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-11111-1-1-1-1-1-11111-1-1111-11-1-1111-1
χ131111111111-1-1-1-1111111-1-11-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1111111-1-1-1-1111111-1-11-11-11-1-1-11
χ141111111111-1-1-1-1111111-1-11-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-11111-1-11111-1-1-1-111-1-1-11-11-1111-1
χ151111111111-1-1-1-1111111-1-11-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-111-11111-1-1-1-111-1-1-1-11111-1-111-11-111-1-11-1
χ161111111111-1-1-1-1111111-1-11-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-111-11111-1-1-1-1-1-11111-1-1-1-1-1-1111-11-1-111-11
χ1722222222−1+52−1−522222−1+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+52−1−52−1−52−1−52−1−52222−1+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+52−1−52−1−52−1−52−1−522222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000000−1+52−1−52−1+52−1−52000000000
χ1822222222−1+52−1−522222−1+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+52−1−52−1−52−1−52−1−52222−1+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+52−1−52−1−52−1−52−1−52-2-2-2-21−521−521+521+521−521−521+521+5200000000001−521+521−521+52000000000
χ1922222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-2-2222−1+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+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+5222-2-21−521−521+521+521−521−521+521+520000000000−1+52−1−52−1+52−1−52000000000
χ2022222222−1+52−1−522222−1+52−1−52−1+52−1−52−1+52−1−52-2-2222−1+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+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52-2-222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000001−521+521−521+52000000000
χ2122222222−1+52−1−52-2-2-2-2−1+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+52−1−521−521−521−521−521+521+521+521+522-2-2−1+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+522-22-2−1+52−1+52−1−52−1−521−521−521+521+520000000000−1+52−1−521−521+52000000000
χ2222222222−1+52−1−52-2-2-2-2−1+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+52−1−521−521−521−521−521+521+521+521+522-2-2−1+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+52-22-221−521−521+521+52−1+52−1+52−1−52−1−5200000000001−521+52−1+52−1−52000000000
χ2322222222−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52-2-22-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-2221−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−522-2-221−521−521+521+52−1+52−1+52−1−52−1−520000000000−1+52−1−521−521+52000000000
χ2422222222−1+52−1−52-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52-2-22-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521−521−521+521+521+521+52-2221−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-222-2−1+52−1+52−1−52−1−521−521−521+521+5200000000001−521+52−1+52−1−52000000000
χ2522222222−1−52−1+522222−1−52−1+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+52222−1−52−1−52−1+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+522222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000000000−1−52−1+52−1−52−1+52000000000
χ2622222222−1−52−1+522222−1−52−1+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+52222−1−52−1−52−1+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+52-2-2-2-21+521+521−521−521+521+521−521−5200000000001+521−521+521−52000000000
χ2722222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+52-2-2222−1−52−1+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+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−5222-2-21+521+521−521−521+521+521−521−520000000000−1−52−1+52−1−52−1+52000000000
χ2822222222−1−52−1+522222−1−52−1+52−1−52−1+52−1−52−1+52-2-2222−1−52−1+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+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52-2-222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000001+521−521+521−52000000000
χ2922222222−1−52−1+52-2-2-2-2−1−52−1+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+521+521+521+521+521−521−521−521−522-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−522-22-2−1−52−1−52−1+52−1+521+521+521−521−520000000000−1−52−1+521+521−52000000000
χ3022222222−1−52−1+52-2-2-2-2−1−52−1+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+521+521+521+521+521−521−521−521−522-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52-22-221+521+521−521−52−1−52−1−52−1+52−1+5200000000001+521−52−1−52−1+52000000000
χ3122222222−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52-2-22-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-2221+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+522-2-221+521+521−521−52−1−52−1−52−1+52−1+520000000000−1−52−1+521+521−52000000000
χ3222222222−1−52−1+52-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52-2-22-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521+521+521−521−521−521−52-2221+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+52-222-2−1−52−1−52−1+52−1+521+521+521−521−5200000000001+521−52−1−52−1+52000000000
χ3322222-2-2222222222222200-2-2-2-2-22222-2-2222222220000000-2-20000-2-2-2-2000000000000000000000000000000000022-2-200000
χ3422222-2-2222222222222200-2-2-2-2-22222-2-2222222220000000-2-20000-2-2-2-20000000000000000000000000000000000-2-22200000
χ3522222-2-2222-2-2-2-222222200-222-2-22222-2-2-2-2-2-2-2-2-2-20000000-2-20000222200000000000000000000000000000000002-2-2200000
χ3622222-2-2222-2-2-2-222222200-222-2-22222-2-2-2-2-2-2-2-2-2-20000000-2-2000022220000000000000000000000000000000000-222-200000
χ372222-222-222000022222222-20022-2-2-2-22200000000-200-2-2-2-2-2-2222200000000000000000000000022-2-222000000000000-20000
χ382222-222-222000022222222-20022-2-2-2-22200000000-200-2-2-2-2-2-22222000000000000000000000000-2-222-2-200000000000020000
χ392222-222-2220000222222-2-2-20022-2-2-2-222000000002002222-2-2-2-2-2-20000000000000000000000002222-2-2000000000000-20000
χ402222-222-2220000222222-2-2-20022-2-2-2-222000000002002222-2-2-2-2-2-2000000000000000000000000-2-2-2-22200000000000020000
χ412-22-202-202222−2−2-2-2-2-2222i−2i02−2220000-2-222−2−222−2−20i2−i20000002i−2i2i−2i2−22−2i2i2−i2−i2i2i2−i2−i20000000000002-2002i−2ii2i2−i2−i20000000002−200
χ422-22-202-202222−2−2-2-2-2-2222i−2i02−2220000-2-222−2−222−2−20i2−i20000002i−2i2i−2i2−22−2i2i2−i2−i2i2i2−i2−i2000000000000-2200−2i2i−i2−i2i2i2000000000−2200
χ432-22-202-202222−2−2-2-2-2-222−2i2i02−2220000-2-222−2−222−2−20−i2i2000000−2i2i−2i2i2−22−2−i2−i2i2i2−i2−i2i2i20000000000002-200−2i2i−i2−i2i2i20000000002−200
χ442-22-202-202222−2−2-2-2-2-222−2i2i02−2220000-2-222−2−222−2−20−i2i2000000−2i2i−2i2i2−22−2−i2−i2i2i2−i2−i2i2i2000000000000-22002i−2ii2i2−i2−i2000000000−2200
χ452-22-202-2022−2−222-2-2-2-2222i−2i0−22220000-2-2−2−222−2−2220−i2i20000002i−2i2i−2i−22−22−i2−i2i2i2−i2−i2i2i20000000000002-2002i−2i−i2−i2i2i2000000000−2200
χ462-22-202-2022−2−222-2-2-2-2222i−2i0−22220000-2-2−2−222−2−2220−i2i20000002i−2i2i−2i−22−22−i2−i2i2i2−i2−i2i2i2000000000000-2200−2i2ii2i2−i2−i20000000002−200
χ472-22-202-2022−2−222-2-2-2-222−2i2i0−22220000-2-2−2−222−2−2220i2−i2000000−2i2i−2i2i−22−22i2i2−i2−i2i2i2−i2−i20000000000002-200−2i2ii2i2−i2−i2000000000−2200
χ482-22-202-2022−2−222-2-2-2-222−2i2i0−22220000-2-2−2−222−2−2220i2−i2000000−2i2i−2i2i−22−22i2i2−i2−i2i2i2−i2−i2000000000000-22002i−2i−i2−i2i2i20000000002−200
χ4944444-4-44−1+5−1−54444−1+5−1−5−1+5−1−5−1+5−1−500-4-4-41−51+5−1+5−1−5−1+5−1−51−51+5−1+5−1+5−1+5−1+5−1−5−1−5−1−5−1−500000001−51+500001−51−51+51+50000000000000000000000000000000000000000000
χ5044444-4-44−1+5−1−5-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−500-4441−51+5−1+5−1−5−1+5−1−51−51+51−51−51−51−51+51+51+51+500000001−51+50000−1+5−1+5−1−5−1−50000000000000000000000000000000000000000000
χ5144444-4-44−1−5−1+54444−1−5−1+5−1−5−1+5−1−5−1+500-4-4-41+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+500000001+51−500001+51+51−51−50000000000000000000000000000000000000000000
χ5244444-4-44−1−5−1+5-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+500-4441+51−5−1−5−1+5−1−5−1+51+51−51+51+51+51+51−51−51−51−500000001+51−50000−1−5−1−5−1+5−1+50000000000000000000000000000000000000000000
χ534444-444-4−1+5−1−50000−1+5−1−5−1+5−1−5−1+5−1−544-400−1+5−1−51−51+51−51+5−1+5−1−500000000-4001−51−51+51+51−51+5−1+5−1+5−1−5−1−500000000000000000000000000000000000000000000000
χ544444-444-4−1+5−1−50000−1+5−1−5−1+5−1−5−1+5−1−5-4-4-400−1+5−1−51−51+51−51+5−1+5−1−500000000400−1+5−1+5−1−5−1−51−51+51−51−51+51+500000000000000000000000000000000000000000000000
χ554444-444-4−1−5−1+50000−1−5−1+5−1−5−1+5−1−5−1+544-400−1−5−1+51+51−51+51−5−1−5−1+500000000-4001+51+51−51−51+51−5−1−5−1−5−1+5−1+500000000000000000000000000000000000000000000000
χ564444-444-4−1−5−1+50000−1−5−1+5−1−5−1+5−1−5−1+5-4-4-400−1−5−1+51+51−51+51−5−1−5−1+500000000400−1−5−1−5−1+5−1+51+51−51+51+51−51−500000000000000000000000000000000000000000000000
χ574444-4-4-4-444000044444400400-4-4-4-4-4-4-4-400000000000000044000000000000000000000000000000000000000000000000000
χ584444-4-4-4-4−1+5−1−50000−1+5−1−5−1+5−1−5−1+5−1−5004001−51+51−51+51−51+51−51+5000000000000000−1+5−1−500000000−2ζ22+2ζ382ζ22−2ζ38−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000000
χ594444-4-4-4-4−1+5−1−50000−1+5−1−5−1+5−1−5−1+5−1−5004001−51+51−51+51−51+51−51+5000000000000000−1+5−1−5000000002ζ22−2ζ38−2ζ22+2ζ382ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000000
χ604444-4-4-4-4−1−5−1+50000−1−5−1+5−1−5−1+5−1−5−1+5004001+51−51+51−51+51−51+51−5000000000000000−1−5−1+5000000002ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ382ζ22−2ζ38−2ζ22+2ζ3800000000000000000000000000000000000
χ614444-4-4-4-4−1−5−1+50000−1−5−1+5−1−5−1+5−1−5−1+5004001+51−51+51−51+51−51+51−5000000000000000−1−5−1+500000000−2ζ6+2ζ142ζ6−2ζ14−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ38−2ζ22+2ζ382ζ22−2ζ3800000000000000000000000000000000000
χ6244-4-400004422−2222−2244-4-4-4-4000000000000022−2222−2222−2222−2200000000000000000000000000000000000000022−22002-22-20000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.