Finite Group Databasebeta

← Group #12076829

Character table — Group #12076829

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222224444444444444448888888888888888888888888101010101010161616161616161616161616161616161616202020202020203232404040404040408080
order1222444455101010101010444888820202020202020202444488101010102020202020204040404040404040444444282020202020202020404040404040404022288881010444448848
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-11-111-1-1-1-111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111111-1-1-1-1-11-111-1-1
χ41111111111111111111111111111111-1-1-11-111-1-1-1-111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-111
χ51111111111111111111-1-1-1-11111111111111-1-11111111111-1-1-1-1-1-1-1-1111111-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111-1-1-1-1
χ61111111111111111111-1-1-1-11111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111
χ71111111111111111111-1-1-1-111111111-1-1-11-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-11-1-1-111
χ81111111111111111111-1-1-1-111111111-1-1-11-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1111111111-1111-1-1
χ91111111111111111-1-111111111111111-1-1-11-1-11111-1-1-1-11111111111111111-11-1-111-1-1-1-1-1-1-1-111111-1-11111-1-11-1-1-11-1-1-11
χ101111111111111111-1-111111111111111-1-1-11-1-11111-1-1-1-11111111111-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-11111-111-1-1-1-1-1-1-1111-1111-1
χ111111111111111111-1-11111111111111-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-11111-1-1-1-1-1-1-1-11-1-1111111-111-1-1-1-11-1
χ121111111111111111-1-11111111111111-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-11111-11
χ131111111111111111-1-11-1-1-1-1111111111-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1-111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1111-1-1-11111-1
χ141111111111111111-1-11-1-1-1-1111111111-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1-1-11111-1-1-1-1-111111111-1111-1-1-1-11
χ151111111111111111-1-11-1-1-1-111111111-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-11-1-1-1-11111111111111-1-1-1-1-1-1-1-1-111-1-111-11
χ161111111111111111-1-11-1-1-1-111111111-111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111111-1111111-1-11-1-111-1-11-1
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+52−1−522222222−1+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+52−1−52−1−52−1−52−1−5200000022−1+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+52−1−52−1−520000000−1+52−1−52000000000
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+52−1−52-2-2-22-2221−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52000000-2-2−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+5200000001−521+52000000000
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+52−1−5222222-2-2−1+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+52000000-2-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+5200000001−521+52000000000
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+52−1−52-2-2-22-2-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521−521−521−521+521+521+521+5200000022−1+52−1−521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−520000000−1+52−1−52000000000
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+52−1−522-2-2-22-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52000000-221−521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−5200000001−521+52000000000
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+52−1−52-222-2-2-2-21−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−520000002-21−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+520000000−1+52−1−52000000000
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+52−1−522-2-2-2222−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+520000002-21−521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+520000000−1+52−1−52000000000
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+52−1−52-222-2-2221−521−521+521+521−521−521+521+52−1+52−1−521−521−521−521−521+521+521+521+52000000-221−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000001−521+52000000000
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+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+52−1+52−1+5200000022−1−52−1+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+520000000−1−52−1+52000000000
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+52-2-2-22-2221+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+52000000-2-2−1−52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−5200000001+521−52000000000
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+5222222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−52000000-2-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5200000001+521−52000000000
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+52-2-2-22-2-2-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521+521+521+521−521−521−521−5200000022−1−52−1+521+521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+520000000−1−52−1+52000000000
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+522-2-2-22-2-2−1−52−1−52−1+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+52000000-221+521−52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+5200000001+521−52000000000
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+52-222-2-2-2-21+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+520000002-21+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−520000000−1−52−1+52000000000
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+522-2-2-2222−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−520000002-21+521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−520000000−1−52−1+52000000000
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+52-222-2-2221+521+521−521−521+521+521−521−52−1−52−1+521+521+521+521+521−521−521−521−52000000-221+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+5200000001+521−52000000000
χ3322222-22-22222222222-20000-2-222-2-222000-200000002222-2-20000000022-2-22200-2-200000000000000-222000000000-200000
χ3422222-22-22222222222-20000-2-222-2-222000-200000002222-2-200000000-2-222-2-200-2-2000000000000002-2-2000000000200000
χ3522222-22-222222222-2-2-20000-2-222-2-22200020000000-2-2-2-2-2-20000000022-2-222002200000000000000-2-2-2000000000200000
χ3622222-22-222222222-2-2-20000-2-222-2-22200020000000-2-2-2-2-2-200000000-2-222-2-2002200000000000000222000000000-200000
χ372222-22-222222222200-2000022-2-222-2-22000-20022220000-2-2000000002222-2-20000-2-2000000000000-200000000-200020000
χ382222-22-222222222200-2000022-2-222-2-22000-20022220000-2-200000000-2-2-2-2220000-2-20000000000002000000002000-20000
χ392222-22-222222222200-2000022-2-222-2-2-2000200-2-2-2-20000-2-2000000002222-2-2000022000000000000-2000000002000-20000
χ402222-22-222222222200-2000022-2-222-2-2-2000200-2-2-2-20000-2-200000000-2-2-2-222000022000000000000200000000-200020000
χ412222-2-2-2-2222222220020000-2-2-2-2-2-2-2-202-2000000000000220000000022-2-2-2-20000002-22-20000000020000000002-2000000
χ422222-2-2-2-2222222220020000-2-2-2-2-2-2-2-202-20000000000002200000000-2-222220000002-22-200000000-2000000000-22000000
χ432222-2-2-2-2222222220020000-2-2-2-2-2-2-2-20-22000000000000220000000022-2-2-2-2000000-22-22000000002000000000-22000000
χ442222-2-2-2-2222222220020000-2-2-2-2-2-2-2-20-220000000000002200000000-2-22222000000-22-2200000000-20000000002-2000000
χ452-22-2-202022-2-222-2-22i−2i0i2i2−i2−i2002200-2-2000002−200002i−2i2i−2i00i2i2−i2−i2i2i2−i2−i22i−2i002i−2i00000000002−22−2000002-222−2−20000000i2−i200
χ462-22-2-202022-2-222-2-22i−2i0i2i2−i2−i2002200-2-2000002−200002i−2i2i−2i00i2i2−i2−i2i2i2−i2−i2−2i2i00−2i2i00000000002−22−200000-22−2−2220000000−i2i200
χ472-22-2-202022-2-222-2-22i−2i0−i2−i2i2i2002200-2-200000−2200002i−2i2i−2i00−i2−i2i2i2−i2−i2i2i22i−2i002i−2i0000000000−22−22000002-2−2−2220000000−i2i200
χ482-22-2-202022-2-222-2-22i−2i0−i2−i2i2i2002200-2-200000−2200002i−2i2i−2i00−i2−i2i2i2−i2−i2i2i2−2i2i00−2i2i0000000000−22−2200000-2222−2−20000000i2−i200
χ492-22-2-202022-2-222-2-2−2i2i0i2i2−i2−i2002200-2-200000−220000−2i2i−2i2i00i2i2−i2−i2i2i2−i2−i22i−2i002i−2i0000000000−22−2200000-2222−2−20000000−i2i200
χ502-22-2-202022-2-222-2-2−2i2i0i2i2−i2−i2002200-2-200000−220000−2i2i−2i2i00i2i2−i2−i2i2i2−i2−i2−2i2i00−2i2i0000000000−22−22000002-2−2−2220000000i2−i200
χ512-22-2-202022-2-222-2-2−2i2i0−i2−i2i2i2002200-2-2000002−20000−2i2i−2i2i00−i2−i2i2i2−i2−i2i2i22i−2i002i−2i00000000002−22−200000-22−2−2220000000i2−i200
χ522-22-2-202022-2-222-2-2−2i2i0−i2−i2i2i2002200-2-2000002−20000−2i2i−2i2i00−i2−i2i2i2−i2−i2i2i2−2i2i00−2i2i00000000002−22−2000002-222−2−20000000−i2i200
χ5344444-44-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−544-400001−51+5−1+5−1−51−51+5−1+5−1−5000-40000000−1+5−1+5−1−5−1−51−51+500000000000000001−51+500000000000000000000000000000000
χ5444444-44-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-4-400001−51+5−1+5−1−51−51+5−1+5−1−5000400000001−51−51+51+51−51+50000000000000000−1+5−1−500000000000000000000000000000000
χ5544444-44-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+544-400001+51−5−1−5−1+51+51−5−1−5−1+5000-40000000−1−5−1−5−1+5−1+51+51−500000000000000001+51−500000000000000000000000000000000
χ5644444-44-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4-4-400001+51−5−1−5−1+51+51−5−1−5−1+5000400000001+51+51−51−51+51−50000000000000000−1−5−1+500000000000000000000000000000000
χ574444-44-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500-40000−1+5−1−51−51+5−1+5−1−51−51+54000-400−1+5−1+5−1−5−1−500001−51+50000000000000000001−51+5000000000000000000000000000000
χ584444-44-44−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500-40000−1+5−1−51−51+5−1+5−1−51−51+5-40004001−51−51+51+500001−51+5000000000000000000−1+5−1−5000000000000000000000000000000
χ594444-44-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500-40000−1−5−1+51+51−5−1−5−1+51+51−54000-400−1−5−1−5−1+5−1+500001+51−50000000000000000001+51−5000000000000000000000000000000
χ604444-44-44−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500-40000−1−5−1+51+51−5−1−5−1+51+51−5-40004001+51+51−51−500001+51−5000000000000000000−1−5−1+5000000000000000000000000000000
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+504-4000000000000−1+5−1−500000000000000000000−1+51−5−1−51+500000000000000000000000000
χ624444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−500400001−51+51−51+51−51+51−51+50-44000000000000−1+5−1−5000000000000000000001−5−1+51+5−1−500000000000000000000000000
χ634444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500400001+51−51+51−51+51−51+51−504-4000000000000−1−5−1+500000000000000000000−1−51+5−1+51−500000000000000000000000000
χ644444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+500400001+51−51+51−51+51−51+51−50-44000000000000−1−5−1+5000000000000000000001+5−1−51−5−1+500000000000000000000000000
χ6544-4-4000044-4-4-4-4440002-22-200000000000000000000000002-22-22-22-2004i−4i000000000000000000000002i−2i2i−2i00000000000
χ6644-4-4000044-4-4-4-4440002-22-200000000000000000000000002-22-22-22-200−4i4i00000000000000000000000−2i2i−2i2i00000000000
χ6744-4-4000044-4-4-4-444000-22-220000000000000000000000000-22-22-22-22004i−4i00000000000000000000000−2i2i−2i2i00000000000
χ6844-4-4000044-4-4-4-444000-22-220000000000000000000000000-22-22-22-2200−4i4i000000000000000000000002i−2i2i−2i00000000000
χ694-44-440-4044-4-444-4-4000000000-4-4004400000000000000000000000004i−4i00−4i4i000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.