Finite Group Databasebeta

← Group #10609923

Character table — Group #10609923

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size1111111122222222222222224444444444888888888888888888888888888888101010101010101020202020202020204040
order1222222255101010101010101010101010101044444444444420202020202020202020202020202020202020202020202020202020444444444444444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111-1
χ41111111111111111111111111111-1-1-1-1-1-11-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-11
χ511111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-111-1-1
χ611111111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-111-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-11
χ811111111111111111111111111-1-1-1-1-1-111-111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1
χ9111111111111111111111111-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ10111111111111111111111111-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ11111111111111111111111111-1-111-1-111-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-11
χ12111111111111111111111111-1-111-1-111-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111-1
χ13111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ14111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1
χ15111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ16111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ1722222222−1+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+52−1−52−1−52222222222222−1+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+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000000
χ1822222222−1+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+52−1−52−1−522222-2-2-2-2-2-22-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+521−521−521+521+52000000000000000000
χ1922222222−1+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+52−1−52−1−5222-2-22222-2-2-2-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52000000000000000000
χ2022222222−1+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+52−1−52−1−5222-2-2-2-2-2-222-22−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000000
χ2122222222−1+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+52−1−52−1−52-2-22222-2-222-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52000000000000000000
χ2222222222−1+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+52−1−52−1−52-2-222-2-222-2-2-221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000000000
χ2322222222−1+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+52−1−52−1−52-2-2-2-222-2-2-2-2221−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52000000000000000000
χ2422222222−1+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+52−1−52−1−52-2-2-2-2-2-222222-21−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52000000000000000000
χ2522222222−1−52−1+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+52222222222222−1−52−1−52−1+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+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000000
χ2622222222−1−52−1+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+522222-2-2-2-2-2-22-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521+521−521−52000000000000000000
χ2722222222−1−52−1+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+5222-2-22222-2-2-2-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000000
χ2822222222−1−52−1+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+5222-2-2-2-2-2-222-22−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52000000000000000000
χ2922222222−1−52−1+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+52-2-22222-2-222-2-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000000000000000000
χ3022222222−1−52−1+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+52-2-222-2-222-2-2-221+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000000000
χ3122222222−1−52−1+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+52-2-2-2-222-2-2-2-2221+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+52000000000000000000
χ3222222222−1−52−1+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+52-2-2-2-2-2-222222-21+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52000000000000000000
χ33222-2-2-22-22222222-2-22-2-2-2-2-2-22-200000000002-22-200000000000000000000000022-2-200000000002-200
χ34222-2-2-22-22222222-2-22-2-2-2-2-2-22-200000000002-22-2000000000000000000000000-2-2220000000000-2200
χ35222-2-2-22-22222222-2-22-2-2-2-2-2-2-220000000000-22-2200000000000000000000000022-2-20000000000-2200
χ36222-2-2-22-22222222-2-22-2-2-2-2-2-2-220000000000-22-22000000000000000000000000-2-22200000000002-200
χ3722-2-22-2-22222-22-2-22-2-22-22-22-2002i−2i0000000000002i−2i2i−2i00000000000000000000000022-2-200002i−2i0000
χ3822-2-22-2-22222-22-2-22-2-22-22-22-2002i−2i0000000000002i−2i2i−2i000000000000000000000000-2-2220000−2i2i0000
χ3922-2-22-2-22222-22-2-22-2-22-22-22-200−2i2i000000000000−2i2i−2i2i00000000000000000000000022-2-20000−2i2i0000
χ4022-2-22-2-22222-22-2-22-2-22-22-22-200−2i2i000000000000−2i2i−2i2i000000000000000000000000-2-22200002i−2i0000
χ412-222-2-2-2222-2-2-2-2222222-2-2-2-20000002i−2i0000000000000000000000002i−2i2i−2i00002i−2i2i−2i00002-200000000
χ422-222-2-2-2222-2-2-2-2222222-2-2-2-20000002i−2i0000000000000000000000002i−2i2i−2i0000−2i2i−2i2i0000-2200000000
χ432-222-2-2-2222-2-2-2-2222222-2-2-2-2000000−2i2i000000000000000000000000−2i2i−2i2i00002i−2i2i−2i0000-2200000000
χ442-222-2-2-2222-2-2-2-2222222-2-2-2-2000000−2i2i000000000000000000000000−2i2i−2i2i0000−2i2i−2i2i00002-200000000
χ452-22-222-2-222-2-2-2-22-2-22-2-2222200002-200000000000000000000002-22-2000000002i−2i−2i2i2i−2i2i−2i0000000000
χ462-22-222-2-222-2-2-2-22-2-22-2-2222200002-200000000000000000000002-22-200000000−2i2i2i−2i−2i2i−2i2i0000000000
χ472-22-222-2-222-2-2-2-22-2-22-2-222220000-220000000000000000000000-22-22000000002i−2i−2i2i−2i2i−2i2i0000000000
χ482-22-222-2-222-2-2-2-22-2-22-2-222220000-220000000000000000000000-22-2200000000−2i2i2i−2i2i−2i2i−2i0000000000
χ492-2-222-22-222-22-22-2-22-2-222-22-2000000002i−2i00000000002i−2i2i−2i000000000000000000002i−2i−2i2i002-2000000
χ502-2-222-22-222-22-22-2-22-2-222-22-2000000002i−2i00000000002i−2i2i−2i00000000000000000000−2i2i2i−2i00-22000000
χ512-2-222-22-222-22-22-2-22-2-222-22-200000000−2i2i0000000000−2i2i−2i2i000000000000000000002i−2i−2i2i00-22000000
χ522-2-222-22-222-22-22-2-22-2-222-22-200000000−2i2i0000000000−2i2i−2i2i00000000000000000000−2i2i2i−2i002-2000000
χ53444-4-4-44-4−1+5−1−5−1+5−1+5−1−5−1−5−1+51−51−5−1−51+51+51−51−51+51+54-40000000000−1+51−5−1−51+5000000000000000000000000000000000000000000
χ54444-4-4-44-4−1+5−1−5−1+5−1+5−1−5−1−5−1+51−51−5−1−51+51+51−51−51+51+5-4400000000001−5−1+51+5−1−5000000000000000000000000000000000000000000
χ55444-4-4-44-4−1−5−1+5−1−5−1−5−1+5−1+5−1−51+51+5−1+51−51−51+51+51−51−54-40000000000−1−51+5−1+51−5000000000000000000000000000000000000000000
χ56444-4-4-44-4−1−5−1+5−1−5−1−5−1+5−1+5−1−51+51+5−1+51−51−51+51+51−51−5-4400000000001+5−1−51−5−1+5000000000000000000000000000000000000000000
χ5744-44-44-4-4444-44-4-4-44-4-44-44-440000000000000000000000000000000000000000000000000000000000
χ5844-44-44-4-4−1+5−1−5−1+51−5−1−51+51−51−5−1+51+51+5−1−51−5−1+51+5−1−5000000000000000000000000−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ7000000000000000000000000000000
χ5944-44-44-4-4−1+5−1−5−1+51−5−1−51+51−51−5−1+51+51+5−1−51−5−1+51+5−1−50000000000000000000000002ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7000000000000000000000000000000
χ6044-44-44-4-4−1−5−1+5−1−51+5−1+51−51+51+5−1−51−51−5−1+51+5−1−51−5−1+50000000000000000000000002ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ19000000000000000000000000000000
χ6144-44-44-4-4−1−5−1+5−1−51+5−1+51−51+51+5−1−51−51−5−1+51+5−1−51−5−1+5000000000000000000000000−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19000000000000000000000000000000
χ6244-4-44-4-44−1+5−1−5−1+51−5−1−51+51−5−1+51−51+5−1−51+5−1+51−5−1−51+5004i−4i000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ700000000000000000000000000000000000000
χ6344-4-44-4-44−1+5−1−5−1+51−5−1−51+51−5−1+51−51+5−1−51+5−1+51−5−1−51+500−4i4i0000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ700000000000000000000000000000000000000
χ6444-4-44-4-44−1−5−1+5−1−51+5−1+51−51+5−1−51+51−5−1+51−5−1−51+5−1+51−5004i−4i000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ1900000000000000000000000000000000000000
χ6544-4-44-4-44−1−5−1+5−1−51+5−1+51−51+5−1−51+51−5−1+51−5−1−51+5−1+51−500−4i4i0000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ1900000000000000000000000000000000000000
χ664-444-4-4-44−1+5−1−51−51−51+51+5−1+5−1+5−1+5−1−5−1−5−1−51−51−51+51+50000004i−4i000000000000000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ70000000000000000000000
χ674-444-4-4-44−1+5−1−51−51−51+51+5−1+5−1+5−1+5−1−5−1−5−1−51−51−51+51+5000000−4i4i0000000000000000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ70000000000000000000000
χ684-444-4-4-44−1−5−1+51+51+51−51−5−1−5−1−5−1−5−1+5−1+5−1+51+51+51−51−50000004i−4i000000000000000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ190000000000000000000000
χ694-444-4-4-44−1−5−1+51+51+51−51−5−1−5−1−5−1−5−1+5−1+5−1+51+51+51−51−5000000−4i4i0000000000000000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ190000000000000000000000
χ704-44-444-4-4−1+5−1−51−51−51+51+5−1+51−51−5−1−51+51+5−1+5−1+5−1−5−1−500004-40000000000000000000000−1+51−5−1−51+500000000000000000000000000
χ714-44-444-4-4−1+5−1−51−51−51+51+5−1+51−51−5−1−51+51+5−1+5−1+5−1−5−1−50000-4400000000000000000000001−5−1+51+5−1−500000000000000000000000000
χ724-44-444-4-4−1−5−1+51+51+51−51−5−1−51+51+5−1+51−51−5−1−5−1−5−1+5−1+500004-40000000000000000000000−1−51+5−1+51−500000000000000000000000000
χ734-44-444-4-4−1−5−1+51+51+51−51−5−1−51+51+5−1+51−51−5−1−5−1−5−1+5−1+50000-4400000000000000000000001+5−1−51−5−1+500000000000000000000000000
χ744-4-444-44-4−1+5−1−51−5−1+51+5−1−51−51−5−1+51+51+5−1−5−1+51−5−1−51+5000000004i−4i0000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ70000000000000000000000000000000000
χ754-4-444-44-4−1+5−1−51−5−1+51+5−1−51−51−5−1+51+51+5−1−5−1+51−5−1−51+500000000−4i4i00000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ70000000000000000000000000000000000
χ764-4-444-44-4−1−5−1+51+5−1−51−5−1+51+51+5−1−51−51−5−1+5−1−51+5−1+51−5000000004i−4i0000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ190000000000000000000000000000000000
χ774-4-444-44-4−1−5−1+51+5−1−51−5−1+51+51+5−1−51−51−5−1+5−1−51+5−1+51−500000000−4i4i00000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ190000000000000000000000000000000000
χ784-4-4-4-444444-44-44-44-4-44-4-44-440000000000000000000000000000000000000000000000000000000000
χ794-4-4-4-4444−1+5−1−51−5−1+51+5−1−51−5−1+51−51+5−1−51+51−5−1+51+5−1−5000000000000000000000000000000000000−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ7000000000000000000
χ804-4-4-4-4444−1+5−1−51−5−1+51+5−1−51−5−1+51−51+5−1−51+51−5−1+51+5−1−50000000000000000000000000000000000002ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ7000000000000000000
χ814-4-4-4-4444−1−5−1+51+5−1−51−5−1+51+5−1−51+51−5−1+51−51+5−1−51−5−1+50000000000000000000000000000000000002ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ19000000000000000000
χ824-4-4-4-4444−1−5−1+51+5−1−51−5−1+51+5−1−51+51−5−1+51−51+5−1−51−5−1+5000000000000000000000000000000000000−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.