Finite Group Databasebeta

← Group #10608607

Character table — Group #10608607

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size111111112222222222222222444444888888888888888888888888888888882020202020202020202020204040
order1222222255101010101010101010101010101022444444441010101020202020202020202020202020202020202020202020202022222244444444
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11
χ41111111111111111111111111111-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1
χ511111111111111111111111111-1-111-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-1
χ611111111111111111111111111-1-111-11-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-11
χ711111111111111111111111111-1-1-1-11-11-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ811111111111111111111111111-1-1-1-11-11-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ9111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-1
χ10111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11
χ11111111111111111111111111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-11111-1-1
χ12111111111111111111111111-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-111
χ13111111111111111111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111
χ14111111111111111111111111-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1
χ15111111111111111111111111-1-1-1-1-1-111-11-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-11
χ16111111111111111111111111-1-1-1-1-1-111-11-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-111-1-11-1
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+52−1−522222222222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000000
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+52−1−522222-2-2-2-2-22−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+5200000000000000
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+52−1−5222-2-222-22-2-2−1+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+52−1+52−1+52−1−52−1−521−521−521+521+5200000000000000
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+52−1−5222-2-2-2-22-22-2−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−5200000000000000
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+52−1−52-2-222222-2-2-21−521−521+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+52−1−52−1−521−521−521+521+521−521−521+521+5200000000000000
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+52−1−52-2-222-2-2-222-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000000
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+52−1−52-2-2-2-222-2-2221−521−521+521+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+52−1+52−1+52−1−52−1−5200000000000000
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+52−1−52-2-2-2-2-2-222-221−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+5200000000000000
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+522222222222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000000000
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+522222-2-2-2-2-22−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5200000000000000
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+5222-2-222-22-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−5200000000000000
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+5222-2-2-2-22-22-2−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+5200000000000000
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+52-2-222222-2-2-21+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5200000000000000
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+52-2-222-2-2-222-21+521+521−521−521+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+52−1−52−1−52−1+52−1+5200000000000000
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+52-2-2-2-222-2-2221+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+5200000000000000
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+52-2-2-2-2-2-222-221+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−5200000000000000
χ33222-2-22-2-2222-2-22-2-222-222-2-2-200002i−2i0000000000002i−2i2i−2i0000000000000000002-20000002i−2i00
χ34222-2-22-2-2222-2-22-2-222-222-2-2-200002i−2i0000000000002i−2i2i−2i000000000000000000-22000000−2i2i00
χ35222-2-22-2-2222-2-22-2-222-222-2-2-20000−2i2i000000000000−2i2i−2i2i0000000000000000002-2000000−2i2i00
χ36222-2-22-2-2222-2-22-2-222-222-2-2-20000−2i2i000000000000−2i2i−2i2i000000000000000000-220000002i−2i00
χ3722-2-22-2-2222222222-2-2-2-2-2-2-2-22-2000000002-22-20000000000000000000000000000002i−2i2i−2i0000
χ3822-2-22-2-2222222222-2-2-2-2-2-2-2-22-2000000002-22-2000000000000000000000000000000−2i2i−2i2i0000
χ3922-2-22-2-2222222222-2-2-2-2-2-2-2-2-2200000000-22-220000000000000000000000000000002i−2i−2i2i0000
χ4022-2-22-2-2222222222-2-2-2-2-2-2-2-2-2200000000-22-22000000000000000000000000000000−2i2i2i−2i0000
χ412-2-22-22-2222-22-2-22-22-2-22-2-222002-200000000000000000000002-22-2000000002-2002-200000000
χ422-2-22-22-2222-22-2-22-22-2-22-2-222002-200000000000000000000002-22-200000000-2200-2200000000
χ432-2-22-22-2222-22-2-22-22-2-22-2-22200-220000000000000000000000-22-22000000002-200-2200000000
χ442-2-22-22-2222-22-2-22-22-2-22-2-22200-220000000000000000000000-22-2200000000-22002-200000000
χ45444-4-44-4-4−1+5−1−5−1+51−51−5−1−51+51+5−1+5−1+51−5−1−5−1−51+51−51+500004i−4i000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7000000000000000000000000000000
χ46444-4-44-4-4−1+5−1−5−1+51−51−5−1−51+51+5−1+5−1+51−5−1−5−1−51+51−51+50000−4i4i0000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7000000000000000000000000000000
χ47444-4-44-4-4−1−5−1+5−1−51+51+5−1+51−51−5−1−5−1−51+5−1+5−1+51−51+51−500004i−4i000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19000000000000000000000000000000
χ48444-4-44-4-4−1−5−1+5−1−51+51+5−1+51−51−5−1−5−1−51+5−1+5−1+51−51+51−50000−4i4i0000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19000000000000000000000000000000
χ4944-44-4-44-4444-4-44-4-4-4-44-4-44440000000000000000000000000000000000000000000000000000
χ5044-44-4-44-4−1+5−1−5−1+51−51−5−1−51+51+51−51−5−1+51+51+5−1−5−1+5−1−50000000000000000000000000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18000000000000000000
χ5144-44-4-44-4−1+5−1−5−1+51−51−5−1−51+51+51−51−5−1+51+51+5−1−5−1+5−1−5000000000000000000000000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ18000000000000000000
χ5244-44-4-44-4−1−5−1+5−1−51+51+5−1+51−51−51+51+5−1−51−51−5−1+5−1−5−1+5000000000000000000000000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ14000000000000000000
χ5344-44-4-44-4−1−5−1+5−1−51+51+5−1+51−51−51+51+5−1−51−51−5−1+5−1−5−1+50000000000000000000000000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14000000000000000000
χ5444-4-44-4-44−1+5−1−5−1+5−1+5−1+5−1−5−1−5−1−51−51−51−51+51+51+51−51+54-400000000−1+51−5−1−51+500000000000000000000000000000000000000
χ5544-4-44-4-44−1+5−1−5−1+5−1+5−1+5−1−5−1−5−1−51−51−51−51+51+51+51−51+5-44000000001−5−1+51+5−1−500000000000000000000000000000000000000
χ5644-4-44-4-44−1−5−1+5−1−5−1−5−1−5−1+5−1+5−1+51+51+51+51−51−51−51+51−54-400000000−1−51+5−1+51−500000000000000000000000000000000000000
χ5744-4-44-4-44−1−5−1+5−1−5−1−5−1−5−1+5−1+5−1+51+51+51+51−51−51−51+51−5-44000000001+5−1−51−5−1+500000000000000000000000000000000000000
χ584-4444-4-4-444-4-44-4-44-44-4-44-4440000000000000000000000000000000000000000000000000000
χ594-4444-4-4-4−1+5−1−51−51−5−1+51+51+5−1−51−5−1+51−51+5−1−51+5−1+5−1−500000000000000000000000000000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ1800000000000000
χ604-4444-4-4-4−1+5−1−51−51−5−1+51+51+5−1−51−5−1+51−51+5−1−51+5−1+5−1−50000000000000000000000000000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ1800000000000000
χ614-4444-4-4-4−1−5−1+51+51+5−1−51−51−5−1+51+5−1−51+51−5−1+51−5−1−5−1+50000000000000000000000000000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ1400000000000000
χ624-4444-4-4-4−1−5−1+51+51+5−1−51−51−5−1+51+5−1−51+51−5−1+51−5−1−5−1+500000000000000000000000000000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ1400000000000000
χ634-44-4-4-44444-44-4-44-4-444-444-4-40000000000000000000000000000000000000000000000000000
χ644-44-4-4-444−1+5−1−51−5−1+51−51+5−1−51+51−5−1+5−1+51+5−1−5−1−51−51+500000000000000−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ70000000000000000000000000000000000
χ654-44-4-4-444−1+5−1−51−5−1+51−51+5−1−51+51−5−1+5−1+51+5−1−5−1−51−51+5000000000000002ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ70000000000000000000000000000000000
χ664-44-4-4-444−1−5−1+51+5−1−51+51−5−1+51−51+5−1−5−1−51−5−1+5−1+51+51−5000000000000002ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ190000000000000000000000000000000000
χ674-44-4-4-444−1−5−1+51+5−1−51+51−5−1+51−51+5−1−5−1−51−5−1+5−1+51+51−500000000000000−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ190000000000000000000000000000000000
χ684-4-44-44-44−1+5−1−51−5−1+51−51+5−1−51+5−1+51−51−5−1−51+51+5−1+5−1−5004-40000000000000000000000−1+51−5−1−51+50000000000000000000000
χ694-4-44-44-44−1+5−1−51−5−1+51−51+5−1−51+5−1+51−51−5−1−51+51+5−1+5−1−500-4400000000000000000000001−5−1+51+5−1−50000000000000000000000
χ704-4-44-44-44−1−5−1+51+5−1−51+51−5−1+51−5−1−51+51+5−1+51−51−5−1−5−1+5004-40000000000000000000000−1−51+5−1+51−50000000000000000000000
χ714-4-44-44-44−1−5−1+51+5−1−51+51−5−1+51−5−1−51+51+5−1+51−51−5−1−5−1+500-4400000000000000000000001+5−1−51−5−1+50000000000000000000000
χ724-4-4-4444-444-4-44-4-444-444-44-4-40000000000000000000000000000000000000000000000000000
χ734-4-4-4444-4−1+5−1−51−51−5−1+51+51+5−1−5−1+51−5−1+5−1−51+5−1−51−51+50000000000000000000000−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ700000000000000000000000000
χ744-4-4-4444-4−1+5−1−51−51−5−1+51+51+5−1−5−1+51−5−1+5−1−51+5−1−51−51+500000000000000000000002ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ700000000000000000000000000
χ754-4-4-4444-4−1−5−1+51+51+5−1−51−51−5−1+5−1−51+5−1−5−1+51−5−1+51+51−500000000000000000000002ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ1900000000000000000000000000
χ764-4-4-4444-4−1−5−1+51+51+5−1−51−51−5−1+5−1−51+5−1−5−1+51−5−1+51+51−50000000000000000000000−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ1900000000000000000000000000

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