Finite Group Databasebeta

← Group #66037

Character table — Group #66037

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111122222244442222444444888822224444448888555510101010101020202020
order1222444444244451010102020202020201020202051010102020202020201020202022224444442444
χ111111111111111111111111111111111111111111111111111111111
χ21111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1
χ3111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1
χ4111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111
χ51111-1-111-1-11-11-11111-1-111-1-11-11-11111-1-111-1-11-11-11111-1-111-1-11-11-1
χ61111-1-111-1-1-11-111111-1-111-1-1-11-111111-1-111-1-1-11-111111-1-111-1-1-11-11
χ71111-1-1-1-1111-1-111111-1-1-1-1111-1-111111-1-1-1-1111-1-111111-1-1-1-1111-1-11
χ81111-1-1-1-111-111-11111-1-1-1-111-111-11111-1-1-1-111-111-11111-1-1-1-111-111-1
χ922-2-200002i−2i000022-2-200002i−2i000022-2-200002i−2i000022-2-200002i−2i0000
χ1022-2-20000−2i2i000022-2-20000−2i2i000022-2-20000−2i2i000022-2-20000−2i2i0000
χ112-22-2002i−2i0000002-22-2002i−2i0000002-22-2002i−2i0000002-22-2002i−2i000000
χ122-22-200−2i2i0000002-22-200−2i2i0000002-22-200−2i2i0000002-22-200−2i2i000000
χ132-2-222i−2i000000002-2-222i−2i000000002-2-222i−2i000000002-2-222i−2i00000000
χ142-2-22−2i2i000000002-2-22−2i2i000000002-2-22−2i2i000000002-2-22−2i2i00000000
χ15111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ161111111111-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ17111111-1-1-1-111-1-1111111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111
χ18111111-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1
χ191111-1-111-1-11-11-11111-1-111-1-11-11-11111-1-111-1-11-11-1-1-1-1-111-1-111-11-11
χ201111-1-111-1-1-11-111111-1-111-1-1-11-111111-1-111-1-1-11-11-1-1-1-111-1-1111-11-1
χ211111-1-1-1-1111-1-111111-1-1-1-1111-1-111111-1-1-1-1111-1-11-1-1-1-11111-1-1-111-1
χ221111-1-1-1-111-111-11111-1-1-1-111-111-11111-1-1-1-111-111-1-1-1-1-11111-1-11-1-11
χ2322-2-200002i−2i000022-2-200002i−2i000022-2-200002i−2i0000-2-2220000−2i2i0000
χ2422-2-20000−2i2i000022-2-20000−2i2i000022-2-20000−2i2i0000-2-22200002i−2i0000
χ252-22-2002i−2i0000002-22-2002i−2i0000002-22-2002i−2i000000-22-2200−2i2i000000
χ262-22-200−2i2i0000002-22-200−2i2i0000002-22-200−2i2i000000-22-22002i−2i000000
χ272-2-222i−2i000000002-2-222i−2i000000002-2-222i−2i00000000-222-2−2i2i00000000
χ282-2-22−2i2i000000002-2-22−2i2i000000002-2-22−2i2i00000000-222-22i−2i00000000
χ2922222222222222−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−5200000000000000
χ302222222222-2-2-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+5200000000000000
χ31222222-2-2-2-222-2-2−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+521−521−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−521+521+5200000000000000
χ32222222-2-2-2-2-2-222−1+52−1+52−1+52−1+52−1+52−1+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+521+521+52−1−52−1−5200000000000000
χ332222-2-222-2-22-22-2−1+52−1+52−1+52−1+521−521−52−1+52−1+521−521−52−1+521−52−1+521−52−1−52−1−52−1−52−1−521+521+52−1−52−1−521+521+52−1−521+52−1−521+5200000000000000
χ342222-2-222-2-2-22-22−1+52−1+52−1+52−1+521−521−52−1+52−1+521−521−521−52−1+521−52−1+52−1−52−1−52−1−52−1−521+521+52−1−52−1−521+521+521+52−1−521+52−1−5200000000000000
χ352222-2-2-2-2222-2-22−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+52−1+521−521−52−1+52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−52−1−521+521+52−1−5200000000000000
χ362222-2-2-2-222-222-2−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+521−52−1+52−1+521−52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−521+52−1−52−1−521+5200000000000000
χ3744-4-400004i−4i0000−1+5−1+51−51−50000−2ζ11−2ζ192ζ11+2ζ190000−1−5−1−51+51+50000−2ζ3−2ζ72ζ3+2ζ7000000000000000000
χ3844-4-40000−4i4i0000−1+5−1+51−51−500002ζ11+2ζ19−2ζ11−2ζ190000−1−5−1−51+51+500002ζ3+2ζ7−2ζ3−2ζ7000000000000000000
χ394-44-4004i−4i000000−1+51−5−1+51−500−2ζ11−2ζ192ζ11+2ζ19000000−1−51+5−1−51+500−2ζ3−2ζ72ζ3+2ζ700000000000000000000
χ404-44-400−4i4i000000−1+51−5−1+51−5002ζ11+2ζ19−2ζ11−2ζ19000000−1−51+5−1−51+5002ζ3+2ζ7−2ζ3−2ζ700000000000000000000
χ414-4-444i−4i00000000−1+51−51−5−1+5−2ζ11−2ζ192ζ11+2ζ1900000000−1−51+51+5−1−5−2ζ3−2ζ72ζ3+2ζ70000000000000000000000
χ424-4-44−4i4i00000000−1+51−51−5−1+52ζ11+2ζ19−2ζ11−2ζ1900000000−1−51+51+5−1−52ζ3+2ζ7−2ζ3−2ζ70000000000000000000000
χ4322222222222222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+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
χ442222222222-2-2-2-2−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−5200000000000000
χ45222222-2-2-2-222-2-2−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−521+521+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+521−521−5200000000000000
χ46222222-2-2-2-2-2-222−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+521+521+52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−521−521−52−1+52−1+5200000000000000
χ472222-2-222-2-22-22-2−1−52−1−52−1−52−1−521+521+52−1−52−1−521+521+52−1−521+52−1−521+52−1+52−1+52−1+52−1+521−521−52−1+52−1+521−521−52−1+521−52−1+521−5200000000000000
χ482222-2-222-2-2-22-22−1−52−1−52−1−52−1−521+521+52−1−52−1−521+521+521+52−1−521+52−1−52−1+52−1+52−1+52−1+521−521−52−1+52−1+521−521−521−52−1+521−52−1+5200000000000000
χ492222-2-2-2-2222-2-22−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−52−1−521+521+52−1−52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+52−1+521−521−52−1+5200000000000000
χ502222-2-2-2-222-222-2−1−52−1−52−1−52−1−521+521+521+521+52−1−52−1−521+52−1−52−1−521+52−1+52−1+52−1+52−1+521−521−521−521−52−1+52−1+521−52−1+52−1+521−5200000000000000
χ5144-4-400004i−4i0000−1−5−1−51+51+50000−2ζ3−2ζ72ζ3+2ζ70000−1+5−1+51−51−50000−2ζ11−2ζ192ζ11+2ζ19000000000000000000
χ5244-4-40000−4i4i0000−1−5−1−51+51+500002ζ3+2ζ7−2ζ3−2ζ70000−1+5−1+51−51−500002ζ11+2ζ19−2ζ11−2ζ19000000000000000000
χ534-44-4004i−4i000000−1−51+5−1−51+500−2ζ3−2ζ72ζ3+2ζ7000000−1+51−5−1+51−500−2ζ11−2ζ192ζ11+2ζ1900000000000000000000
χ544-44-400−4i4i000000−1−51+5−1−51+5002ζ3+2ζ7−2ζ3−2ζ7000000−1+51−5−1+51−5002ζ11+2ζ19−2ζ11−2ζ1900000000000000000000
χ554-4-444i−4i00000000−1−51+51+5−1−5−2ζ3−2ζ72ζ3+2ζ700000000−1+51−51−5−1+5−2ζ11−2ζ192ζ11+2ζ190000000000000000000000
χ564-4-44−4i4i00000000−1−51+51+5−1−52ζ3+2ζ7−2ζ3−2ζ700000000−1+51−51−5−1+52ζ11+2ζ19−2ζ11−2ζ190000000000000000000000

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