Finite Group Databasebeta

← Group #65243

Character table — Group #65243

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1122222222222444444444444442020202011222222222224444444444444420202020
order1222255101010101010441010101020202020202020202444222221010101010101010441010101020202020202020202444
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1111111111111111111111111111-1-1-1-1
χ31111111111111-1-11111-1-1-1-1-1-1-1-111-1-11111111111111-1-11111-1-1-1-1-1-1-1-111-1-1
χ41111111111111-1-11111-1-1-1-1-1-1-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111
χ5111-1-11111-1-1-1-1i−i11-1-1iiii−i−i−i−i1-1i−i111-1-11111-1-1-1-1i−i11-1-1iiii−i−i−i−i1-1i−i
χ6111-1-11111-1-1-1-1i−i11-1-1iiii−i−i−i−i-11−ii111-1-11111-1-1-1-1i−i11-1-1iiii−i−i−i−i-11−ii
χ7111-1-11111-1-1-1-1−ii11-1-1−i−i−i−iiiii1-1−ii111-1-11111-1-1-1-1−ii11-1-1−i−i−i−iiiii1-1−ii
χ8111-1-11111-1-1-1-1−ii11-1-1−i−i−i−iiiii-11i−i111-1-11111-1-1-1-1−ii11-1-1−i−i−i−iiiii-11i−i
χ922222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000022222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000
χ1022222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52000022222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+520000
χ1122222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000022222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000
χ1222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52000022222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−520000
χ13222-2-2−1+52−1−52−1+52−1−521−521−521+521+522i−2i−1+52−1−521−521+52−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ70000222-2-2−1+52−1−52−1+52−1−521−521−521+521+522i−2i−1+52−1−521−521+52−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ70000
χ14222-2-2−1+52−1−52−1+52−1−521−521−521+521+52−2i2i−1+52−1−521−521+52ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ70000222-2-2−1+52−1−52−1+52−1−521−521−521+521+52−2i2i−1+52−1−521−521+52ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ70000
χ15222-2-2−1−52−1+52−1−52−1+521+521+521−521−522i−2i−1−52−1+521+521−52−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ190000222-2-2−1−52−1+52−1−52−1+521+521+521−521−522i−2i−1−52−1+521+521−52−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ190000
χ16222-2-2−1−52−1+52−1−52−1+521+521+521−521−52−2i2i−1−52−1+521+521−52ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ190000222-2-2−1−52−1+52−1−52−1+521+521+521−521−52−2i2i−1−52−1+521+521−52ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ190000
χ1722-22-22222222200-2-2-2-200000000000022-22-22222222200-2-2-2-2000000000000
χ1822-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52001−521+521−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18000022-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52001−521+521−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000
χ1922-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52001−521+521−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18000022-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52001−521+521−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000
χ2022-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52001+521−521+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14000022-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52001+521−521+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000
χ2122-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52001+521−521+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14000022-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52001+521−521+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000
χ2222-2-222222-2-2-2-200-2-22200000000000022-2-222222-2-2-2-200-2-222000000000000
χ2322-2-22−1+52−1−52−1+52−1−521−521−521+521+52001−521+52−1+52−1−52−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7000022-2-22−1+52−1−52−1+52−1−521−521−521+521+52001−521+52−1+52−1−52−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ70000
χ2422-2-22−1+52−1−52−1+52−1−521−521−521+521+52001−521+52−1+52−1−52ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7000022-2-22−1+52−1−52−1+52−1−521−521−521+521+52001−521+52−1+52−1−52ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ70000
χ2522-2-22−1−52−1+52−1−52−1+521+521+521−521−52001+521−52−1−52−1+52ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19000022-2-22−1−52−1+52−1−52−1+521+521+521−521−52001+521−52−1−52−1+52ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ190000
χ2622-2-22−1−52−1+52−1−52−1+521+521+521−521−52001+521−52−1−52−1+52−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19000022-2-22−1−52−1+52−1−52−1+521+521+521−521−52001+521−52−1−52−1+52−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ190000
χ274-400044-4-400000000000000000000004-400044-4-40000000000000000000000
χ284-4000−1+5−1−51−51+52ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ180000000000000000004-4000−1+5−1−51−51+52ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18000000000000000000
χ294-4000−1+5−1−51−51+5−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ180000000000000000004-4000−1+5−1−51−51+5−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ18000000000000000000
χ304-4000−1−5−1+51+51−5−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ140000000000000000004-4000−1−5−1+51+51−5−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ14000000000000000000
χ314-4000−1−5−1+51+51−52ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ140000000000000000004-4000−1−5−1+51+51−52ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14000000000000000000
χ321111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ33111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ341111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111
χ351111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1
χ36111-1-11111-1-1-1-1i−i11-1-1iiii−i−i−i−i1-1i−i-1-1-111-1-1-1-11111−ii-1-111−i−i−i−iiiii-11−ii
χ37111-1-11111-1-1-1-1i−i11-1-1iiii−i−i−i−i-11−ii-1-1-111-1-1-1-11111−ii-1-111−i−i−i−iiiii1-1i−i
χ38111-1-11111-1-1-1-1−ii11-1-1−i−i−i−iiiii1-1−ii-1-1-111-1-1-1-11111i−i-1-111iiii−i−i−i−i-11i−i
χ39111-1-11111-1-1-1-1−ii11-1-1−i−i−i−iiiii-11i−i-1-1-111-1-1-1-11111i−i-1-111iiii−i−i−i−i1-1−ii
χ4022222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000-2-2-2-2-21−521+521−521+521−521−521+521+52-2-21−521+521−521+521−521−521+521+521−521−521+521+520000
χ4122222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+520000-2-2-2-2-21−521+521−521+521−521−521+521+52221−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000
χ4222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000-2-2-2-2-21+521−521+521−521+521+521−521−52-2-21+521−521+521−521+521+521−521−521+521+521−521−520000
χ4322222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−520000-2-2-2-2-21+521−521+521−521+521+521−521−52221+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+520000
χ44222-2-2−1+52−1−52−1+52−1−521−521−521+521+522i−2i−1+52−1−521−521+52−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ70000-2-2-2221−521+521−521+52−1+52−1+52−1−52−1−52−2i2i1−521+52−1+52−1−52ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ70000
χ45222-2-2−1+52−1−52−1+52−1−521−521−521+521+52−2i2i−1+52−1−521−521+52ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ70000-2-2-2221−521+521−521+52−1+52−1+52−1−52−1−522i−2i1−521+52−1+52−1−52−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ70000
χ46222-2-2−1−52−1+52−1−52−1+521+521+521−521−522i−2i−1−52−1+521+521−52−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ190000-2-2-2221+521−521+521−52−1−52−1−52−1+52−1+52−2i2i1+521−52−1−52−1+52ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ190000
χ47222-2-2−1−52−1+52−1−52−1+521+521+521−521−52−2i2i−1−52−1+521+521−52ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ190000-2-2-2221+521−521+521−52−1−52−1−52−1+52−1+522i−2i1+521−52−1−52−1+52−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ190000
χ4822-22-22222222200-2-2-2-2000000000000-2-22-22-2-2-2-2-2-2-2-2002222000000000000
χ4922-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52001−521+521−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000-2-22-221−521+521−521+521−521−521+521+5200−1+52−1−52−1+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000
χ5022-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52001−521+521−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ180000-2-22-221−521+521−521+521−521−521+521+5200−1+52−1−52−1+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ180000
χ5122-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52001+521−521+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000-2-22-221+521−521+521−521+521+521−521−5200−1−52−1+52−1−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000
χ5222-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52001+521−521+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ140000-2-22-221+521−521+521−521+521+521−521−5200−1−52−1+52−1−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ140000
χ5322-2-222222-2-2-2-200-2-222000000000000-2-222-2-2-2-2-222220022-2-2000000000000
χ5422-2-22−1+52−1−52−1+52−1−521−521−521+521+52001−521+52−1+52−1−52−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ70000-2-222-21−521+521−521+52−1+52−1+52−1−52−1−5200−1+52−1−521−521+52ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ70000
χ5522-2-22−1+52−1−52−1+52−1−521−521−521+521+52001−521+52−1+52−1−52ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ70000-2-222-21−521+521−521+52−1+52−1+52−1−52−1−5200−1+52−1−521−521+52−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ70000
χ5622-2-22−1−52−1+52−1−52−1+521+521+521−521−52001+521−52−1−52−1+52ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ190000-2-222-21+521−521+521−52−1−52−1−52−1+52−1+5200−1−52−1+521+521−52−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ190000
χ5722-2-22−1−52−1+52−1−52−1+521+521+521−521−52001+521−52−1−52−1+52−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ190000-2-222-21+521−521+521−52−1−52−1−52−1+52−1+5200−1−52−1+521+521−52ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ190000
χ584-400044-4-40000000000000000000000-44000-4-4440000000000000000000000
χ594-4000−1+5−1−51−51+52ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18000000000000000000-440001−51+5−1+5−1−5−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ18000000000000000000
χ604-4000−1+5−1−51−51+5−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ18000000000000000000-440001−51+5−1+5−1−52ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ18000000000000000000
χ614-4000−1−5−1+51+51−5−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ14000000000000000000-440001+51−5−1−5−1+52ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14000000000000000000
χ624-4000−1−5−1+51+51−52ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ14000000000000000000-440001+51−5−1−5−1+5−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ14000000000000000000

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