Finite Group Databasebeta

← Group #13103715

Character table — Group #13103715

Order 1600.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size1124445588810101010102020202248881010161616202020202040404022488810101616162020202020404040551020202025254040405050505050100100100
order12425104410102024444488510201051020201010201020202020204040510201051020201010201020202020204040224210104410102024444488
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111-1-1-1-11-1-1111111111111-1-1-1-11-1-1111111111111-1-1-1-11-1-1111111111111-1-1-1-11-1-1
χ3111111-1-1111-1ii−i−i-1i−i111111-1-1111-1ii−i−i-1i−i111111-1-1111-1ii−i−i-1i−i111111-1-1111-1ii−i−i-1i−i
χ4111111-1-1111-1−i−iii-1−ii111111-1-1111-1−i−iii-1−ii111111-1-1111-1−i−iii-1−ii111111-1-1111-1−i−iii-1−ii
χ5111-11111-1-1111111-1-1-1111-11111-1-1111111-1-1-1111-11111-1-1111111-1-1-1111-11111-1-1111111-1-1-1
χ6111-11111-1-111-1-1-1-1-111111-11111-1-111-1-1-1-1-111111-11111-1-111-1-1-1-1-111111-11111-1-111-1-1-1-1-111
χ7111-111-1-1-1-11-1ii−i−i1−ii111-111-1-1-1-11-1ii−i−i1−ii111-111-1-1-1-11-1ii−i−i1−ii111-111-1-1-1-11-1ii−i−i1−ii
χ8111-111-1-1-1-11-1−i−iii1i−i111-111-1-1-1-11-1−i−iii1i−i111-111-1-1-1-11-1−i−iii1i−i111-111-1-1-1-11-1−i−iii1i−i
χ922-20222200-2-2000000022-20222200-2-2000000022-20222200-2-2000000022-20222200-2-20000000
χ1022-2022-2-200-22000000022-2022-2-200-22000000022-2022-2-200-22000000022-2022-2-200-220000000
χ112-2002-22i−2i00001+i−1−i1−i−1+i0002-2002-22i−2i00001+i−1−i1−i−1+i0002-2002-22i−2i00001+i−1−i1−i−1+i0002-2002-22i−2i00001+i−1−i1−i−1+i000
χ122-2002-22i−2i0000−1−i1+i−1+i1−i0002-2002-22i−2i0000−1−i1+i−1+i1−i0002-2002-22i−2i0000−1−i1+i−1+i1−i0002-2002-22i−2i0000−1−i1+i−1+i1−i000
χ132-2002-2−2i2i00001−i−1+i1+i−1−i0002-2002-2−2i2i00001−i−1+i1+i−1−i0002-2002-2−2i2i00001−i−1+i1+i−1−i0002-2002-2−2i2i00001−i−1+i1+i−1−i000
χ142-2002-2−2i2i0000−1+i1−i−1−i1+i0002-2002-2−2i2i0000−1+i1−i−1−i1+i0002-2002-2−2i2i0000−1+i1−i−1−i1+i0002-2002-2−2i2i0000−1+i1−i−1−i1+i000
χ154444-1-100-1-1-1000000004444-1-100-1-1-1000000004444-1-100-1-1-1000000004444-1-100-1-1-100000000
χ16444-4-1-10011-100000000444-4-1-10011-100000000444-4-1-10011-100000000444-4-1-10011-100000000
χ1744-40-1-1005−510000000044-40-1-1005−510000000044-40-1-1005−510000000044-40-1-1005−5100000000
χ1844-40-1-100−5510000000044-40-1-100−5510000000044-40-1-100−5510000000044-40-1-100−55100000000
χ198-800-2200000000000008-800-2200000000000008-800-2200000000000008-800-220000000000000
χ20111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ21111111111111-1-1-1-11-1-1111111111111-1-1-1-11-1-1111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ22111111-1-1111-1ii−i−i-1i−i111111-1-1111-1ii−i−i-1i−i111111-1-1111-1ii−i−i-1i−i-1-1-1-1-1-111-1-1-11−i−iii1−ii
χ23111111-1-1111-1−i−iii-1−ii111111-1-1111-1−i−iii-1−ii111111-1-1111-1−i−iii-1−ii-1-1-1-1-1-111-1-1-11ii−i−i1i−i
χ24111-11111-1-1111111-1-1-1111-11111-1-1111111-1-1-1111-11111-1-1111111-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1111
χ25111-11111-1-111-1-1-1-1-111111-11111-1-111-1-1-1-1-111111-11111-1-111-1-1-1-1-111-1-1-11-1-1-1-111-1-111111-1-1
χ26111-111-1-1-1-11-1ii−i−i1−ii111-111-1-1-1-11-1ii−i−i1−ii111-111-1-1-1-11-1ii−i−i1−ii-1-1-11-1-11111-11−i−iii-1i−i
χ27111-111-1-1-1-11-1−i−iii1i−i111-111-1-1-1-11-1−i−iii1i−i111-111-1-1-1-11-1−i−iii1i−i-1-1-11-1-11111-11ii−i−i-1−ii
χ2822-20222200-2-2000000022-20222200-2-2000000022-20222200-2-20000000-2-220-2-2-2-200220000000
χ2922-2022-2-200-22000000022-2022-2-200-22000000022-2022-2-200-220000000-2-220-2-222002-20000000
χ302-2002-22i−2i00001+i−1−i1−i−1+i0002-2002-22i−2i00001+i−1−i1−i−1+i0002-2002-22i−2i00001+i−1−i1−i−1+i000-2200-22−2i2i0000−1−i1+i−1+i1−i000
χ312-2002-22i−2i0000−1−i1+i−1+i1−i0002-2002-22i−2i0000−1−i1+i−1+i1−i0002-2002-22i−2i0000−1−i1+i−1+i1−i000-2200-22−2i2i00001+i−1−i1−i−1+i000
χ322-2002-2−2i2i00001−i−1+i1+i−1−i0002-2002-2−2i2i00001−i−1+i1+i−1−i0002-2002-2−2i2i00001−i−1+i1+i−1−i000-2200-222i−2i0000−1+i1−i−1−i1+i000
χ332-2002-2−2i2i0000−1+i1−i−1−i1+i0002-2002-2−2i2i0000−1+i1−i−1−i1+i0002-2002-2−2i2i0000−1+i1−i−1−i1+i000-2200-222i−2i00001−i−1+i1+i−1−i000
χ344444-1-100-1-1-1000000004444-1-100-1-1-1000000004444-1-100-1-1-100000000-4-4-4-4110011100000000
χ35444-4-1-10011-100000000444-4-1-10011-100000000444-4-1-10011-100000000-4-4-441100-1-1100000000
χ3644-40-1-1005−510000000044-40-1-1005−510000000044-40-1-1005−5100000000-4-4401100−55-100000000
χ3744-40-1-100−5510000000044-40-1-100−5510000000044-40-1-100−55100000000-4-44011005−5-100000000
χ388-800-2200000000000008-800-2200000000000008-800-220000000000000-88002-20000000000000
χ392222222222222222222−1+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+52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−520000000000000000000
χ40222222222222-2-2-2-22-2-2−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−521−52−1+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+52−1−521+521+520000000000000000000
χ41222222-2-2222-22i2i−2i−2i-22i−2i−1+52−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+52−1+521−52−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ191−52−ζ11−ζ19ζ11+ζ19−1−52−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−52−1−521+52−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ71+52−ζ3−ζ7ζ3+ζ70000000000000000000
χ42222222-2-2222-2−2i−2i2i2i-2−2i2i−1+52−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+52−1+521−52ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ191−52ζ11+ζ19−ζ11−ζ19−1−52−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−52−1−521+52ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ71+52ζ3+ζ7−ζ3−ζ70000000000000000000
χ43222-22222-2-2222222-2-2-2−1+52−1+52−1+521−52−1+52−1+52−1+52−1+521−521−52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−52−1−52−1−52−1−521+52−1−52−1−52−1−52−1−521+521+52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+520000000000000000000
χ44222-22222-2-222-2-2-2-2-222−1+52−1+52−1+521−52−1+52−1+52−1+52−1+521−521−52−1+52−1+521−521−521−521−521−52−1+52−1+52−1−52−1−52−1−521+52−1−52−1−52−1−52−1−521+521+52−1−52−1−521+521+521+521+521+52−1−52−1−520000000000000000000
χ45222-222-2-2-2-22-22i2i−2i−2i2−2i2i−1+52−1+52−1+521−52−1+52−1+521−521−521−521−52−1+521−52−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ19−1+52ζ11+ζ19−ζ11−ζ19−1−52−1−52−1−521+52−1−52−1−521+521+521+521+52−1−521+52−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ7−1−52ζ3+ζ7−ζ3−ζ70000000000000000000
χ46222-222-2-2-2-22-2−2i−2i2i2i22i−2i−1+52−1+52−1+521−52−1+52−1+521−521−521−521−52−1+521−52ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ19−1+52−ζ11−ζ19ζ11+ζ19−1−52−1−52−1−521+52−1−52−1−521+521+521+521+52−1−521+52ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ7−1−52−ζ3−ζ7ζ3+ζ70000000000000000000
χ4744-40444400-4-40000000−1+5−1+51−50−1+5−1+5−1+5−1+5001−51−50000000−1−5−1−51+50−1−5−1−5−1−5−1−5001+51+500000000000000000000000000
χ4844-4044-4-400-440000000−1+5−1+51−50−1+5−1+51−51−5001−5−1+50000000−1−5−1−51+50−1−5−1−51+51+5001+5−1−500000000000000000000000000
χ494-4004-44i−4i00002+2i−2−2i2−2i−2+2i000−1+51−500−1+51−5−2ζ11−2ζ192ζ11+2ζ190000−ζ6−ζ11−ζ14−ζ19ζ6+ζ11+ζ14+ζ19−ζ6+ζ11−ζ14+ζ19ζ6−ζ11+ζ14−ζ19000−1−51+500−1−51+5−2ζ3−2ζ72ζ3+2ζ70000−ζ2−ζ3−ζ7−ζ18ζ2+ζ3+ζ7+ζ18−ζ2+ζ3+ζ7−ζ18ζ2−ζ3−ζ7+ζ180000000000000000000000
χ504-4004-44i−4i0000−2−2i2+2i−2+2i2−2i000−1+51−500−1+51−5−2ζ11−2ζ192ζ11+2ζ190000ζ6+ζ11+ζ14+ζ19−ζ6−ζ11−ζ14−ζ19ζ6−ζ11+ζ14−ζ19−ζ6+ζ11−ζ14+ζ19000−1−51+500−1−51+5−2ζ3−2ζ72ζ3+2ζ70000ζ2+ζ3+ζ7+ζ18−ζ2−ζ3−ζ7−ζ18ζ2−ζ3−ζ7+ζ18−ζ2+ζ3+ζ7−ζ180000000000000000000000
χ514-4004-4−4i4i00002−2i−2+2i2+2i−2−2i000−1+51−500−1+51−52ζ11+2ζ19−2ζ11−2ζ190000−ζ6+ζ11−ζ14+ζ19ζ6−ζ11+ζ14−ζ19−ζ6−ζ11−ζ14−ζ19ζ6+ζ11+ζ14+ζ19000−1−51+500−1−51+52ζ3+2ζ7−2ζ3−2ζ70000−ζ2+ζ3+ζ7−ζ18ζ2−ζ3−ζ7+ζ18−ζ2−ζ3−ζ7−ζ18ζ2+ζ3+ζ7+ζ180000000000000000000000
χ524-4004-4−4i4i0000−2+2i2−2i−2−2i2+2i000−1+51−500−1+51−52ζ11+2ζ19−2ζ11−2ζ190000ζ6−ζ11+ζ14−ζ19−ζ6+ζ11−ζ14+ζ19ζ6+ζ11+ζ14+ζ19−ζ6−ζ11−ζ14−ζ19000−1−51+500−1−51+52ζ3+2ζ7−2ζ3−2ζ70000ζ2−ζ3−ζ7+ζ18−ζ2+ζ3+ζ7−ζ18ζ2+ζ3+ζ7+ζ18−ζ2−ζ3−ζ7−ζ180000000000000000000000
χ538888-2-200-2-2-200000000−2+25−2+25−2+25−2+251−521−52001−521−521−5200000000−2−25−2−25−2−25−2−251+521+52001+521+521+52000000000000000000000000000
χ54888-8-2-20022-200000000−2+25−2+25−2+252−251−521−5200−1+52−1+521−5200000000−2−25−2−25−2−252+251+521+5200−1−52−1−521+52000000000000000000000000000
χ5588-80-2-20025−25200000000−2+25−2+252−2501−521−52005−52−5+52−1+5200000000−2−25−2−252+2501+521+5200−5−525+52−1−52000000000000000000000000000
χ5688-80-2-200−2525200000000−2+25−2+252−2501−521−5200−5+525−52−1+5200000000−2−25−2−252+2501+521+52005+52−5−52−1−52000000000000000000000000000
χ5716-1600-440000000000000−4+454−45001−5−1+50000000000000−4−454+45001+5−1−500000000000000000000000000000000
χ582222222222222222222−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+52−1+520000000000000000000
χ59222222222222-2-2-2-22-2-2−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+521+52−1−521+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+521−521−521−521−52−1+521−521−520000000000000000000
χ60222222-2-2222-22i2i−2i−2i-22i−2i−1−52−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−52−1−521+52−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ71+52−ζ3−ζ7ζ3+ζ7−1+52−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+52−1+521−52−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ191−52−ζ11−ζ19ζ11+ζ190000000000000000000
χ61222222-2-2222-2−2i−2i2i2i-2−2i2i−1−52−1−52−1−52−1−52−1−52−1−521+521+52−1−52−1−52−1−521+52ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ71+52ζ3+ζ7−ζ3−ζ7−1+52−1+52−1+52−1+52−1+52−1+521−521−52−1+52−1+52−1+521−52ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ191−52ζ11+ζ19−ζ11−ζ190000000000000000000
χ62222-22222-2-2222222-2-2-2−1−52−1−52−1−521+52−1−52−1−52−1−52−1−521+521+52−1−52−1−52−1−52−1−52−1−52−1−521+521+521+52−1+52−1+52−1+521−52−1+52−1+52−1+52−1+521−521−52−1+52−1+52−1+52−1+52−1+52−1+521−521−521−520000000000000000000
χ63222-22222-2-222-2-2-2-2-222−1−52−1−52−1−521+52−1−52−1−52−1−52−1−521+521+52−1−52−1−521+521+521+521+521+52−1−52−1−52−1+52−1+52−1+521−52−1+52−1+52−1+52−1+521−521−52−1+52−1+521−521−521−521−521−52−1+52−1+520000000000000000000
χ64222-222-2-2-2-22-22i2i−2i−2i2−2i2i−1−52−1−52−1−521+52−1−52−1−521+521+521+521+52−1−521+52−ζ3−ζ7−ζ3−ζ7ζ3+ζ7ζ3+ζ7−1−52ζ3+ζ7−ζ3−ζ7−1+52−1+52−1+521−52−1+52−1+521−521−521−521−52−1+521−52−ζ11−ζ19−ζ11−ζ19ζ11+ζ19ζ11+ζ19−1+52ζ11+ζ19−ζ11−ζ190000000000000000000
χ65222-222-2-2-2-22-2−2i−2i2i2i22i−2i−1−52−1−52−1−521+52−1−52−1−521+521+521+521+52−1−521+52ζ3+ζ7ζ3+ζ7−ζ3−ζ7−ζ3−ζ7−1−52−ζ3−ζ7ζ3+ζ7−1+52−1+52−1+521−52−1+52−1+521−521−521−521−52−1+521−52ζ11+ζ19ζ11+ζ19−ζ11−ζ19−ζ11−ζ19−1+52−ζ11−ζ19ζ11+ζ190000000000000000000
χ6644-40444400-4-40000000−1−5−1−51+50−1−5−1−5−1−5−1−5001+51+50000000−1+5−1+51−50−1+5−1+5−1+5−1+5001−51−500000000000000000000000000
χ6744-4044-4-400-440000000−1−5−1−51+50−1−5−1−51+51+5001+5−1−50000000−1+5−1+51−50−1+5−1+51−51−5001−5−1+500000000000000000000000000
χ684-4004-44i−4i00002+2i−2−2i2−2i−2+2i000−1−51+500−1−51+5−2ζ3−2ζ72ζ3+2ζ70000−ζ2−ζ3−ζ7−ζ18ζ2+ζ3+ζ7+ζ18−ζ2+ζ3+ζ7−ζ18ζ2−ζ3−ζ7+ζ18000−1+51−500−1+51−5−2ζ11−2ζ192ζ11+2ζ190000−ζ6−ζ11−ζ14−ζ19ζ6+ζ11+ζ14+ζ19−ζ6+ζ11−ζ14+ζ19ζ6−ζ11+ζ14−ζ190000000000000000000000
χ694-4004-44i−4i0000−2−2i2+2i−2+2i2−2i000−1−51+500−1−51+5−2ζ3−2ζ72ζ3+2ζ70000ζ2+ζ3+ζ7+ζ18−ζ2−ζ3−ζ7−ζ18ζ2−ζ3−ζ7+ζ18−ζ2+ζ3+ζ7−ζ18000−1+51−500−1+51−5−2ζ11−2ζ192ζ11+2ζ190000ζ6+ζ11+ζ14+ζ19−ζ6−ζ11−ζ14−ζ19ζ6−ζ11+ζ14−ζ19−ζ6+ζ11−ζ14+ζ190000000000000000000000
χ704-4004-4−4i4i00002−2i−2+2i2+2i−2−2i000−1−51+500−1−51+52ζ3+2ζ7−2ζ3−2ζ70000−ζ2+ζ3+ζ7−ζ18ζ2−ζ3−ζ7+ζ18−ζ2−ζ3−ζ7−ζ18ζ2+ζ3+ζ7+ζ18000−1+51−500−1+51−52ζ11+2ζ19−2ζ11−2ζ190000−ζ6+ζ11−ζ14+ζ19ζ6−ζ11+ζ14−ζ19−ζ6−ζ11−ζ14−ζ19ζ6+ζ11+ζ14+ζ190000000000000000000000
χ714-4004-4−4i4i0000−2+2i2−2i−2−2i2+2i000−1−51+500−1−51+52ζ3+2ζ7−2ζ3−2ζ70000ζ2−ζ3−ζ7+ζ18−ζ2+ζ3+ζ7−ζ18ζ2+ζ3+ζ7+ζ18−ζ2−ζ3−ζ7−ζ18000−1+51−500−1+51−52ζ11+2ζ19−2ζ11−2ζ190000ζ6−ζ11+ζ14−ζ19−ζ6+ζ11−ζ14+ζ19ζ6+ζ11+ζ14+ζ19−ζ6−ζ11−ζ14−ζ190000000000000000000000
χ728888-2-200-2-2-200000000−2−25−2−25−2−25−2−251+521+52001+521+521+5200000000−2+25−2+25−2+25−2+251−521−52001−521−521−52000000000000000000000000000
χ73888-8-2-20022-200000000−2−25−2−25−2−252+251+521+5200−1−52−1−521+5200000000−2+25−2+25−2+252−251−521−5200−1+52−1+521−52000000000000000000000000000
χ7488-80-2-20025−25200000000−2−25−2−252+2501+521+5200−5−525+52−1−5200000000−2+25−2+252−2501−521−52005−52−5+52−1+52000000000000000000000000000
χ7588-80-2-200−2525200000000−2−25−2−252+2501+521+52005+52−5−52−1−5200000000−2+25−2+252−2501−521−5200−5+525−52−1+52000000000000000000000000000
χ7616-1600-440000000000000−4−454+45001+5−1−50000000000000−4+454−45001−5−1+500000000000000000000000000000000

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