Finite Group Databasebeta

← Group #10615708

Character table — Group #10615708

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size112222222444444448888888888888810102020204040112222222444444448888888888888810102020204040
order1224455101024101020202020481010202020202020404040408888848222441010101024101020202020481010202020202020404040408888848
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-11111111111111111111111111111111-1-1-1-1-1-1-1
χ311111111111111111-1-11111-1-1-1-1-1-1-1-111111-1-111111111111111111-1-11111-1-1-1-1-1-1-1-111111-1-1
χ411111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111
χ5111111111-1-11111111-1-1-1-1-11111-1-1-1-1111-1-11-1111111111-1-11111111-1-1-1-1-11111-1-1-1-1111-1-11-1
χ6111111111-1-11111111-1-1-1-1-11111-1-1-1-1-1-1-111-11111111111-1-11111111-1-1-1-1-11111-1-1-1-1-1-1-111-11
χ7111111111-1-1111111-11-1-1-1-1-1-1-1-11111111-1-1-11111111111-1-1111111-11-1-1-1-1-1-1-1-11111111-1-1-11
χ8111111111-1-1111111-11-1-1-1-1-1-1-1-11111-1-1-1111-1111111111-1-1111111-11-1-1-1-1-1-1-1-11111-1-1-1111-1
χ922222−1+52−1−52−1+52−1−5222−1+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+52−1−52−1−52000000022222−1+52−1−52−1+52−1−5222−1+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+52−1−52−1−520000000
χ1022222−1+52−1−52−1+52−1−5222−1+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+52000000022222−1+52−1−52−1+52−1−5222−1+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+520000000
χ1122222−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−522-21−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+52000000022222−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−522-21−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+520000000
χ1222222−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−52-221−521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−52000000022222−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−52-221−521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−520000000
χ1322222−1−52−1+52−1−52−1+5222−1−52−1+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+52000000022222−1−52−1+52−1−52−1+5222−1−52−1+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+520000000
χ1422222−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52000000022222−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−520000000
χ1522222−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+522-21+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−52000000022222−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+522-21+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−520000000
χ1622222−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+52-221+521−521+521−521+521+521−521−52−1−52−1−52−1+52−1+52000000022222−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+52-221+521−521+521−521+521+521−521−52−1−52−1−52−1+52−1+520000000
χ17222-2-222220022-2-2-2-2000000000000000002i−2i00222-2-222220022-2-2-2-2000000000000000002i−2i00
χ18222-2-222220022-2-2-2-200000000000000000−2i2i00222-2-222220022-2-2-2-200000000000000000−2i2i00
χ1922-22-222222-2-2-2-2-2220022-2-200000000000000022-22-222222-2-2-2-2-2220022-2-2000000000000000
χ2022-22-22222-22-2-2-2-22200-2-22200000000000000022-22-22222-22-2-2-2-22200-2-222000000000000000
χ2122-22-2−1+52−1−52−1+52−1−522-21−521+521−521+52−1+52−1−5200−1+52−1−521−521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000022-22-2−1+52−1−52−1+52−1−522-21−521+521−521+52−1+52−1−5200−1+52−1−521−521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000000
χ2222-22-2−1+52−1−52−1+52−1−522-21−521+521−521+52−1+52−1−5200−1+52−1−521−521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000022-22-2−1+52−1−52−1+52−1−522-21−521+521−521+52−1+52−1−5200−1+52−1−521−521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000000
χ2322-22-2−1+52−1−52−1+52−1−52-221−521+521−521+52−1+52−1−52001−521+52−1+52−1−52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000022-22-2−1+52−1−52−1+52−1−52-221−521+521−521+52−1+52−1−52001−521+52−1+52−1−52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000000
χ2422-22-2−1+52−1−52−1+52−1−52-221−521+521−521+52−1+52−1−52001−521+52−1+52−1−52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000022-22-2−1+52−1−52−1+52−1−52-221−521+521−521+52−1+52−1−52001−521+52−1+52−1−52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000000
χ2522-22-2−1−52−1+52−1−52−1+522-21+521−521+521−52−1−52−1+5200−1−52−1+521+521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000022-22-2−1−52−1+52−1−52−1+522-21+521−521+521−52−1−52−1+5200−1−52−1+521+521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000000
χ2622-22-2−1−52−1+52−1−52−1+522-21+521−521+521−52−1−52−1+5200−1−52−1+521+521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000022-22-2−1−52−1+52−1−52−1+522-21+521−521+521−52−1−52−1+5200−1−52−1+521+521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000000
χ2722-22-2−1−52−1+52−1−52−1+52-221+521−521+521−52−1−52−1+52001+521−52−1−52−1+52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000022-22-2−1−52−1+52−1−52−1+52-221+521−521+521−52−1−52−1+52001+521−52−1−52−1+52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000000
χ2822-22-2−1−52−1+52−1−52−1+52-221+521−521+521−52−1−52−1+52001+521−52−1−52−1+52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000022-22-2−1−52−1+52−1−52−1+52-221+521−521+521−52−1−52−1+52001+521−52−1−52−1+52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000000
χ2922-2-22222200-2-222-2-20000000000000022-2000022-2-22222200-2-222-2-20000000000000022-20000
χ3022-2-22222200-2-222-2-200000000000000-2-22000022-2-22222200-2-222-2-200000000000000-2-220000
χ31444-4-4−1+5−1−5−1+5−1−500−1+5−1−51−51+51−51+5000000000000000000000444-4-4−1+5−1−5−1+5−1−500−1+5−1−51−51+51−51+5000000000000000000000
χ32444-4-4−1−5−1+5−1−5−1+500−1−5−1+51+51−51+51−5000000000000000000000444-4-4−1−5−1+5−1−5−1+500−1−5−1+51+51−51+51−5000000000000000000000
χ3344-4-44−1+5−1−5−1+5−1−5001−51+5−1+5−1−51−51+500000000000000000000044-4-44−1+5−1−5−1+5−1−5001−51+5−1+5−1−51−51+5000000000000000000000
χ3444-4-44−1−5−1+5−1−5−1+5001+51−5−1−5−1+51+51−500000000000000000000044-4-44−1−5−1+5−1−5−1+5001+51−5−1−5−1+51+51−5000000000000000000000
χ354-400044-4-4000000000000000000000022−22000004-400044-4-4000000000000000000000022−2200000
χ364-400044-4-40000000000000000000000−2222000004-400044-4-40000000000000000000000−222200000
χ378-8000−2+25−2−252−252+25000000000000000000000000000008-8000−2+25−2−252−252+2500000000000000000000000000000
χ388-8000−2−25−2+252+252−25000000000000000000000000000008-8000−2−25−2+252+252−2500000000000000000000000000000
χ3911111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ401111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ4111111111111111111-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-111
χ4211111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111111-1-1
χ43111111111-1-11111111-1-1-1-1-11111-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-11111-1-1-111-11
χ44111111111-1-11111111-1-1-1-1-11111-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111-1-1-1-11111111-1-11-1
χ45111111111-1-1111111-11-1-1-1-1-1-1-1-11111111-1-1-11-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1111-1
χ46111111111-1-1111111-11-1-1-1-1-1-1-1-11111-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111111111-1-1-1-1111-1-1-11
χ4722222−1+52−1−52−1+52−1−5222−1+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+52−1−52−1−520000000-2-2-2-2-21−521+521−521+52-2-21−521+521−521+521−521+52-2-21−521+521−521+521−521−521+521+521−521−521+521+520000000
χ4822222−1+52−1−52−1+52−1−5222−1+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+520000000-2-2-2-2-21−521+521−521+52-2-21−521+521−521+521−521+52221−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000000
χ4922222−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−522-21−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+520000000-2-2-2-2-21−521+521−521+52221−521+521−521+521−521+52-22−1+52−1−52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000000
χ5022222−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−52-221−521+521−521+521−521−521+521+52−1+52−1+52−1−52−1−520000000-2-2-2-2-21−521+521−521+52221−521+521−521+521−521+522-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000000
χ5122222−1−52−1+52−1−52−1+5222−1−52−1+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+520000000-2-2-2-2-21+521−521+521−52-2-21+521−521+521−521+521−52-2-21+521−521+521−521+521+521−521−521+521+521−521−520000000
χ5222222−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−520000000-2-2-2-2-21+521−521+521−52-2-21+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+520000000
χ5322222−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+522-21+521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−520000000-2-2-2-2-21+521−521+521−52221+521−521+521−521+521−52-22−1−52−1+52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000000
χ5422222−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+52-221+521−521+521−521+521+521−521−52−1−52−1−52−1+52−1+520000000-2-2-2-2-21+521−521+521−52221+521−521+521−521+521−522-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000000
χ55222-2-222220022-2-2-2-2000000000000000002i−2i00-2-2-222-2-2-2-200-2-2222200000000000000000−2i2i00
χ56222-2-222220022-2-2-2-200000000000000000−2i2i00-2-2-222-2-2-2-200-2-22222000000000000000002i−2i00
χ5722-22-222222-2-2-2-2-2220022-2-2000000000000000-2-22-22-2-2-2-2-222222-2-200-2-222000000000000000
χ5822-22-22222-22-2-2-2-22200-2-222000000000000000-2-22-22-2-2-2-22-22222-2-20022-2-2000000000000000
χ5922-22-2−1+52−1−52−1+52−1−522-21−521+521−521+52−1+52−1−5200−1+52−1−521−521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000000-2-22-221−521+521−521+52-22−1+52−1−52−1+52−1−521−521+52001−521+52−1+52−1−52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000000
χ6022-22-2−1+52−1−52−1+52−1−522-21−521+521−521+52−1+52−1−5200−1+52−1−521−521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000000-2-22-221−521+521−521+52-22−1+52−1−52−1+52−1−521−521+52001−521+52−1+52−1−52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000000
χ6122-22-2−1+52−1−52−1+52−1−52-221−521+521−521+52−1+52−1−52001−521+52−1+52−1−52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000000-2-22-221−521+521−521+522-2−1+52−1−52−1+52−1−521−521+5200−1+52−1−521−521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000000
χ6222-22-2−1+52−1−52−1+52−1−52-221−521+521−521+52−1+52−1−52001−521+52−1+52−1−52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ360000000-2-22-221−521+521−521+522-2−1+52−1−52−1+52−1−521−521+5200−1+52−1−521−521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ360000000
χ6322-22-2−1−52−1+52−1−52−1+522-21+521−521+521−52−1−52−1+5200−1−52−1+521+521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000000-2-22-221+521−521+521−52-22−1−52−1+52−1−52−1+521+521−52001+521−52−1−52−1+52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000000
χ6422-22-2−1−52−1+52−1−52−1+522-21+521−521+521−52−1−52−1+5200−1−52−1+521+521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000000-2-22-221+521−521+521−52-22−1−52−1+52−1−52−1+521+521−52001+521−52−1−52−1+52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000000
χ6522-22-2−1−52−1+52−1−52−1+52-221+521−521+521−52−1−52−1+52001+521−52−1−52−1+52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000000-2-22-221+521−521+521−522-2−1−52−1+52−1−52−1+521+521−5200−1−52−1+521+521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000000
χ6622-22-2−1−52−1+52−1−52−1+52-221+521−521+521−52−1−52−1+52001+521−52−1−52−1+52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ280000000-2-22-221+521−521+521−522-2−1−52−1+52−1−52−1+521+521−5200−1−52−1+521+521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ280000000
χ6722-2-22222200-2-222-2-20000000000000022-20000-2-222-2-2-2-2-20022-2-22200000000000000-2-220000
χ6822-2-22222200-2-222-2-200000000000000-2-220000-2-222-2-2-2-2-20022-2-2220000000000000022-20000
χ69444-4-4−1+5−1−5−1+5−1−500−1+5−1−51−51+51−51+5000000000000000000000-4-4-4441−51+51−51+5001−51+5−1+5−1−5−1+5−1−5000000000000000000000
χ70444-4-4−1−5−1+5−1−5−1+500−1−5−1+51+51−51+51−5000000000000000000000-4-4-4441+51−51+51−5001+51−5−1−5−1+5−1−5−1+5000000000000000000000
χ7144-4-44−1+5−1−5−1+5−1−5001−51+5−1+5−1−51−51+5000000000000000000000-4-444-41−51+51−51+500−1+5−1−51−51+5−1+5−1−5000000000000000000000
χ7244-4-44−1−5−1+5−1−5−1+5001+51−5−1−5−1+51+51−5000000000000000000000-4-444-41+51−51+51−500−1−5−1+51+51−5−1−5−1+5000000000000000000000
χ734-400044-4-4000000000000000000000022−2200000-44000-4-4440000000000000000000000−222200000
χ744-400044-4-40000000000000000000000−222200000-44000-4-444000000000000000000000022−2200000
χ758-8000−2+25−2−252−252+2500000000000000000000000000000-880002−252+25−2+25−2−2500000000000000000000000000000
χ768-8000−2−25−2+252+252−2500000000000000000000000000000-880002+252−25−2−25−2+2500000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.