Finite Group Databasebeta

← Group #10601774

Character table — Group #10601774

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61
size11112222222222444444444488888888888888888888888816161616202040404040404040
order1222225510101010101044101010102020202044448820202020202020202020404040404040404020202020442244488
χ11111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1
χ411111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1
χ6111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111
χ7111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-1-1-111
χ8111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1
χ922222222222222-2-22222-2-2-2-2000000-2-20000000000000000000022-2000000
χ1022222222222222-2-22222-2-2-2-2000000-2-200000000000000000000-2-22000000
χ11222222−1+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+52−1−52−1−52222222−1+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+52−1−52000000000
χ12222222−1+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+52−1−52−1−5222-2-2-2-2−1+52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521−521−521−521+521+521+521+521−521+521−521+52000000000
χ13222222−1+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+52−1−52−1−52-2-222-2-2−1+52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+52−1+52−1−52−1+52−1−52000000000
χ14222222−1+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+52−1−52−1−52-2-2-2-222−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−521−521+521−521+52000000000
χ15222222−1−52−1+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+52222222−1−52−1+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+52000000000
χ16222222−1−52−1+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+5222-2-2-2-2−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−521+521−521+521−52000000000
χ17222222−1−52−1+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+52-2-222-2-2−1−52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−52−1−52−1+52−1−52−1+52000000000
χ18222222−1−52−1+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+52-2-2-2-222−1−52−1+521+521+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+521−52000000000
χ192222-2-2222222222-2-2-2-2-22222002-200-2-20000000000000000-2-222000000000
χ202222-2-2222222222-2-2-2-2-2222200-2200-2-2000000000000000022-2-2000000000
χ212222-2-222222222-22-2-2-2-2-2-2-2-200000022000000000000000000000002-20000
χ222222-2-222222222-22-2-2-2-2-2-2-2-20000002200000000000000000000000-220000
χ232222-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−52002-2001−521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ361−521+52−1+52−1−52000000000
χ242222-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−52002-2001−521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ361−521+52−1+52−1−52000000000
χ252222-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−5200-22001−521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36−1+52−1−521−521+52000000000
χ262222-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−5200-22001−521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−1+52−1−521−521+52000000000
χ272222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522-21+521+521−521−52−1−52−1−52−1+52−1+52002-2001+521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ281+521−52−1−52−1+52000000000
χ282222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522-21+521+521−521−52−1−52−1−52−1+52−1+52002-2001+521−52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ281+521−52−1−52−1+52000000000
χ292222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522-21+521+521−521−52−1−52−1−52−1+52−1+5200-22001+521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−1−52−1+521+521−52000000000
χ302222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+522-21+521+521−521−52−1−52−1−52−1+52−1+5200-22001+521−52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28−1−52−1+521+521−52000000000
χ312-22-2-222222-2-2-2-2002-22-2000000002−200000000002−22−22−22−200002i−2i00000i2−i2
χ322-22-2-222222-2-2-2-2002-22-2000000002−200000000002−22−22−22−20000−2i2i00000−i2i2
χ332-22-2-222222-2-2-2-2002-22-200000000−220000000000−22−22−22−2200002i−2i00000−i2i2
χ342-22-2-222222-2-2-2-2002-22-200000000−220000000000−22−22−22−220000−2i2i00000i2−i2
χ35444444−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-4−1+5−1+5−1−5−1−51−51−51+51+50000001−51+500000000000000000000000000000
χ36444444−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4-4−1−5−1−5−1+5−1+51+51+51−51−50000001+51−500000000000000000000000000000
χ374444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-441−51−51+51+51−51−51+51+5000000−1+5−1−500000000000000000000000000000
χ384444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-441+51+51−51−51+51+51−51−5000000−1−5−1+500000000000000000000000000000
χ3944-4-40044-4-4-4-44400000000002-20000002-22-22-22-2000000000000000000000
χ4044-4-40044-4-4-4-4440000000000-22000000-22-22-22-22000000000000000000000
χ4144-4-400−1+5−1−51−51+51−51+5−1+5−1−50000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ362-2000000−2ζ282ζ28−2ζ122ζ12−2ζ42ζ4−2ζ362ζ36000000000000000000000
χ4244-4-400−1+5−1−51−51+51−51+5−1+5−1−50000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36-220000002ζ28−2ζ282ζ12−2ζ122ζ4−2ζ42ζ36−2ζ36000000000000000000000
χ4344-4-400−1+5−1−51−51+51−51+5−1+5−1−5000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ362-2000000−2ζ122ζ12−2ζ282ζ28−2ζ362ζ36−2ζ42ζ4000000000000000000000
χ4444-4-400−1+5−1−51−51+51−51+5−1+5−1−5000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36-220000002ζ12−2ζ122ζ28−2ζ282ζ36−2ζ362ζ4−2ζ4000000000000000000000
χ4544-4-400−1−5−1+51+51−51+51−5−1−5−1+5000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ282-2000000−2ζ42ζ4−2ζ362ζ36−2ζ122ζ12−2ζ282ζ28000000000000000000000
χ4644-4-400−1−5−1+51+51−51+51−5−1−5−1+5000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28-220000002ζ4−2ζ42ζ36−2ζ362ζ12−2ζ122ζ28−2ζ28000000000000000000000
χ4744-4-400−1−5−1+51+51−51+51−5−1−5−1+50000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ282-2000000−2ζ362ζ36−2ζ42ζ4−2ζ282ζ28−2ζ122ζ12000000000000000000000
χ4844-4-400−1−5−1+51+51−51+51−5−1−5−1+50000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28-220000002ζ36−2ζ362ζ4−2ζ42ζ28−2ζ282ζ12−2ζ12000000000000000000000
χ494-44-44-44444-4-4-4-400-44-4400000000000000000000000000000000000000000
χ504-44-44-4−1+5−1−5−1+5−1−51−51+51−51+5001−5−1+51+5−1−500000000000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ390000000000000
χ514-44-44-4−1+5−1−5−1+5−1−51−51+51−51+5001−5−1+51+5−1−500000000000000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ390000000000000
χ524-44-44-4−1−5−1+5−1−5−1+51+51−51+51−5001+5−1−51−5−1+500000000000000000000−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ370000000000000
χ534-44-44-4−1−5−1+5−1−5−1+51+51−51+51−5001+5−1−51−5−1+500000000000000000000ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ370000000000000
χ544-44-4-44−1+5−1−5−1+5−1−51−51+51−51+500−1+51−5−1−51+50000000022−220000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ390000000000000
χ554-44-4-44−1+5−1−5−1+5−1−51−51+51−51+500−1+51−5−1−51+500000000−22220000000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ390000000000000
χ564-44-4-44−1−5−1+5−1−5−1+51+51−51+51−500−1−51+5−1+51−50000000022−220000000000ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ370000000000000
χ574-44-4-44−1−5−1+5−1−5−1+51+51−51+51−500−1−51+5−1+51−500000000−22220000000000−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ370000000000000
χ584-4-440044-4-444-4-400000000000000000000000000000000000000000002i−2i00
χ594-4-440044-4-444-4-40000000000000000000000000000000000000000000−2i2i00
χ608-8-8800−2+25−2−252−252+25−2+25−2−252−252+2500000000000000000000000000000000000000000000000
χ618-8-8800−2−25−2+252+252−25−2−25−2+252+252−2500000000000000000000000000000000000000000000000

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