Finite Group Databasebeta

← Group #10599208

Character table — Group #10599208

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61
size111122222222222244444444488888888888888888888881616161616202020204040404080
order1222444455101010101010420202020202020208888202040404040404040404040404040404040210101010888844884
χ11111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1
χ4111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11
χ51111111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1111111-1-1-1
χ61111111111111111111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111
χ71111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-11
χ81111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-11111-1
χ922222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522222−1+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+52−1−52−1−52−1−52−1−522−1+52−1+52−1−52−1−52000000000
χ1022222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-2−1+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+52-21−521−521+521+52000000000
χ1122222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-222−1+52−1−521−521−521−521−521+521+521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52-21−521−521+521+52000000000
χ1222222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−522−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-2−1+52−1−521−521−521−521−521+521+521+521+521−521−521−521−521+521+521+521+522−1+52−1+52−1−52−1−52000000000
χ1322222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522222−1−52−1+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+522−1−52−1−52−1+52−1+52000000000
χ1422222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-2−1−52−1+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+521+521+521+521+521−521−521−521−52-21+521+521−521−52000000000
χ1522222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-222−1−52−1+521+521+521+521+521−521−521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52-21+521+521−521−52000000000
χ1622222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+522−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-2−1−52−1+521+521+521+521+521−521−521−521−521+521+521+521+521−521−521−521−522−1−52−1−52−1+52−1+52000000000
χ1722222-2-2222222222-22-22-22-22-20000-2-200000000000000000000000002-2000
χ1822222-2-2222222222-22-22-22-22-20000-2-20000000000000000000000000-22000
χ192222-222-222222222-2-22-22-22-220000-2-200000000000000000000022-2-200000
χ202222-222-222222222-2-22-22-22-220000-2-2000000000000000000000-2-22200000
χ212222-2-2-2-2222222222-2-2-2-2-2-2-2-2002i−2i22000000002i2i−2i−2i2i2i−2i−2i00000000000000
χ222222-2-2-2-2222222222-2-2-2-2-2-2-2-200−2i2i2200000000−2i−2i2i2i−2i−2i2i2i00000000000000
χ232222-2-2-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−5221−521−521+521+521−521−521+521+52002i−2i−1+52−1−52−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ140ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000000
χ242222-2-2-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−5221−521−521+521+521−521−521+521+52002i−2i−1+52−1−52ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ38−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ140−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000000
χ252222-2-2-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−5221−521−521+521+521−521−521+521+5200−2i2i−1+52−1−52−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ22+ζ38ζ22+ζ38−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14−ζ6−ζ14−ζ6−ζ140−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000000
χ262222-2-2-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−5221−521−521+521+521−521−521+521+5200−2i2i−1+52−1−52ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14ζ22+ζ38ζ22+ζ38−ζ22−ζ38−ζ22−ζ38ζ6+ζ14ζ6+ζ14−ζ6−ζ14−ζ6−ζ140ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000000
χ272222-2-2-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+5221+521+521−521−521+521+521−521−52002i−2i−1−52−1+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ380ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000000
χ282222-2-2-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+5221+521+521−521−521+521+521−521−52002i−2i−1−52−1+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38−ζ6−ζ14−ζ6−ζ14ζ6+ζ14ζ6+ζ14−ζ22−ζ38−ζ22−ζ38ζ22+ζ38ζ22+ζ380−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000000
χ292222-2-2-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+5221+521+521−521−521+521+521−521−5200−2i2i−1−52−1+52ζ6−ζ14ζ6−ζ14−ζ6+ζ14−ζ6+ζ14ζ22−ζ38ζ22−ζ38−ζ22+ζ38−ζ22+ζ38ζ6+ζ14ζ6+ζ14−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38−ζ22−ζ38−ζ22−ζ380−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000000
χ302222-2-2-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+5221+521+521−521−521+521+521−521−5200−2i2i−1−52−1+52−ζ6+ζ14−ζ6+ζ14ζ6−ζ14ζ6−ζ14−ζ22+ζ38−ζ22+ζ38ζ22−ζ38ζ22−ζ38ζ6+ζ14ζ6+ζ14−ζ6−ζ14−ζ6−ζ14ζ22+ζ38ζ22+ζ38−ζ22−ζ38−ζ22−ζ380ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000000
χ3122-2-20-220222-2-22-2-200-20-202022−200002−22−22−22−200000000000002i−2i0000i2−i20
χ3222-2-20-220222-2-22-2-200-20-202022−200002−22−22−22−20000000000000−2i2i0000−i2i20
χ3322-2-20-220222-2-22-2-200-20-20202−220000−22−22−22−2200000000000002i−2i0000−i2i20
χ3422-2-20-220222-2-22-2-200-20-20202−220000−22−22−22−220000000000000−2i2i0000i2−i20
χ3544444-4-44−1+5−1−5−1+5−1+5−1+5−1−5−1−5−1−5-4−1+51−5−1−51+5−1+51−5−1−51+500001−51+5000000000000000000000000000000
χ3644444-4-44−1−5−1+5−1−5−1−5−1−5−1+5−1+5−1+5-4−1−51+5−1+51−5−1−51+5−1+51−500001+51−5000000000000000000000000000000
χ374444-444-4−1+5−1−5−1+5−1+5−1+5−1−5−1−5−1−5-41−5−1+51+5−1−51−5−1+51+5−1−500001−51+5000000000000000000000000000000
χ384444-444-4−1−5−1+5−1−5−1−5−1−5−1+5−1+5−1+5-41+5−1−51−5−1+51+5−1−51−5−1+500001+51−5000000000000000000000000000000
χ3944-4-404-40444-4-44-4-4004040-40-4000000000000000000000000000000000000
χ4044-4-404-40−1+5−1−5−1+51−51−5−1−51+51+500−1+50−1−501−501+5000000ζ7−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+ζ390000000000000000000000
χ4144-4-404-40−1+5−1−5−1+51−51−5−1−51+51+500−1+50−1−501−501+5000000−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−ζ390000000000000000000000
χ4244-4-404-40−1−5−1+5−1−51+51+5−1+51−51−500−1−50−1+501+501−5000000−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−ζ370000000000000000000000
χ4344-4-404-40−1−5−1+5−1−51+51+5−1+51−51−500−1−50−1+501+501−5000000ζ21−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+ζ370000000000000000000000
χ4444-4-40-440−1+5−1−5−1+51−51−5−1−51+51+5001−501+50−1+50−1−522−220000−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+ζ390000000000000000000000
χ4544-4-40-440−1+5−1−5−1+51−51−5−1−51+51+5001−501+50−1+50−1−5−22220000ζ7−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−ζ390000000000000000000000
χ4644-4-40-440−1−5−1+5−1−51+51+5−1+51−51−5001+501−50−1−50−1+522−220000ζ21+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−ζ370000000000000000000000
χ4744-4-40-440−1−5−1+5−1−51+51+5−1+51−51−5001+501−50−1−50−1+5−22220000−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+ζ370000000000000000000000
χ484-44-4000044-44-4-44-4000000000000000000000000000000000000002i2−2i200000
χ494-44-4000044-44-4-44-400000000000000000000000000000000000000−2i22i200000
χ504-4-44400-444-4-44-4-440-40-404040000000000000000000000000000000000000
χ514-4-44400-4−1+5−1−51−51−5−1+51+51+5−1−501−501+50−1+50−1−5000000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ3900000000000000
χ524-4-44400-4−1+5−1−51−51−5−1+51+51+5−1−501−501+50−1+50−1−5000000000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ3900000000000000
χ534-4-44400-4−1−5−1+51+51+5−1−51−51−5−1+501+501−50−1−50−1+5000000000000000−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+ζ3700000000000000
χ544-4-44400-4−1−5−1+51+51+5−1−51−51−5−1+501+501−50−1−50−1+5000000000000000ζ21−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−ζ3700000000000000
χ554-4-44-400444-4-44-4-4404040-40-40000000000000000000000000000000000000
χ564-4-44-4004−1+5−1−51−51−5−1+51+51+5−1−50−1+50−1−501−501+5000000000000000ζ7−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+ζ3900000000000000
χ574-4-44-4004−1+5−1−51−51−5−1+51+51+5−1−50−1+50−1−501−501+5000000000000000−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−ζ3900000000000000
χ584-4-44-4004−1−5−1+51+51+5−1−51−51−5−1+50−1−50−1+501+501−5000000000000000−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−ζ3700000000000000
χ594-4-44-4004−1−5−1+51+51+5−1−51−51−5−1+50−1−50−1+501+501−5000000000000000ζ21−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+ζ3700000000000000
χ608-88-80000−2+25−2−252−25−2+252−252+25−2−252+25000000000000000000000000000000000000000000000
χ618-88-80000−2−25−2+252+25−2−252+252−25−2+252−25000000000000000000000000000000000000000000000

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