Finite Group Databasebeta

← Group #10601817

Character table — Group #10601817

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61
size111122222222222244444444488888888888888888888881616161616202020204040404080
order1222444455101010101010420202020202020204488202020202020202020204040404040404040210101010888888884
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
χ1722222-22-222222222-2-2-2-2-222222-200-2-222-2-222-2-20000000000000000000000
χ1822222-22-222222222-2-2-2-2-22222-2200-2-2-2-222-2-2220000000000000000000000
χ1922222-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-21−521−521+521+52−1+52−1−52−1+52−1−522-2001−521+52−1+52−1+521−521−52−1−52−1−521+521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ360ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000000
χ2022222-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-21−521−521+521+52−1+52−1−52−1+52−1−522-2001−521+52−1+52−1+521−521−52−1−52−1−521+521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ360−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000000
χ2122222-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-21−521−521+521+52−1+52−1−52−1+52−1−52-22001−521+521−521−52−1+52−1+521+521+52−1−52−1−52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ360−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36000000000
χ2222222-22-2−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-21−521−521+521+52−1+52−1−52−1+52−1−52-22001−521+521−521−52−1+52−1+521+521+52−1−52−1−52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ360ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36000000000
χ2322222-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-21+521+521−521−52−1−52−1+52−1−52−1+522-2001+521−52−1−52−1−521+521+52−1+52−1+521−521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ280−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000000
χ2422222-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-21+521+521−521−52−1−52−1+52−1−52−1+522-2001+521−52−1−52−1−521+521+52−1+52−1+521−521−52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ280ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000000
χ2522222-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-21+521+521−521−52−1−52−1+52−1−52−1+52-22001+521−521+521+52−1−52−1−521−521−52−1+52−1+52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ280ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28000000000
χ2622222-22-2−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-21+521+521−521−52−1−52−1+52−1−52−1+52-22001+521−521+521+52−1−52−1−521−521−52−1+52−1+52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ280−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28000000000
χ272222-22-2222222222-22222-2-2-2-20000-2-200000000000000000000022-2-200000
χ282222-22-2222222222-22222-2-2-2-20000-2-2000000000000000000000-2-22200000
χ292222-2-2-2-2222222222-2-2-2-2-2-2-2-20000220000000000000000000000000002i−2i0
χ302222-2-2-2-2222222222-2-2-2-2-2-2-2-2000022000000000000000000000000000−2i2i0
χ312-2-22020-22222-2-2-2-202-22-2000000i2−i20000000000i2−i2i2−i2i2−i2i2−i2000002-200i2−i2000
χ322-2-22020-22222-2-2-2-202-22-2000000i2−i20000000000i2−i2i2−i2i2−i2i2−i200000-2200−i2i2000
χ332-2-22020-22222-2-2-2-202-22-2000000−i2i20000000000−i2i2−i2i2−i2i2−i2i2000002-200−i2i2000
χ342-2-22020-22222-2-2-2-202-22-2000000−i2i20000000000−i2i2−i2i2−i2i2−i2i200000-2200i2−i2000
χ354444-44-44−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5-4−1+5−1+5−1−5−1−51−51+51−51+500001−51+5000000000000000000000000000000
χ364444-44-44−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5-4−1−5−1−5−1+5−1+51+51−51+51−500001+51−5000000000000000000000000000000
χ374444-4-4-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−541−51−51+51+51−51+51−51+50000−1+5−1−5000000000000000000000000000000
χ384444-4-4-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+541+51+51−51−51+51−51+51−50000−1−5−1+5000000000000000000000000000000
χ3944-4-4000044-4-44-44-4000000000000000000000000000000000000002i2−2i200000
χ4044-4-4000044-4-44-44-400000000000000000000000000000000000000−2i22i200000
χ414-44-440-4044-4-4-44-440000044-4-4000000000000000000000000000000000000
χ424-44-440-40−1+5−1−51−51+51−5−1+51+5−1−500000−1+5−1−51−51+5000000−2ζ22+2ζ382ζ22−2ζ38002ζ6−2ζ14−2ζ6+2ζ14000000000000000000000000
χ434-44-440-40−1+5−1−51−51+51−5−1+51+5−1−500000−1+5−1−51−51+50000002ζ22−2ζ38−2ζ22+2ζ3800−2ζ6+2ζ142ζ6−2ζ14000000000000000000000000
χ444-44-440-40−1−5−1+51+51−51+5−1−51−5−1+500000−1−5−1+51+51−50000002ζ6−2ζ14−2ζ6+2ζ14002ζ22−2ζ38−2ζ22+2ζ38000000000000000000000000
χ454-44-440-40−1−5−1+51+51−51+5−1−51−5−1+500000−1−5−1+51+51−5000000−2ζ6+2ζ142ζ6−2ζ1400−2ζ22+2ζ382ζ22−2ζ38000000000000000000000000
χ464-44-4-404044-4-4-44-4400000-4-444000000000000000000000000000000000000
χ474-44-4-4040−1+5−1−51−51+51−5−1+51+5−1−5000001−51+5−1+5−1−5000000002ζ12−2ζ28−2ζ12+2ζ2800−2ζ4+2ζ362ζ4−2ζ360000000000000000000000
χ484-44-4-4040−1+5−1−51−51+51−5−1+51+5−1−5000001−51+5−1+5−1−500000000−2ζ12+2ζ282ζ12−2ζ28002ζ4−2ζ36−2ζ4+2ζ360000000000000000000000
χ494-44-4-4040−1−5−1+51+51−51+5−1−51−5−1+5000001+51−5−1−5−1+500000000−2ζ4+2ζ362ζ4−2ζ3600−2ζ12+2ζ282ζ12−2ζ280000000000000000000000
χ504-44-4-4040−1−5−1+51+51−51+5−1−51−5−1+5000001+51−5−1−5−1+5000000002ζ4−2ζ36−2ζ4+2ζ36002ζ12−2ζ28−2ζ12+2ζ280000000000000000000000
χ514-4-44040-4−1+5−1−5−1+5−1−51−51−51+51+50−1+51−5−1−51+50000002i2−2i20000000000ζ7+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
χ524-4-44040-4−1+5−1−5−1+5−1−51−51−51+51+50−1+51−5−1−51+5000000−2i22i20000000000−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
χ534-4-44040-4−1−5−1+5−1−5−1+51+51+51−51−50−1−51+5−1+51−50000002i2−2i20000000000ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ3700000000000000
χ544-4-44040-4−1−5−1+5−1−5−1+51+51+51−51−50−1−51+5−1+51−5000000−2i22i20000000000−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ3700000000000000
χ554-4-440-4044444-4-4-4-40-44-440000000000000000000000000000000000000000
χ564-4-440-404−1+5−1−5−1+5−1−51−51−51+51+501−5−1+51+5−1−5000000000000000000ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ3900000000000000
χ574-4-440-404−1+5−1−5−1+5−1−51−51−51+51+501−5−1+51+5−1−5000000000000000000−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ3900000000000000
χ584-4-440-404−1−5−1+5−1−5−1+51+51+51−51−501+5−1−51−5−1+5000000000000000000−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ3700000000000000
χ594-4-440-404−1−5−1+5−1−5−1+51+51+51−51−501+5−1−51−5−1+5000000000000000000ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ3700000000000000
χ6088-8-80000−2+25−2−252−252+25−2+252−25−2−252+25000000000000000000000000000000000000000000000
χ6188-8-80000−2−25−2+252+252−25−2−252+25−2+252−25000000000000000000000000000000000000000000000

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