Finite Group Databasebeta

← Group #10612103

Character table — Group #10612103

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67
size111122222222224444444444444488888888888888888888881010161616162020202020202040404040
order1222445510101010101044448820202020202020202248202020202020202020204040404040404040441010101044444882448
χ11111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-111111111-1-11-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-111-1
χ4111111111111111111-1-111111111-1-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11
χ51111111111111111-1-111-1-1-1-111111-1-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-11-1-11111-11-1-1
χ61111111111111111-1-111-1-1-1-111111-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-111-1-1-1-11-111
χ71111111111111111-1-1-1-1-1-1-1-11111-11-111111-1-1-1-1-1-1-1-1-1-1111111-1-1111-1-1-1-1-1-111-11
χ81111111111111111-1-1-1-1-1-1-1-11111-11-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1111111-1-11-1
χ911111111111111-1-1111111111111-1-1-11-1-1-1-111-1-1-1-11111111111-1-1-1-1111-1-111-1-1-11
χ1011111111111111-1-1111111111111-1-1-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1111-1
χ1111111111111111-1-111-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-1-1
χ1211111111111111-1-111-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-1111
χ1311111111111111-1-1-1-111-1-1-1-11111-111-1-1-1-1-1-1-111111111-1-1-1-111-1-1111-1-1-1-1111-11-1
χ1411111111111111-1-1-1-111-1-1-1-11111-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-11111-1-1-11-11
χ1511111111111111-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-1-1-11111-1-1-1-111111111-1-11-1-111-1-1-1-111
χ1611111111111111-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1-111-1-11111-1-1
χ17222222−1+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+52−1−522222−1+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+52−1−52−1−5200−1+52−1−52−1+52−1−5200000000000
χ18222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−522222-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-2-22-2−1+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+52001−521+521−521+5200000000000
χ19222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222-2-2221−521−521+521+52−1+52−1−52−1+52−1−522-2-2-2−1+52−1+52−1−52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+5200−1+52−1−521−521+5200000000000
χ20222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−5222-2-2-2-21−521−521+521+52−1+52−1−52−1+52−1−52-22-22−1+52−1+52−1−52−1−521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52001−521+52−1+52−1−5200000000000
χ21222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-22222−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−52-2-2-221−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52001−521+521−521+5200000000000
χ22222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-222-2-2−1+52−1+52−1−52−1−52−1+52−1−52−1+52−1−5222-2-21−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+5200−1+52−1−52−1+52−1−5200000000000
χ23222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2-2-2221−521−521+521+52−1+52−1−52−1+52−1−52-222-21−521−521+521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+52001−521+52−1+52−1−5200000000000
χ24222222−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52-2-2-2-2-2-21−521−521+521+52−1+52−1−52−1+52−1−522-2221−521−521+521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200−1+52−1−521−521+5200000000000
χ25222222−1−52−1+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+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+5200−1−52−1+52−1−52−1+5200000000000
χ26222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+522222-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52-2-22-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52001+521−521+521−5200000000000
χ27222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222-2-2221+521+521−521−52−1−52−1+52−1−52−1+522-2-2-2−1−52−1−52−1+52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−5200−1−52−1+521+521−5200000000000
χ28222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+5222-2-2-2-21+521+521−521−52−1−52−1+52−1−52−1+52-22-22−1−52−1−52−1+52−1+521+521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52001+521−52−1−52−1+5200000000000
χ29222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-22222−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+52-2-2-221+521+521−521−52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52001+521−521+521−5200000000000
χ30222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-222-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1+5222-2-21+521+521−521−52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−5200−1−52−1+52−1−52−1+5200000000000
χ31222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2-2-2221+521+521−521−52−1−52−1+52−1−52−1+52-222-21+521+521−521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−52001+521−52−1−52−1+5200000000000
χ32222222−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52-2-2-2-2-2-21+521+521−521−52−1−52−1+52−1−52−1+522-2221+521+521−521−521+521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1−52−1+52−1+5200−1−52−1+521+521−5200000000000
χ332222-2-222222222002-2002222-2-2-2-200000000-2-2000000000000220000-22-200000000
χ342222-2-222222222002-2002222-2-2-2-200000000-2-2000000000000-2-200002-2200000000
χ352222-2-22222222200-2200-2-2-2-2-2-2-2-20000000022000000000000220000-2-2200000000
χ362222-2-22222222200-2200-2-2-2-2-2-2-2-20000000022000000000000-2-2000022-200000000
χ3722-2-2-2222-2-22-22-22-200000000-2-22200002-22-2000000000000000000000002i−2i2i−2i0000
χ3822-2-2-2222-2-22-22-22-200000000-2-22200002-22-200000000000000000000000−2i2i−2i2i0000
χ3922-2-2-2222-2-22-22-2-2200000000-2-2220000-22-22000000000000000000000002i−2i−2i2i0000
χ4022-2-2-2222-2-22-22-2-2200000000-2-2220000-22-2200000000000000000000000−2i2i2i−2i0000
χ414444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−5004-400−1+5−1+5−1−5−1−51−51+51−51+5000000001−51+500000000000000000000000000000
χ424444-4-4−1+5−1−5−1+5−1−5−1+5−1+5−1−5−1−500-44001−51−51+51+51−51+51−51+500000000−1+5−1−500000000000000000000000000000
χ434444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+5004-400−1−5−1−5−1+5−1+51+51−51+51−5000000001+51−500000000000000000000000000000
χ444444-4-4−1−5−1+5−1−5−1+5−1−5−1−5−1+5−1+500-44001+51+51−51−51+51−51+51−500000000−1−5−1+500000000000000000000000000000
χ4544-4-44-444-4-44-44-4000000000044-4-4000000000000000000000000000000000000000
χ4644-4-44-4−1+5−1−51−51+5−1+51−5−1−51+50000000000−1+5−1−51−51+50000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ140000000000000000000000000
χ4744-4-44-4−1+5−1−51−51+5−1+51−5−1−51+50000000000−1+5−1−51−51+500000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ140000000000000000000000000
χ4844-4-44-4−1−5−1+51+51−5−1−51+5−1+51−50000000000−1−5−1+51+51−500000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ380000000000000000000000000
χ4944-4-44-4−1−5−1+51+51−5−1−51+5−1+51−50000000000−1−5−1+51+51−50000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ380000000000000000000000000
χ5044-4-4-44−1+5−1−51−51+5−1+51−5−1−51+54-4000000001−51+5−1+5−1−50000−1+51−5−1−51+50000000000000000000000000000000
χ5144-4-4-44−1+5−1−51−51+5−1+51−5−1−51+5-44000000001−51+5−1+5−1−500001−5−1+51+5−1−50000000000000000000000000000000
χ5244-4-4-44−1−5−1+51+51−5−1−51+5−1+51−54-4000000001+51−5−1−5−1+50000−1−51+5−1+51−50000000000000000000000000000000
χ5344-4-4-44−1−5−1+51+51−5−1−51+5−1+51−5-44000000001+51−5−1−5−1+500001+5−1−51−5−1+50000000000000000000000000000000
χ544-44-4004444-4-4-4-400002i2−2i200000000000000000000002i2−2i22i2−2i2000000000000000000000
χ554-44-4004444-4-4-4-40000−2i22i20000000000000000000000−2i22i2−2i22i2000000000000000000000
χ564-44-400−1+5−1−5−1+5−1−51−51−51+51+500002i2−2i22ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36000000000000000000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ3900000000000000000
χ574-44-400−1+5−1−5−1+5−1−51−51−51+51+500002i2−2i2−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36000000000000000000ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ3900000000000000000
χ584-44-400−1+5−1−5−1+5−1−51−51−51+51+50000−2i22i22ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36000000000000000000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ3900000000000000000
χ594-44-400−1+5−1−5−1+5−1−51−51−51+51+50000−2i22i2−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36000000000000000000−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ3900000000000000000
χ604-44-400−1−5−1+5−1−5−1+51+51+51−51−500002i2−2i2−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28000000000000000000ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ3700000000000000000
χ614-44-400−1−5−1+5−1−5−1+51+51+51−51−500002i2−2i22ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28000000000000000000ζ21+ζ29+ζ31+ζ39−ζ21−ζ29−ζ31−ζ39ζ7+ζ13+ζ23+ζ37−ζ7−ζ13−ζ23−ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ3700000000000000000
χ624-44-400−1−5−1+5−1−5−1+51+51+51−51−50000−2i22i2−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28000000000000000000−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37−ζ21+ζ29−ζ31+ζ39ζ21−ζ29+ζ31−ζ39−ζ7+ζ13+ζ23−ζ37ζ7−ζ13−ζ23+ζ3700000000000000000
χ634-44-400−1−5−1+5−1−5−1+51+51+51−51−50000−2i22i22ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28000000000000000000−ζ21−ζ29−ζ31−ζ39ζ21+ζ29+ζ31+ζ39−ζ7−ζ13−ζ23−ζ37ζ7+ζ13+ζ23+ζ37ζ21−ζ29+ζ31−ζ39−ζ21+ζ29−ζ31+ζ39ζ7−ζ13−ζ23+ζ37−ζ7+ζ13+ζ23−ζ3700000000000000000
χ644-4-440044-4-4-44-440000000000000000000000000000000000004-4000000000000000
χ654-4-440044-4-4-44-44000000000000000000000000000000000000-44000000000000000
χ668-8-8800−2+25−2−252−252+252−25−2+252+25−2−2500000000000000000000000000000000000000000000000000000
χ678-8-8800−2−25−2+252+252−252+25−2−252−25−2+2500000000000000000000000000000000000000000000000000000

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