Finite Group Databasebeta

← Group #10612708

Character table — Group #10612708

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1111222222222222444444444888888888888888888888888101016161616202020404040404040
order1222444455101010101010420202020202020202444881010101020202020202040404040404040404420202020244224488
χ11111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-111-1-1
χ4111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1
χ61111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111
χ71111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111111111-1-1-1-1111-1-1-1-111
χ81111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-1
χ91111-1-11111111111-111-1-1-1-1111-11-11-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-11-11-11-11-1
χ101111-1-11111111111-111-1-1-1-1111-11-11-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11-11-11-11-11
χ111111-1-11111111111-111-1-1-1-1111-1-11-111111-1-1-1-1-1-1-1-1-1-1111111-1-111-11-1-111-1-11
χ121111-1-11111111111-111-1-1-1-1111-1-11-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-111-1-111-1
χ131111-1-11111111111-111-1-1-1-111-111-1-11-1-1-1-1-1-11111-1-1-1-111111111-1-1-11-11-1-11-11
χ141111-1-11111111111-111-1-1-1-111-111-1-11-1-1-1-1-1-11111-1-1-1-11111-1-111-1-11-11-111-11-1
χ151111-1-11111111111-111-1-1-1-111-11-111-1-1-1-1-1-1-111111111-1-1-1-111-1-111-11-1-11-111-1
χ161111-1-11111111111-111-1-1-1-111-11-111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-111-11-1-11
χ1722222222−1+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+52−1−52222222−1+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+52−1−52−1−5200−1+52−1−52−1+52−1−52000000000
χ1822222222−1+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+52−1−5222-2-2-2-2−1+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+52001−521+521−521+52000000000
χ1922222222−1+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+52−1−52-2-222-2-21−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+5200−1+52−1−52−1+52−1−52000000000
χ2022222222−1+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+52−1−52-2-2-2-2221−521−521+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+52000000000
χ2122222222−1−52−1+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+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+5200−1−52−1+52−1−52−1+52000000000
χ2222222222−1−52−1+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+5222-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52001+521−521+521−52000000000
χ2322222222−1−52−1+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+52-2-222-2-21+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+52000000000
χ2422222222−1−52−1+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+52-2-2-2-2221+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+521−52000000000
χ25222222-2-222222222-2-2-22222-2-20000000000-2-20000000000002200002-2-2000000
χ26222222-2-222222222-2-2-22222-2-20000000000-2-2000000000000-2-20000-222000000
χ272222-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2−1+52−1−521−521−521+521+52−1+52−1−522-22-22-2−1+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+52000000000
χ282222-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2−1+52−1−521−521−521+521+52−1+52−1−522-2-22-22−1+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+52−1−52000000000
χ292222-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2−1+52−1−521−521−521+521+52−1+52−1−52-222-2-221−521−521+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+52000000000
χ302222-2-222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2−1+52−1−521−521−521+521+52−1+52−1−52-22-222-21−521−521+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+52−1−52000000000
χ312222-2-222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2−1−52−1+521+521+521−521−52−1−52−1+522-22-22-2−1−52−1−52−1+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+521−52000000000
χ322222-2-222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2−1−52−1+521+521+521−521−52−1−52−1+522-2-22-22−1−52−1−52−1+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+52000000000
χ332222-2-222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2−1−52−1+521+521+521−521−52−1−52−1+52-222-2-221+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+521−52000000000
χ342222-2-222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2−1−52−1+521+521+521−521−52−1−52−1+52-22-222-21+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+52000000000
χ352222-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000022000000000000220000-2-22000000
χ362222-2-2-2-2222222222-2-2-2-2-2-2-2-2000000000022000000000000-2-2000022-2000000
χ37444444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-41−51+5−1+5−1+5−1−5−1−51−51+500000000001−51+5000000000000000000000000000
χ38444444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-41+51−5−1−5−1−5−1+5−1+51+51−500000000001+51−5000000000000000000000000000
χ394444-4-4-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−541−51+51−51−51+51+51−51+50000000000−1+5−1−5000000000000000000000000000
χ404444-4-4-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+541+51−51+51+51−51−51+51−50000000000−1−5−1+5000000000000000000000000000
χ4144-4-44-40044-4-4-4-4440004-44-400000000000000000000000000000000000000000
χ4244-4-44-400−1+5−1−51−51−51+51+5−1+5−1−5000−1+51−5−1−51+5000000000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000
χ4344-4-44-400−1+5−1−51−51−51+51+5−1+5−1−5000−1+51−5−1−51+5000000000000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39000000000000000
χ4444-4-44-400−1−5−1+51+51+51−51−5−1−5−1+5000−1−51+5−1+51−5000000000000000000−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37000000000000000
χ4544-4-44-400−1−5−1+51+51+51−51−5−1−5−1+5000−1−51+5−1+51−5000000000000000000ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37000000000000000
χ4644-4-4-440044-4-4-4-444000-44-4400000000000000000000000000000000000000000
χ4744-4-4-4400−1+5−1−51−51−51+51+5−1+5−1−50001−5−1+51+5−1−5000000000000000000−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39000000000000000
χ4844-4-4-4400−1+5−1−51−51−51+51+5−1+5−1−50001−5−1+51+5−1−5000000000000000000ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000
χ4944-4-4-4400−1−5−1+51+51+51−51−5−1−5−1+50001+5−1−51−5−1+5000000000000000000−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37000000000000000
χ5044-4-4-4400−1−5−1+51+51+51−51−5−1−5−1+50001+5−1−51−5−1+5000000000000000000ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37000000000000000
χ514-44-40000444-44-4-4-40000000000000000000000000000000004i−4i0000000000000
χ524-44-40000444-44-4-4-4000000000000000000000000000000000−4i4i0000000000000
χ534-4-44004-444-44-44-4-40440000-4-4000000000000000000000000000000000000000
χ544-4-44004-4−1+5−1−51−5−1+51+5−1−51−51+50−1+5−1−500001−51+50000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000000000
χ554-4-44004-4−1+5−1−51−5−1+51+5−1−51−51+50−1+5−1−500001−51+5000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000000000
χ564-4-44004-4−1−5−1+51+5−1−51−5−1+51+51−50−1−5−1+500001+51−5000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000000000
χ574-4-44004-4−1−5−1+51+5−1−51−5−1+51+51−50−1−5−1+500001+51−50000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000000000
χ584-4-4400-4444-44-44-4-40-4-4000044000000000000000000000000000000000000000
χ594-4-4400-44−1+5−1−51−5−1+51+5−1−51−51+501−51+50000−1+5−1−5000000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000
χ604-4-4400-44−1+5−1−51−5−1+51+5−1−51−51+501−51+50000−1+5−1−50000000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000
χ614-4-4400-44−1−5−1+51+5−1−51−5−1+51+51−501+51−50000−1−5−1+50000000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ3800000000000000000000000
χ624-4-4400-44−1−5−1+51+5−1−51−5−1+51+51−501+51−50000−1−5−1+5000000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ3800000000000000000000000
χ638-88-80000−2+25−2−25−2+252−25−2−252+252−252+25000000000000000000000000000000000000000000000000
χ648-88-80000−2−25−2+25−2−252+25−2+252−252+252−25000000000000000000000000000000000000000000000000

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