Finite Group Databasebeta

← Group #10612078

Character table — Group #10612078

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size1111222222222244444444444488888888888888888888888161616162020202020204040404040
order1222445510101010101044882020202020202020222481010101020202020202040404040404040401010101024448824448
χ11111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-111111111-1-1-1-1111111-1-1-1-11
χ411111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1
χ51111111111111111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1-1
χ61111111111111111-1-11111111111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-1-111
χ71111111111111111-1-111111111-1-111-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-11-1
χ81111111111111111-1-111111111-1-111-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-11
χ911111111111111-1-11111-1-1-1-1111-11-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1
χ1011111111111111-1-11111-1-1-1-1111-11-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-11
χ1111111111111111-1-11111-1-1-1-111-11-11-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111-1-1-1
χ1211111111111111-1-11111-1-1-1-111-11-11-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1111
χ1311111111111111-1-1-1-111-1-1-1-1111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-11-11-11
χ1411111111111111-1-1-1-111-1-1-1-1111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-11-11-1
χ1511111111111111-1-1-1-111-1-1-1-111-111-111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-11-111
χ1611111111111111-1-1-1-111-1-1-1-111-111-111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111111-11-1-1
χ17222222−1+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+52−1−5222222−1+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+52−1−5200000000000
χ18222222−1+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+52−1−52-2-2-2-221−521−521+521+52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+5200000000000
χ19222222−1+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+52−1−5222-2-2-21−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−5200000000000
χ20222222−1+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+52−1−52-2-222-2−1+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+5200000000000
χ21222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-222−1+52−1−521−521−521+521+52−1+52−1−522-22-2-2−1+52−1+52−1−52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521+5200000000000
χ22222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-222−1+52−1−521−521−521+521+52−1+52−1−52-22-22-21−521−521+521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521+52−1+52−1−5200000000000
χ23222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2−1+52−1−521−521−521+521+52−1+52−1−522-2-2221−521−521+521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+5200000000000
χ24222222−1+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+52−1+52−1−52-222-22−1+52−1+52−1−52−1−521−521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−5200000000000
χ25222222−1−52−1+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+5222222−1−52−1−52−1+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+5200000000000
χ26222222−1−52−1+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+52-2-2-2-221+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+521+521−521+521−5200000000000
χ27222222−1−52−1+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+5222-2-2-21+521+521−521−52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+5200000000000
χ28222222−1−52−1+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+52-2-222-2−1−52−1−52−1+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+521−5200000000000
χ29222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-222−1−52−1+521+521+521−521−52−1−52−1+522-22-2-2−1−52−1−52−1+52−1+521+521−521+521+521−521−52−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+521+521−5200000000000
χ30222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-222−1−52−1+521+521+521−521−52−1−52−1+52-22-22-21+521+521−521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521−52−1−52−1+5200000000000
χ31222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-2−1−52−1+521+521+521−521−52−1−52−1+522-2-2221+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+52−1−52−1+521+521−5200000000000
χ32222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-2−1−52−1+521+521+521−521−52−1−52−1+52-222-22−1−52−1−52−1+52−1+521+521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+521+521−52−1−52−1+5200000000000
χ332222-2-2222222222-200-2-22222-2-2000000000-2-200000000000000002-2-220000000
χ342222-2-2222222222-200-2-22222-2-2000000000-2-20000000000000000-222-20000000
χ352222-2-222222222-2200-2-2-2-2-2-2-2-20000000002200000000000000002-22-20000000
χ362222-2-222222222-2200-2-2-2-2-2-2-2-2000000000220000000000000000-22-220000000
χ374444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−54-4001−51+5−1+5−1+5−1−5−1−51−51+50000000001−51+5000000000000000000000000000
χ384444-4-4−1+5−1−5−1+5−1+5−1−5−1−5−1+5−1−5-44001−51+51−51−51+51+51−51+5000000000−1+5−1−5000000000000000000000000000
χ394444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+54-4001+51−5−1−5−1−5−1+5−1+51+51−50000000001+51−5000000000000000000000000000
χ404444-4-4−1−5−1+5−1−5−1−5−1+5−1+5−1−5−1+5-44001+51−51+51+51−51−51+51−5000000000−1−5−1+5000000000000000000000000000
χ4144-4-44-4444-44-4-4-40000440000-4-400000000000000000000000000000000000000
χ4244-4-44-4−1+5−1−5−1+51−5−1−51+51−51+50000−1+5−1−500001−51+500000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000
χ4344-4-44-4−1+5−1−5−1+51−5−1−51+51−51+50000−1+5−1−500001−51+5000000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000
χ4444-4-44-4−1−5−1+5−1−51+5−1+51−51+51−50000−1−5−1+500001+51−5000000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ3800000000000000000000000
χ4544-4-44-4−1−5−1+5−1−51+5−1+51−51+51−50000−1−5−1+500001+51−500000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ3800000000000000000000000
χ4644-4-4-44444-44-4-4-40000-4-400004400000000000000000000000000000000000000
χ4744-4-4-44−1+5−1−5−1+51−5−1−51+51−51+500001−51+50000−1+5−1−5000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000000000000000
χ4844-4-4-44−1+5−1−5−1+51−5−1−51+51−51+500001−51+50000−1+5−1−500000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000000000000000
χ4944-4-4-44−1−5−1+5−1−51+5−1+51−51+51−500001+51−50000−1−5−1+500000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000000000000000
χ5044-4-4-44−1−5−1+5−1−51+5−1+51−51+51−500001+51−50000−1−5−1+5000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000000000000000
χ514-44-40044-4-4-4-4440022−220000000000000000000000022−2222−220000000000000000000
χ524-44-40044-4-4-4-44400−222200000000000000000000000−2222−22220000000000000000000
χ534-44-400−1+5−1−51−51−51+51+5−1+5−1−50022−22002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000
χ544-44-400−1+5−1−51−51−51+51+5−1+5−1−50022−2200−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000−ζ7+ζ13−ζ23+ζ37ζ7−ζ13+ζ23−ζ37ζ21+ζ29−ζ31−ζ39−ζ21−ζ29+ζ31+ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39000000000000000
χ554-44-400−1+5−1−51−51−51+51+5−1+5−1−500−2222002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3600000000000000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39ζ7+ζ13−ζ23−ζ37−ζ7−ζ13+ζ23+ζ37ζ21−ζ29−ζ31+ζ39−ζ21+ζ29+ζ31−ζ39000000000000000
χ564-44-400−1+5−1−51−51−51+51+5−1+5−1−500−222200−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3600000000000000000ζ7−ζ13+ζ23−ζ37−ζ7+ζ13−ζ23+ζ37−ζ21−ζ29+ζ31+ζ39ζ21+ζ29−ζ31−ζ39−ζ7−ζ13+ζ23+ζ37ζ7+ζ13−ζ23−ζ37−ζ21+ζ29+ζ31−ζ39ζ21−ζ29−ζ31+ζ39000000000000000
χ574-44-400−1−5−1+51+51+51−51−5−1−5−1+50022−2200−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000ζ21+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
χ584-44-400−1−5−1+51+51+51−51−5−1−5−1+50022−22002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000ζ21+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
χ594-44-400−1−5−1+51+51+51−51−5−1−5−1+500−222200−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2800000000000000000−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
χ604-44-400−1−5−1+51+51+51−51−5−1−5−1+500−2222002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2800000000000000000−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
χ614-4-440044-44-44-4-4000000000000000000000000000000000000000000022−2200000
χ624-4-440044-44-44-4-40000000000000000000000000000000000000000000−222200000
χ638-8-8800−2+25−2−252−25−2+252+25−2−252−252+2500000000000000000000000000000000000000000000000000
χ648-8-8800−2−25−2+252+25−2−252−25−2+252+252−2500000000000000000000000000000000000000000000000000

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