Finite Group Databasebeta

← Group #12011987

Character table — Group #12011987

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111222222222244444488888888881616161616161616161616161616161616161616161616161616161616161616404080808080808080
order1222225510101010101044101010104420202020202020202244881010101010101010202020202020202020204040404040404040442448888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-11-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-1
χ41111111111111111111111111111111-11-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ5111111111111111111111111111111-11-11-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1
χ6111111111111111111111111111111-11-11-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-11111-1-1
χ922222222222222222222-2-22222-2-2-2-200000000000000-2-2000000000000000022-2000000
χ1022222222222222222222-2-22222-2-2-2-200000000000000-2-20000000000000000-2-22000000
χ1122222222222222-2-222222-2-2-2-2-22222020-20000002222-2-20000-2-2-2-200000000000000000
χ1222222222222222-2-222222-2-2-2-2-222220-202000000-2-2-2-2-2-20000222200000000000000000
χ1322222222222222-2-22222-22-2-2-2-2-2-2-2-2000000000000002200000000000000000002-20000
χ1422222222222222-2-22222-22-2-2-2-2-2-2-2-200000000000000220000000000000000000-220000
χ15222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−5222−1+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+52−1−52−1−52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52000000000
χ16222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522-22-2-2-2−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521−521−521+521+521+521+52000000000
χ17222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-22-22-2-21−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521−521+521+52−1+52−1+52−1−52−1−521−521−521−521−521+521+521+521+52000000000
χ18222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222−1+52−1−52−1+52−1−5222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-2221−521−521+521+521−521−521+521+52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1+52−1+52−1+52−1−52−1−52−1−52−1−52000000000
χ19222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−52020-200ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−1+52−1+52−1−52−1−521−521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ361−521−521+521+52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36000000000
χ20222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−52020-200−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−1+52−1+52−1−52−1−521−521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ361−521−521+521+52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36000000000
χ21222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−520-20200ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ361−521−521+521+521−521+52ζ12−ζ28−ζ12+ζ28−ζ4+ζ36ζ4−ζ36−1+52−1+52−1−52−1−52−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36000000000
χ22222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−522-21−521−521+521+52−1+52−1+52−1−52−1−520-20200−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ361−521−521+521+521−521+52−ζ12+ζ28ζ12−ζ28ζ4−ζ36−ζ4+ζ36−1+52−1+52−1−52−1−52ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36000000000
χ23222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+5222−1−52−1−52−1+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+52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52000000000
χ24222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522-22-2-2-2−1−52−1−52−1+52−1+521+521+521−521−52−1−52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521+521+521−521−521−521−52000000000
χ25222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-22-22-2-21+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1+521+521+521−521−52−1−52−1−52−1+52−1+521+521+521+521+521−521−521−521−52000000000
χ26222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222−1−52−1+52−1−52−1+5222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-2221+521+521−521−521+521+521−521−52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1−52−1−52−1−52−1+52−1+52−1+52−1+52000000000
χ27222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+522-21+521+521−521−52−1−52−1−52−1+52−1+52020-200−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−1−52−1−52−1+52−1+521+521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ281+521+521−521−52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28000000000
χ28222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+522-21+521+521−521−52−1−52−1−52−1+52−1+52020-200ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−1−52−1−52−1+52−1+521+521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ281+521+521−521−52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28000000000
χ29222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+522-21+521+521−521−52−1−52−1−52−1+52−1+520-20200−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ281+521+521−521−521+521−52−ζ4+ζ36ζ4−ζ36−ζ12+ζ28ζ12−ζ28−1−52−1−52−1+52−1+52ζ4−ζ36ζ4−ζ36−ζ4+ζ36−ζ4+ζ36ζ12−ζ28ζ12−ζ28−ζ12+ζ28−ζ12+ζ28000000000
χ30222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+522-21+521+521−521−52−1−52−1−52−1+52−1+520-20200ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ281+521+521−521−521+521−52ζ4−ζ36−ζ4+ζ36ζ12−ζ28−ζ12+ζ28−1−52−1−52−1+52−1+52−ζ4+ζ36−ζ4+ζ36ζ4−ζ36ζ4−ζ36−ζ12+ζ28−ζ12+ζ28ζ12−ζ28ζ12−ζ28000000000
χ312-22-22-222-2-2-2-2222-2-2-222002-22-2000000002−20000000000000000002−22−22−22−22i−2i00000i2−i2
χ322-22-22-222-2-2-2-2222-2-2-222002-22-2000000002−20000000000000000002−22−22−22−2−2i2i00000−i2i2
χ332-22-22-222-2-2-2-2222-2-2-222002-22-200000000−22000000000000000000−22−22−22−222i−2i00000−i2i2
χ342-22-22-222-2-2-2-2222-2-2-222002-22-200000000−22000000000000000000−22−22−22−22−2i2i00000i2−i2
χ35444444−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−544−1+5−1−5−1+5−1−5-4-4−1+5−1+5−1−5−1−51−51−51+51+5000000000000001−51+50000000000000000000000000
χ36444444−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5-4-4−1+5−1−5−1+5−1−5-441−51−51+51+51−51−51+51+500000000000000−1+5−1−50000000000000000000000000
χ37444444−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+544−1−5−1+5−1−5−1+5-4-4−1−5−1−5−1+5−1+51+51+51−51−5000000000000001+51−50000000000000000000000000
χ38444444−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5-4-4−1−5−1+5−1−5−1+5-441+51+51−51−51+51+51−51−500000000000000−1−5−1+50000000000000000000000000
χ394444-4-44444444400-4-4-4-4000000000020-20002222000000-2-2-2-2000000000000000000000
χ404444-4-44444444400-4-4-4-40000000000-202000-2-2-2-20000002222000000000000000000000
χ414444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5001−51+51−51+50000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ3620-2000−2ζ28−2ζ12−2ζ4−2ζ360000002ζ282ζ122ζ42ζ36000000000000000000000
χ424444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5001−51+51−51+50000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36-2020002ζ282ζ122ζ42ζ36000000−2ζ28−2ζ12−2ζ4−2ζ36000000000000000000000
χ434444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5001−51+51−51+5000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ3620-2000−2ζ12−2ζ28−2ζ36−2ζ40000002ζ122ζ282ζ362ζ4000000000000000000000
χ444444-4-4−1+5−1−5−1+5−1−5−1+5−1−5−1+5−1−5001−51+51−51+5000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36-2020002ζ122ζ282ζ362ζ4000000−2ζ12−2ζ28−2ζ36−2ζ4000000000000000000000
χ454444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5001+51−51+51−5000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ2820-2000−2ζ4−2ζ36−2ζ12−2ζ280000002ζ42ζ362ζ122ζ28000000000000000000000
χ464444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5001+51−51+51−5000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28-2020002ζ42ζ362ζ122ζ28000000−2ζ4−2ζ36−2ζ12−2ζ28000000000000000000000
χ474444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5001+51−51+51−50000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ2820-2000−2ζ36−2ζ4−2ζ28−2ζ120000002ζ362ζ42ζ282ζ12000000000000000000000
χ484444-4-4−1−5−1+5−1−5−1+5−1−5−1+5−1−5−1+5001+51−51+51−50000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28-2020002ζ362ζ42ζ282ζ12000000−2ζ36−2ζ4−2ζ28−2ζ12000000000000000000000
χ494-44-44-444-4-4-4-444-44-4-44400-44-44000000000000000000000000000000000000000000000
χ504-44-44-4−1+5−1−51−51+51−51+5−1+5−1−54-41−51+5−1+5−1−500−1+51−5−1−51+50000000022−22000000000000000000−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+ζ39000000000
χ514-44-44-4−1+5−1−51−51+51−51+5−1+5−1−54-41−51+5−1+5−1−500−1+51−5−1−51+500000000−2222000000000000000000ζ7−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−ζ39000000000
χ524-44-44-4−1+5−1−51−51+51−51+5−1+5−1−5-441−51+5−1+5−1−5001−5−1+51+5−1−50000000000000000000000000000−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+ζ39000000000
χ534-44-44-4−1+5−1−51−51+51−51+5−1+5−1−5-441−51+5−1+5−1−5001−5−1+51+5−1−50000000000000000000000000000ζ7+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−ζ39000000000
χ544-44-44-4−1−5−1+51+51−51+51−5−1−5−1+54-41+51−5−1−5−1+500−1−51+5−1+51−50000000022−22000000000000000000ζ21+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−ζ37000000000
χ554-44-44-4−1−5−1+51+51−51+51−5−1−5−1+54-41+51−5−1−5−1+500−1−51+5−1+51−500000000−2222000000000000000000−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+ζ37000000000
χ564-44-44-4−1−5−1+51+51−51+51−5−1−5−1+5-441+51−5−1−5−1+5001+5−1−51−5−1+50000000000000000000000000000−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+ζ37000000000
χ574-44-44-4−1−5−1+51+51−51+51−5−1−5−1+5-441+51−5−1−5−1+5001+5−1−51−5−1+50000000000000000000000000000ζ21−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−ζ37000000000
χ584-44-4-4444-4-4-4-4440044-4-4000000000000000000000000000000000000000000000002-200
χ594-44-4-4444-4-4-4-4440044-4-400000000000000000000000000000000000000000000000-2200
χ6088-8-80088-8-888-8-8000000000000000000000000000000000000000000000000000000000
χ6188-8-800−2+25−2−252−252+25−2+25−2−252−252+25000000000000000000000000002ζ12−2ζ28−2ζ12+2ζ28−2ζ4+2ζ362ζ4−2ζ36000000000000000000000000000
χ6288-8-800−2+25−2−252−252+25−2+25−2−252−252+2500000000000000000000000000−2ζ12+2ζ282ζ12−2ζ282ζ4−2ζ36−2ζ4+2ζ36000000000000000000000000000
χ6388-8-800−2−25−2+252+252−25−2−25−2+252+252−2500000000000000000000000000−2ζ4+2ζ362ζ4−2ζ36−2ζ12+2ζ282ζ12−2ζ28000000000000000000000000000
χ6488-8-800−2−25−2+252+252−25−2−25−2+252+252−25000000000000000000000000002ζ4−2ζ36−2ζ4+2ζ362ζ12−2ζ28−2ζ12+2ζ28000000000000000000000000000
χ658-88-8-88−2+25−2−252−252+252−252+25−2+25−2−2500−2+25−2−252−252+25000000000000000000000000000000000000000000000000000
χ668-88-8-88−2−25−2+252+252−252+252−25−2−25−2+2500−2−25−2+252+252−25000000000000000000000000000000000000000000000000000
χ678-8-88008888-8-8-8-8000000000000000000000000000000000000000000000000000000000
χ688-8-8800−2+25−2−25−2+25−2−252−252+252−252+25000000000000000000000000000000000000−2ζ22+2ζ382ζ22−2ζ382ζ6−2ζ14−2ζ6+2ζ1400000000000000000
χ698-8-8800−2+25−2−25−2+25−2−252−252+252−252+250000000000000000000000000000000000002ζ22−2ζ38−2ζ22+2ζ38−2ζ6+2ζ142ζ6−2ζ1400000000000000000
χ708-8-8800−2−25−2+25−2−25−2+252+252−252+252−250000000000000000000000000000000000002ζ6−2ζ14−2ζ6+2ζ142ζ22−2ζ38−2ζ22+2ζ3800000000000000000
χ718-8-8800−2−25−2+25−2−25−2+252+252−252+252−25000000000000000000000000000000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ22+2ζ382ζ22−2ζ3800000000000000000

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