Finite Group Databasebeta

← Group #13027222

Character table — Group #13027222

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size1122222224444444444445588888888888888881010101010101016161616161616162020202040404040404040404040404080808080
order1224488884458810202040404040221016161616202020202040404040404024488888080808080808080448844448888161616164444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-11111111111111111-1-1-1-1-1-1-111111111-1-1-1-1ii−i−iii−i−i-1-1-1-1ii−i−i
χ6111111111111111111111-1-11111111111111111-1-1-1-1-1-1-111111111-1-1-1-1−i−iii−i−iii-1-1-1-1−i−iii
χ7111111111111111111111-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i1111−i−iii
χ8111111111111111111111-1-11-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii1111ii−i−i
χ911111-1-111-1-111-1111111111111-1-1-1-1-1-1111-1-1-1-111111-1-11111-1-1-1-1-1-11-11111-1-1-1-111-1-11-11-1
χ1011111-1-111-1-111-1111111111111-1-1-1-1-1-1111-1-1-1-111111-1-11111-1-1-1-1-1-11-1-1-1-1-1111111-1-1-11-11
χ1111111-1-111-1-111-11111111111-1-111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-11111-1-11-11111-1-1-1-1-1-111-11-11
χ1211111-1-111-1-111-11111111111-1-111-1-1-1-1111-1-1-1-111111-1-1-1-1-1-11111-1-11-1-1-1-1-11111-1-1111-11-1
χ1311111-1-111-1-111-11111111-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1111111-1-1-1-111-11ii−i−i−i−iii-1-111i−i−ii
χ1411111-1-111-1-111-11111111-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1111111-1-1-1-111-11−i−iiiii−i−i-1-111−iii−i
χ1511111-1-111-1-111-11111111-1-11-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-1-1-1111111-11ii−i−i−i−iii11-1-1−iii−i
χ1611111-1-111-1-111-11111111-1-11-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-111-1-1-1-1111111-11−i−iiiii−i−i11-1-1i−i−ii
χ172222222-2-2-2-22-22222-2-2-2-22220000-2-2-2-22-2-22222222-2-22200000000-2-2-220000000000000000
χ182222222-2-2-2-22-22222-2-2-2-2-2-220000-2-2-2-22-2-22222-2-2-222-2-200000000222-20000000000000000
χ1922222-2-2-2-2222-2-2222-2-2-2-2222000022222-2-2-2-2-2-2222-2-2-2-20000000022-2-20000000000000000
χ2022222-2-2-2-2222-2-2222-2-2-2-2-2-22000022222-2-2-2-2-2-2-2-2-2222200000000-2-2220000000000000000
χ2122-22-20022002-20222222222-200000000-2-2-20000-22-222000000000000-202-22-2000000000000
χ2222-22-20022002-20222222222-200000000-2-2-20000-22-222000000000000-20-22-22000000000000
χ2322-22-20022002-202222222-2-2-200000000-2-2-200002-22-2-2000000000000202i−2i−2i2i000000000000
χ2422-22-20022002-202222222-2-2-200000000-2-2-200002-22-2-200000000000020−2i2i2i−2i000000000000
χ2522-22-200-2-200220222-2-2-2-222-200000000-2220000-22-2-2-20000000000002000002i−2i2i−2i00000000
χ2622-22-200-2-200220222-2-2-2-222-200000000-2220000-22-2-2-2000000000000200000−2i2i−2i2i00000000
χ2722-22-200-2-200220222-2-2-2-2-2-2-200000000-22200002-2222000000000000-2000002-2-2200000000
χ2822-22-200-2-200220222-2-2-2-2-2-2-200000000-22200002-2222000000000000-200000-222-200000000
χ2922-2-2222000020-22-2-2000022-22−22−2000020022-2-2-2-22002222−2−222−2−2000-2000000002−22−20000
χ3022-2-2222000020-22-2-2000022-2−22−22000020022-2-2-2-220022−2−222−2−222000-200000000−22−220000
χ3122-2-2222000020-22-2-20000-2-2-22−22−2000020022-2-222-200-2-222−2−222−2−2000200000000−22−220000
χ3222-2-2222000020-22-2-20000-2-2-2−22−22000020022-2-222-200-2-2−2−222−2−2220002000000002−22−20000
χ3322-2-22-2-200002022-2-2000022-22−2−220000200-2-222-2-2200-2-222−2−2−2−2220002000000002−2−220000
χ3422-2-22-2-200002022-2-2000022-2−222−20000200-2-222-2-2200-2-2−2−22222−2−2000200000000−222−20000
χ3522-2-22-2-200002022-2-20000-2-2-22−2−220000200-2-22222-2002222−2−2−2−222000-200000000−222−20000
χ3622-2-22-2-200002022-2-20000-2-2-2−222−20000200-2-22222-20022−2−22222−2−2000-2000000002−2−220000
χ3744444444444-144-1-1-1-1-1-1-100-14444-1-1-1-1-1-1-1-1-1-1-10000000-1-1-1-1-1-1-1-100000000000000000000
χ3844444444444-144-1-1-1-1-1-1-100-1-4-4-4-4-1-1-1-1-1-1-1-1-1-1-100000001111111100000000000000000000
χ394444444-4-4-4-4-1-44-1-1-1111100-100001111-111-1-1-1-10000000i5−i5i5−i5i5−i5i5−i500000000000000000000
χ404444444-4-4-4-4-1-44-1-1-1111100-100001111-111-1-1-1-10000000−i5i5−i5i5−i5i5−i5i500000000000000000000
χ4144444-4-444-4-4-14-4-1-1-1-1-1-1-100-144-4-41111-1-1-111110000000-1-1-1-1111100000000000000000000
χ4244444-4-444-4-4-14-4-1-1-1-1-1-1-100-1-4-4441111-1-1-1111100000001111-1-1-1-100000000000000000000
χ4344444-4-4-4-444-1-4-4-1-1-1111100-10000-1-1-1-1-11111110000000i5−i5i5−i5−i5i5−i5i500000000000000000000
χ4444444-4-4-4-444-1-4-4-1-1-1111100-10000-1-1-1-1-11111110000000−i5i5−i5i5i5−i5i5−i500000000000000000000
χ45444-4-40000004004-4-4000044400000000-40000004-4-400000000000000000000000000000000
χ46444-4-40000004004-4-40000-4-4400000000-4000000-44400000000000000000000000000000000
χ4744-4-44440000-10-4-111i5i5−i5−i500122−2222−22i5i5−i5−i5-1i5−i5-1-1110000000−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ3900000000000000000000
χ4844-4-44440000-10-4-111i5i5−i5−i5001−2222−2222i5i5−i5−i5-1i5−i5-1-1110000000ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ3900000000000000000000
χ4944-4-44440000-10-4-111−i5−i5i5i500122−2222−22−i5−i5i5i5-1−i5i5-1-1110000000ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ2900000000000000000000
χ5044-4-44440000-10-4-111−i5−i5i5i5001−2222−2222−i5−i5i5i5-1−i5i5-1-1110000000−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ2900000000000000000000
χ5144-4-44-4-40000-104-111i5i5−i5−i500122−22−2222−i5−i5i5i5-1i5−i511-1-10000000−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ3900000000000000000000
χ5244-4-44-4-40000-104-111i5i5−i5−i5001−222222−22−i5−i5i5i5-1i5−i511-1-10000000ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ3900000000000000000000
χ5344-4-44-4-40000-104-111−i5−i5i5i500122−22−2222i5i5−i5−i5-1−i5i511-1-10000000ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ2900000000000000000000
χ5444-4-44-4-40000-104-111−i5−i5i5i5001−222222−22i5i5−i5−i5-1−i5i511-1-10000000−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29ζ13−ζ31+ζ37−ζ39−ζ7+ζ21−ζ23+ζ29−ζ13+ζ31−ζ37+ζ39ζ7−ζ21+ζ23−ζ2900000000000000000000
χ554-40002i2−2i222−222i−2i400-40022−2222−224-4000002i−2i2i−2i0002i2−2i20000022−222i2−2i2000000002i−2i000000000000000000
χ564-40002i2−2i222−222i−2i400-40022−2222−22-44000002i−2i2i−2i0002i2−2i200000−2222−2i22i200000000−2i2i000000000000000000
χ574-40002i2−2i2−2222−2i2i400-400−2222−22224-400000−2i2i−2i2i0002i2−2i200000−22222i2−2i200000000−2i2i000000000000000000
χ584-40002i2−2i2−2222−2i2i400-400−2222−2222-4400000−2i2i−2i2i0002i2−2i20000022−22−2i22i2000000002i−2i000000000000000000
χ594-4000−2i22i222−22−2i2i400-40022−2222−224-400000−2i2i−2i2i000−2i22i20000022−22−2i22i200000000−2i2i000000000000000000
χ604-4000−2i22i222−22−2i2i400-40022−2222−22-4400000−2i2i−2i2i000−2i22i200000−22222i2−2i2000000002i−2i000000000000000000
χ614-4000−2i22i2−22222i−2i400-400−2222−22224-4000002i−2i2i−2i000−2i22i200000−2222−2i22i2000000002i−2i000000000000000000
χ624-4000−2i22i2−22222i−2i400-400−2222−2222-44000002i−2i2i−2i000−2i22i20000022−222i2−2i200000000−2i2i000000000000000000
χ63888-8-8000000-200-2222i52i5−2i5−2i500-2000000002−2i52i5000000000000000000000000000000000000000
χ64888-8-8000000-200-222−2i5−2i52i52i500-20000000022i5−2i5000000000000000000000000000000000000000
χ6588-88-8008800-2-80-2-2-2-2-2-2-200200000000222000000000000000000000000000000000000000
χ6688-88-800-8-800-280-2-2-22222002000000002-2-2000000000000000000000000000000000000000
χ678-80004i2−4i242−424i−4i-20022i5−2i5−2ζ7+2ζ21−2ζ23+2ζ292ζ7−2ζ21+2ζ23−2ζ292ζ13−2ζ31+2ζ37−2ζ39−2ζ13+2ζ31−2ζ37+2ζ390000000ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38000−i2i210−1000000000000000000000000000000000000
χ688-80004i2−4i242−424i−4i-2002−2i52i52ζ13−2ζ31+2ζ37−2ζ39−2ζ13+2ζ31−2ζ37+2ζ39−2ζ7+2ζ21−2ζ23+2ζ292ζ7−2ζ21+2ζ23−2ζ290000000−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38000−i2i2−101000000000000000000000000000000000000
χ698-80004i2−4i2−4242−4i4i-20022i5−2i52ζ7−2ζ21+2ζ23−2ζ29−2ζ7+2ζ21−2ζ23+2ζ29−2ζ13+2ζ31−2ζ37+2ζ392ζ13−2ζ31+2ζ37−2ζ390000000−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38000−i2i210−1000000000000000000000000000000000000
χ708-80004i2−4i2−4242−4i4i-2002−2i52i5−2ζ13+2ζ31−2ζ37+2ζ392ζ13−2ζ31+2ζ37−2ζ392ζ7−2ζ21+2ζ23−2ζ29−2ζ7+2ζ21−2ζ23+2ζ290000000ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38000−i2i2−101000000000000000000000000000000000000
χ718-8000−4i24i242−42−4i4i-20022i5−2i5−2ζ7+2ζ21−2ζ23+2ζ292ζ7−2ζ21+2ζ23−2ζ292ζ13−2ζ31+2ζ37−2ζ39−2ζ13+2ζ31−2ζ37+2ζ390000000−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38000i2−i2−101000000000000000000000000000000000000
χ728-8000−4i24i242−42−4i4i-2002−2i52i52ζ13−2ζ31+2ζ37−2ζ39−2ζ13+2ζ31−2ζ37+2ζ39−2ζ7+2ζ21−2ζ23+2ζ292ζ7−2ζ21+2ζ23−2ζ290000000ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38000i2−i210−1000000000000000000000000000000000000
χ738-8000−4i24i2−42424i−4i-20022i5−2i52ζ7−2ζ21+2ζ23−2ζ29−2ζ7+2ζ21−2ζ23+2ζ29−2ζ13+2ζ31−2ζ37+2ζ392ζ13−2ζ31+2ζ37−2ζ390000000ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38000i2−i2−101000000000000000000000000000000000000
χ748-8000−4i24i2−42424i−4i-2002−2i52i5−2ζ13+2ζ31−2ζ37+2ζ392ζ13−2ζ31+2ζ37−2ζ392ζ7−2ζ21+2ζ23−2ζ29−2ζ7+2ζ21−2ζ23+2ζ290000000−ζ4−ζ6+ζ12−ζ14−ζ22+ζ28−ζ36−ζ38ζ4+ζ6−ζ12+ζ14+ζ22−ζ28+ζ36+ζ38ζ4−ζ6−ζ12−ζ14−ζ22−ζ28+ζ36−ζ38−ζ4+ζ6+ζ12+ζ14+ζ22+ζ28−ζ36+ζ38000i2−i210−1000000000000000000000000000000000000

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